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... In an ecient system, margin collateral is minimized subject to the constraint of achieving the desired level of protection. Telser (1981), Figlewski (1984), and Fenn and Kupiec (1993) provide more detailed discussions of the design of an ecient margining system. ...

... This out ow is greater than the maximum possible loss on the position, however, because it is oset by a n y cash in ow from the premiums that the original creation of the position generated. Similar margin cover is allowed for put spreads in Reg T. 7 In the event the margin for either a call spread or a put spread is greater than that for the naked written position, the margin for the uncovered position can instead be posted. More complex positions such as butter y spreads using calls, butter y spreads using puts, and box spreads can be analyzed as groups of written (credit) spreads and purchased (debit) spreads. ...

... As margins are set to protect the clearinghouse against the overall risk generated by the daily uctuations in the values of all positions held by a clearing member, it is more natural that a portfolio margining scheme would develop. Originally, the futures exchanges used a delta-based system to convert options positions into futures equivalents in order to margin them ( Figlewski (1984)). Delta-based techniques did not produce accurate re ections of the risk of option positions, and this weakness was widely recognized within the industry. ...

Although margin requirements would arise naturally in the context of unregulated trading of clearinghouse-guaranteed derivative contracts, the margin requirements on U.S. exchange-traded derivative products are subject to government regulatory oversight. At present, two alternative methodologies are used for margining exchange-traded derivative contracts. Customer positions in securities and securities options are margined using a strategy-based approach. Futures, futures-options, and securities-option clearinghouse margins are set using a portfolio margining system. This study evaluates the relative efficiency of these alternative margining techniques using data on S&P500; futures-option contracts traded on the Chicago Mercantile Exchange. The results indicate that the portfolio margining approach is a much more efficient system for collateralizing the one-day risk exposures of equity derivative portfolios. Given the overwhelming efficiency advantage of the portfolio approach, the simultaneous existence of these alternative margining methods is somewhat puzzling. It is argued that the co-existence of these systems can in part be explained in the context of Kane's (1984) model of regulatory competition. The efficiency comparison also provides insight into other industry and regulatory issues including the design of bilateral collateralization agreements and the efficiency of alternative schemes that have been proposed for setting regulatory capital requirements for market risk in banks and other financial institutions.

... Futures contracts are commonly used to hedge spot price risk. We refer this rich field to Figlewski (1984), Daskalaki and Skiadopoulos (2016) and Alexander et al. (2019) for traditional equity, commodity and currency markets. For bitcoin futures markets, the hedge effectiveness and improvement of portfolio performance are well studied in Alexander et al. (2020a), Sebastião and Godinho (2020), Deng et al. (2019) and others. ...

... In this paper, our leitmotif to study optimal margins stems from several facts observed in bitcoin futures markets. First, as is well-known, the margin requirement is one of the key market designs by exchanges to maintain the integrity, liquidity, and efficiency of futures markets, see Figlewski (1984). ...

Using the generalized extreme value theory to characterize tail distributions, we address liquidation, leverage, and optimal margins for bitcoin long and short futures positions. The empirical analysis of perpetual bitcoin futures on BitMEX shows that (1) daily forced liquidations to out- standing futures are substantial at 3.51%, and 1.89% for long and short; (2) investors got forced liquidation do trade aggressively with average leverage of 60X; and (3) exchanges should elevate current 1% margin requirement to 33% (3X leverage) for long and 20% (5X leverage) for short to reduce the daily margin call probability to 1%. Our results further suggest normality assumption on return significantly underestimates optimal margins. Policy implications are also discussed.

... Statistical models typically assume simple underlying dynamics, such as Geometric Brownian Motion (GBM) and derive the probability for the Initial Margin (IM) to be exceeded within a given time horizon. A typical paper along these lines is Figlewski (1984) [12] who calculated the probability of a margin call given a certain percentage of initial and maintenance margin. ...

... Statistical models typically assume simple underlying dynamics, such as Geometric Brownian Motion (GBM) and derive the probability for the Initial Margin (IM) to be exceeded within a given time horizon. A typical paper along these lines is Figlewski (1984) [12] who calculated the probability of a margin call given a certain percentage of initial and maintenance margin. ...

We propose a model for the credit and liquidity risks faced by clearing members of Central Counterparty Clearing houses (CCPs). This model aims to capture the features of: gap risk; feedback between clearing member default, market volatility and margining requirements; the different risks faced by various types of market participant and the changes in margining requirements a clearing member faces as the system evolves. By considering the entire network of CCPs and clearing members, we investigate the distribution of losses to default fund contributions and contingent liquidity requirements for each clearing member; further, we identify wrong-way risks between defaults of clearing members and market turbulence.

... For instance, Duffie (1989) points to the fact that a clearinghouse often uses statistical theories to determine the margin level to guard against defaults. Figlewski (1984) suggests a methodology for analyzing the degree of protection afforded by different margin levels based on the computation of a "first passage time" probability distribution. Gay, Hunter and Kolb (1986) derive the probability of a margin violation on a given date for a given margin level. ...

... Nevertheless, it is not in the public interest if too high a margin is charged to investors, as the market liquidity is affected. In this regard, Figlewski (1984) notes that a liquid futures or options market is in the public interest, and that it would be counter-productive to impose too high a margin on investors as market liquidity will decrease. Hence, considerations should also be given to the investors' opportunity costs. ...

The margin system is a clearinghouse's first line of defense against the default risk. From the perspectives of a clearinghouse, the utmost concern is to have a prudential system to control the default exposure. Once the level of prudentiality is set, the next concern is the opportunity cost to the investors. It is because high opportunity cost discourages people from hedging futures and thus defeats the function of a futures market. In this paper, we first develop different measures of prudentiality and opportunity cost. We then formulate a statistical framework to evaluate different margin-setting methodologies, all of which strike a balance between prudentiality and opportunity cost. Four margin-setting methodologies, namely, one using simple moving averages, one using exponentially weighted moving averages, one using a GARCH-GJR approach, and the last one using the lagged implied volatility (whenever it is available), are applied to Hang Seng Index Futures. The lagged implied volatility by and large has the best performance, while the GARCH-GJR approach is a best substitute when implied volatility is not available.

... Research on futures margin setting has a long history, with the earliest studies being Figlewski (1984) and Gay et al. (1986). They assumed that the distribution of stock index futures returns obeyed a normal distribution and set the margin levels for different trading positions. ...

In addition to the characteristics of leptokurtic fat-tailed distribution, financial sequences also exhibit typical volatility and jumps. Moreover, jumps exhibit self-exciting and clustering characteristics under extreme events. However, studies on dynamic margin levels often ignore jumps. In this study, we combine the self-exciting stochastic volatility with correlated jumps (SE-SVCJ) model with a generalized Pareto distribution (GPD) to measure the optimal margin level for the stock index futures market. Value at risk (VaR) is estimated and forecasted using the SE-SVCJ-GPD, SVCJ-GPD, and generalized autoregressive conditional heteroskedasticity with GPD (GARCH-GPD) models. SE-SVCJ-GPD can undertake more risks in the long or short trading position of stock index futures contracts. Moreover, the backtesting experiment results show that the SE-SVCJ-GPD model provides a more accurate margin level forecast than the other methods in both positions. This study’s findings have practical significance and theoretical value for assessing the level of risk and taking corresponding risk-prevention measures.

... More precisely, the exchange's matching engine instantly triggers a liquidation as soon as the bitcoin price falls below a 'liquidation price' which is calculated using a highly complex formula, but which is in fact very close to the 'fair mark price' less the collateral in the account. 2 In standard analysis, the hedger's choice of collateral is ignored and our work is the first to analyse how collateral influences the optimal solution for a hedger with loss aversion to automatic liquidations. Efficient margin mechanisms are essential for ensuring the stability and integrity of futures markets, and there is abundant research on this topic for traditional futures like commodities, precious metals, stock indexes, and currencies; see Figlewski (1984b), Longin (1999), Cotter (2001), Basu and Miffre (2013), Daskalaki andSkiadopoulos (2016), Alexander et al. (2019) and many others. However, this paper is the first deep dive into how margin levels affect the optimal hedging problem of bitcoin futures. ...

We consider the hedging problem where a futures position can be automatically liquidated by the exchange without notice. We derive a semi-closed form for an optimal hedging strategy with dual objectives -- to minimise both the variance of the hedged portfolio and the probability of liquidations due to insufficient collateral. The optimal solution depends on the statistical characteristics of the spot and futures extreme returns and parameters that characterise the hedger by loss aversion, choice of leverage and collateral management. An empirical analysis of bitcoin shows that the optimal strategy combines superior hedge effectiveness with a reduction in the probability of liquidation. We compare the performance of seven major direct and inverse hedging instruments traded on five different exchanges, based on minute-level data. We also link this performance to novel speculative trading metrics, which differ markedly between venues.

... Volatility is considered the most important determinant of margin requirements. For example, some authors, such as Figlewski (1984), Gay, Hunter, and Kolb (1986), and Fenn and Kupiec (1993), use a normal distribution model that suggests that margin levels be proportional to the level of volatility, while others, such as Cotter (2001) and Longin (1999), use extreme value theory to capture the tails of return distributions. Yet, little is known about what kind of a volatility proxy has been used in margin setting by CCPs. ...

Margin regulation raises two policy concerns. First, an alignment of margins to volatility can amplify procyclicality, leading to a build-up of excess leverage in good times and a forced deleverage in bad times. Second, competition among central counterparties (CCPs) can result in lower margin levels in order to attract more trading volume, which is referred to as a 'race to the bottom.' Motivated by these issues, we empirically analyze the determinants of margin changes by using a data set of various futures margins from Chicago Mercantile Exchange (CME) Group. We first find that CME Group raises margins quickly following volatility spikes but does not immediately lower margins following volatility declines, implying that margin-induced procyclicality is more of a concern in recessions than in expansions. In addition, we find some evidence that the margin difference between CME Group and its competitor, Intercontinental Exchange (ICE), is an important driver of margin changes after changes in other margin determinants are controlled for, implying that competition may be factored into margin setting.

... (seeFama, 1989;Telser, 1989;Lehmann, 1989;Lauterbach and Ben-Zion, 1993;and Kim and Rhee, 1997).3 (seeFama, 1989;Lehmann, 1989;Lee et al., 1994;Figlewski, 1984;Kim and Rhee, 1997;Meltzner, 1989;Miller et al., 1987;Telser, 1981;Lee and Kim, 1995;Ma et al., 1989aMa et al., , 1989bChiang et al, 1997;Kim and Rhee, 1997). 4 (seeKim and Rhee, 1997;Lehmann, 1989;Fama, 1989;Kyle, 1988;Kuhn et al., 1991;Lee and Kim, 1995). ...

... In addition to the liquidity problem, the delay in price discovery is another costly problem induced by price limits. This happens because price limits prevent prices from reaching their equilibrium level effectively (see Fama, 1989;Lehmann, 1989;Lee et al., 1994;Figlewski, 1984;Kim and Rhee, 1997;Meltzner, 1989;Miller et al., 1987;Telser, 1981;Lee and Kim, 1995;Ma et al., 1989aMa et al., , 1989bChiang et al, 1997;Kim and Rhee, 1997). The effects of trading interference using price limits may also weaken market efficiency (Fama, 1989;Lehmann, 1989;Lee et al, 1994). ...

... (See Wei and Chiang, 2004;Fama, 1989;Telser, 1989;Lehmann, 1989;Lauterbach and Ben-Zion, 1993;and Kim and Rhee, 1997). Price limits rules could delay the price discovery process by preventing prices from effectively reaching their equilibrium level (See Fama, 1989;Lehmann, 1989;Lee et al., 1994;Figlewski, 1984;Kim and Rhee, 1997;Meltzner, 1989;Miller et al., 1987;Telser, 1981;Lee and Kim, 1995;Ma et al., 1989aMa et al., , 1989bChiang et al, 1997;Kim and Rhee, 1997). ...

Many stock exchanges around the world enforce daily price limits on the amount asset prices can change to prevent the market from overreacting and to reduce volatility. Using a methodology of comparing volatility based on the Extreme-Value technique, we empirically investigate the impact of price limits on the volatility of the Stock Exchange of Thailand. Our empirical results support price limits advocates suggesting that price limits moderate stock price volatility. Code JEL: G10, C53

... In the literature, there are three main approaches proposed for setting the IM: (i) a statistical approach to calculate the margin for each contract, which is often adjusted by the subjective judgment of an expert to reflect information not present in the historical dataset, see Figlewski (1984) and Gay, Hunter, and Kolb (1986); (ii) optimization models of an efficient prudential margin management policy which minimizes the account overall margin, settlement, default and any other costs, see Dewacher and Gielens (1999); (iii) a third approach, proposed by Barone-Adesi, Giannopoulos, and Vosper (2002), calculates the overall portfolio benchmark margin as a percentile of the simulated portfolio values at the investment horizon. That is the approach followed in our simulations. ...

The estimation of joint tail risk is necessary to evaluate the size of portfolio margins and default funds of central counterparties. The ability of filtered historical simulation to satisfy new regulatory requirements in this area is examined at the very high confidence levels, necessary to ensure market integrity over time.

... The first one is based on the economic model (e.g., Brennan 1986;Fenn and Kupiec 1993;Telser 1981). The second approach focuses on the application of statistical theory, which may evolve from various techniques (e.g., Cotter and Longin 2006;Figlewski 1984;Gay et al. 1986;Warshawsky 1989). ...

Price limits are artificial boundaries established by regulators to establish the maximum price movement permitted in a single day. We propose using a new censoring method that incorporates the effect of price limits on the futures price distribution and investigates how to set an appropriate daily margin level using single-stock futures in Taiwan. We compare our estimations with those obtained using the method in Longin (J Bus 69:383–408, 1999). The results show that (1) the margin levels derived from the Longin method, which ignore price limits in the estimation, are lower than those in our censoring method; and (2) the legal margin for single-stock futures set at 13.5 % by the Taiwan Futures Exchange to avoid default risk appears to be too high.

... 2 In this paper, we propose a new margining methodology, called CoMargin, which accounts for the variability and interdependence of the profits and losses (P&Ls) of clearing members. Indeed, other margining systems commonly used in CCPs, such as the Standard Portfolio Analysis of Risk (SPAN) or the Value-at-Risk (VaR) approach, estimate collateral requirements based on a coverage level of potential losses for an individual contract or portfolio of contracts (Figlewski 1984;Kupiec 1994;Booth et al., 1997;Cotter, 2001;Day and Lewis, 2004; Chicago Mercantile Exchange (CME), 2012). ...

We present CoMargin, a new methodology to estimate collateral requirements in derivatives central counterparties (CCPs). CoMargin depends on both the tail risk of a given market participant and its interdependence with other participants. Our approach internalizes trading externalities and enhances the stability of CCPs, thus, reducing systemic risk concerns. We assess our methodology using proprietary data from the Canadian Derivatives Clearing Corporation that includes daily observations of the actual trading positions of all of its members from 2003 to 2011. We show that CoMargin outperforms existing margining systems by stabilizing the probability and minimizing the shortfall of simultaneous margin-exceeding losses.

... Figlewski describes the current structure of margin requirements on stocks and equity-based derivative securities and the principles used in setting these requirements. He discusses alternative procedures which may be easier, more equitable to apply, and more effective in meeting the most important objectives of margin setting [13]. ...

In this paper, we focus on designing a real-time risk management system. The system will be using CME SPAN and will consist of a multithreaded daemon process to evaluate portfolios using SPAN calculation engines and programs to determine parameters fed to SPAN. SPAN parameters can be estimated by several methods using historical data. One of the goals is to determine the best method for each parameter for every asset class. The other goal is to develop a responsive system to analyze portfolios and orders in real-time and to update the portfolio risks accordingly. Ultimately when these two parts are combined, we"ll be constructing a real-time system to evaluate portfolio risks and to determine optimum margin requirements.

... A margin loan is secured by the client's collateral which is a portfolio of securities and typically carries a margin rate (the interest charged on the loan) that is favorable due to the presence of collateral. Moore (1966) and Figlewski (1984) explain reasons for implementing margin requirement. The first rationale is to ensure credit and resources are allocated to productive economic activities that are not including speculation activities. ...

Officially margin requirements in bourses in Bangladesh were initiated on April 28, 1999, to limit the amount of credit available for the purpose of buying stocks. The goal of this paper is to measure the impact of changing margin requirements on stock returns’ volatility in Dhaka Stock Exchange (DSE). The effect of margin requirement on stock price volatility has been extensively studied with mixed and ambiguous results. Using daily return of DGEN Index, we found no evidence that SEC’s margin requirements have statistically significant impact on return volatility in DSE. Of course, findings from this study could be source of comfort for the regulators in Bangladesh.

... Figlewski 1984Fama 1989Kim Rhee 1997 ...

Extreme value theory has recently been applied to margin setting in futures markets. Price limits, however, may undermine the benefits associated with the extreme-value method. This has not to be accomplished in the literature. This article proposes an empirical method to examine the impacts of price limits on the results of extreme value parameter estimation. Both index futures in Taiwan Futures Exchange and Singapore Exchange are used as empirical samples. The results indicate that price limits impede the extreme price behaviors, and the excess kurtosis of distribution become less significant. Besides, the price limits may affect the tail parameters, default probability, and margin ratios estimation. Especially, because the 7% price limits in Singapore Exchange are just set in the positions of extreme values, they imply more significant impacts. Price limits may also substitute the function of margins in the sense of lowering the price volatility by impeding the extreme price change directly. This explains why both Taiwan Futures Exchange and Singapore Exchange set the margin ratios lower than theatrical ones.

Bitcoin derivatives positions are maintained with a self-selected margin, which is often too low to avoid automatic liquidation by the exchange, without notice, especially during periods of excessive volatility. Indeed, according to CryptoQuant, almost $80 billion of positions on centralised exchanges were liquidated during 2021, that is an average of over $200 million per day. So hedgers of bitcoin price risk should account for the possibility of automatic liquidation when taking positions on bitcoin futures. We derive a semi-closed form for an optimal hedging strategy with dual objectives – to minimize both the variance of the hedged portfolio and the probability of liquidation due to insufficient collateral. The solution depends on the statistical characteristics of the spot and futures extreme returns, and other parameters that characterize the hedger by choice of leverage, loss aversion and collateral management. An empirical analysis based on minute-level data compares the performance of the major direct and inverse bitcoin hedging instruments traded on five major exchanges.

In this paper, we explore a novel dataset of daily cleared credit default swap (CDS) positions along with the posted margins to study how collateral varies with portfolio risks and market conditions. Contrary to many theoretical models, where collateral constraints follow Value-at-Risk rules, we find strong evidence that collateral requirements are set an order of magnitude larger than what Value-at-Risk rules imply. The panel variation in collateralization rates is well captured by measures of extreme tail risks. We develop a model of endogenous collateral, which explains the conservativeness of collateral levels through disagreement of market participants about extreme states.

There are different types of margin requirements for margin buying and this paper focuses on setting both initial and maintenance margin levels. By using the data of stock portfolio returns over the period from March 31, 2010 to December 31, 2020, the research computes and compares margins derived by several margin setting methods using extreme value theory (EVT) for margin buying in China. Important findings are summarized as follows. First, the VaR-x method generates more accurate forecasts of both unconditional and conditional margin levels than the parametric and the Hill non-parametric methods particularly given lower probabilities of margin violation. This is robust to different portfolios, market conditions and sample periods. Second, margins derived actually vary over time, becoming higher (lower) when market volatility increases (decreases). The findings have important economic and practical implications.

Using the generalized extreme value theory to characterize tail distributions, we address liquidation, leverage and optimal margins for bitcoin long and short futures positions. The empirical analysis of perpetual bitcoin futures on BitMEX shows that (1) daily forced liquidations to outstanding futures are substantial at 3.51% and 1.89% for long and short; (2) investors got forced liquidation do trade aggressively with average leverage of 60X; and (3) exchanges should elevate current 1% margin requirement to 33% (3X leverage) for long and 20% (5X leverage) for short to reduce the daily margin call probability to 1%. Our results further suggest that normality assumption on return significantly underestimates optimal margins. Policy implications are also discussed.

Ryzyko inwestowania na rynku kontraktów terminowych futures jest nieporównywalnie wyższe niż na tradycyjnych rynkach akcji czy obligacji. Stopa zwrotu z inwestycji w kontrakty terminowe jest wypadkową dwóch czynników: zmiany kursu terminowego i wysokości depozytu zabezpieczającego.
W niniejszej monografii zostały przedstawione badania dotyczące ryzyka ekstremalnego jakiego doświadczają inwestorzy na rynku kontraktów futures notowanych na Giełdzie Papierów Wartościowych w Warszawie. Po raz pierwszy w literaturze do analizy ryzyka wykorzystany został rzeczywisty rozkład zysków i strat z inwestycji w kontrakty terminowe. Wyniki przedstawionych badań będą stanowić dla inwestorów i badaczy źródło lepszego poznania mechanizmów rządzących rynkiem terminowym.

Purpose
The purpose of this paper is to propose a new dynamic margin setting method for margin buying in China and evaluate the validity of its performance with the current margin system adopted by stock exchanges in extreme episodes.
Design/methodology/approach
This paper adopts the dynamic conceptual model of Huang et al. (2012) (which is based on Figlewski (1984)) but incorporates Markov chain to describe the data generation process of stock price changes. By applying the model to margin buying contracts for the period of March 16, 2018, to May 2, 2018 (baseline study) and June 15, 2015, to July 27, 2015 (robustness test), the model’s superiority to the current margin system adopted by stock exchanges is also tested.
Findings
The paper has several important findings. First, the margins derived by this system vary with market conditions, rising (declining) when stock prices go down (up), and are generally lower than the requirements imposed by stock exchanges. Second, this margin system induces lower overall percentage of costs than that adopted by stock exchanges. Third, parameter estimation plays an important role on shaping empirical results.
Research limitations/implications
The primary limitation of this paper lies in the fact that it does not solve the issue of determining optimal parameters of the Markov chain model. On the implication of findings, policy-makers and regulators on supervising margin buying activities may need a tune-up on the current margin system which features static margin requirements. Dynamic margins that incorporate market factors are virtually useful to balance the trade-off between liquidity and prudence.
Originality/value
To the best of the authors’ knowledge, this study is the first of its kind to develop a dynamic margin setting method for margin buying in China, aiming to balance the trade-off between liquidity and prudence. It not only takes into account the uniqueness of Chinese markets but also allows for time variations in both initial and maintenance margins.

We investigate two issues in this article. First, this study employs almost stochastic dominance and the power spectrum to investigate the maturity effect, a hypothesis proposed by Samuelson (1965. Proof that properly anticipated prices fluctuate randomly. Industrial Management Review, 1965, 6(2), 41–49; 1976. Is real-world price a tale told by the idiot of chance? The Review of Economics and Statistics, 1976, 58(1), 120–123) in the stochastic variance framework. Second, we also reevaluate the argument in Bessembinder et al. (1996. Is there a term structure of futures volatilities? Reevaluating the Samuelson hypothesis. Journal of Derivatives, 1996, 4(2), 45–58) that spot price seasonality plays a role in explaining this hypothesis. We include five types of energy futures for empirical examination. The outcomes provide evidence ranging from supporting, to being contrary to the hypothesis. For empirical analysis, we also highlight that the periodic pattern of the futures return series explains the difference in outcomes. Those in the spot price, futures price, or spot return series do not contribute to these outcomes.

We investigate the optimal level of margin requirement in centralized or decentralized clearing and settlement systems. We prove in an analytical model that aggressively risk-sensitive margins are not optimal, and the actual position of the clients and the general macroeconomic conditions, like overall funding liquidity should also be taken into consideration. For example, in a crisis period characterized by high volatility, the clearing institution may be tempted to require larger margins to cover potential losses, however, clients just have difficulties to finance higher margins, hence, the probability of non-payment increases, and the expected loss of the clearing institution may also increase. We show that under realistic specifications, there exists a unique optimal margin minimizing the expected loss of the clearing institution. Characterizing this optimum, we provide a micro-level foundation for anti-cyclical risk management techniques (margins, collaterals, haircuts etc.) in general.

We model the decision problem faced by a profit-maximizing clearinghouse, which sets fee and margin requirements for heterogeneous traders who may default. We capture the main trade-offs underpinning the clearinghouse’s choices: higher fee and better default protection come at the cost of decreased market volume. We show that the equilibrium margin requirements are determined not only by price volatility but also by trader fundamentals and funding costs. Our results (i) explain why margins are often comparatively high relative to fees and daily price movements; (ii) capture the “term-structure” of margins, in particular that some long maturity futures contracts tend to have lower margins; and (iii) predict high sensitivity of margins to funding costs.
The online appendix is available at https://doi.org/10.1287/opre.2018.1742 .

Closeout procedures enable central counterparties (CCPs) to respond to events that challenge the continuity of their normal operations, most frequently triggered by the default of one or more clearing members. The procedures typically entail three main phases: splitting, hedging, and liquidation. Together, these ensure the regularity of the settlement process through the prudent and orderly liquidation of the defaulters’ portfolios. Traditional approaches to CCPs’ margin requirements typically assume a simple closeout profile, not accounting for the ‘real life’ constraints embedded in the management of a default. The paper proposes an approach to assess how distinct closeout strategies may expose a CCP to different sets of risks and costs taking into account real-life frictions. The proposed approach enables the evaluation of a full spectrum of hedging strategies and the assessment of the trade-offs between the risk-reducing benefits of hedging and the transaction costs associated with it. Using an unexplored set of transactional level data, the proposed framework is evaluated assuming the hypothetical default of a real CCP clearing member. We consider the worst-case loss of a large interest rate swap portfolio observed over the past 10 years (i.e. 2005–2015) and show that an efficient hedging strategy which minimises risk may not be optimal when transaction costs are taken into account. The empirical analysis suggests that transaction costs are a significant factor and should be accounted for when designing a hedging strategy. Specifically, it is shown that the risk-reducing benefits arising from more tailored hedging strategies may introduce higher transaction costs, and therefore may change the effectiveness of the strategies.

This chapter develops a framework to analyse the factors influencing central counterparties' (CCPs') risk controls and the role of regulation. The framework illustrates the importance of sound regulation of CCPs and helps to explain why different CCPs may make different risk management choices. Key factors include ownership, governance and the profile and preferences of participants. International standards for the design and operation of CCPs and other financial market infrastructures (FMIs) are reflected in the Principles for Financial Market Infrastructures (PFMIs). Modelling key elements of these standards, the chapter demonstrates the importance of a flexible regulatory framework that achieves the desired level of stability while allowing the mix of risk controls applied by each CCP to vary according to its particular incentives and operating environment. The chapter goes on to discuss the emerging trends towards competition and interoperability between CCPs and cross-border provision of clearing services, and consider the implications for CCPs' risk management choices.

We analyzed the effects of different margin strategies on the loss distribution of a clearinghouse during different crises. First, we developed a general one-period analytical model and proved the existence of a unique optimal margin which is not necessarily risk-sensitive even in a weaker sense. Then, we simulated the operation of a hypothetical clearinghouse active on the US stock futures market in the period 2008-2015. We found that anti-cyclical margin strategies might be optimal also for clearinghouses focusing on their micro-level financial stability, not only for regulators aiming to reduce systemic risk. Anti-cyclical margin strategies performed especially well in minor crises like Flash Crash.

Clearinghouses have an important role in protecting against counterparty risk through the setting of margins. Margins are also used to ensure the competitiveness of exchanges. Thus the Clearinghouse has an important role in ensuring both of these objectives and there may be a dilemma in trying to minimise the margin to ensure competitiveness and also ensure adequate and prudent margins are in place. Different approaches can be utilised. We examine the use of Extreme Value Theory (EVT) in setting margins. The theoretical framework focuses explicitly on tail returns, thereby properly accounting for large levels of risk in measuring prudent margin levels. Alternative approaches in modelling margins are discussed. In particular, it is common to model margins assuming the underlying distribution of asset returns follow a normal distribution. The chapter shows the underestimation bias in margin levels that are calculated assuming normality. The chapter also provides an overview of the margin account, their different components and their associated modelling. We outline the use of EVT in computing unconditional initial margins as distinct from the other elements of the margin account.

This chapter develops a framework to analyse the factors influencing central counterparties' (CCPs') risk controls and the role of regulation. The framework illustrates the importance of sound regulation of CCPs and helps to explain why different CCPs may make different risk management choices. Key factors include ownership, governance and the profile and preferences of participants. International standards for the design and operation of CCPs and other financial market infrastructures (FMIs) are reflected in the Principles for Financial Market Infrastructures (PFMIs). Modelling key elements of these standards, the chapter demonstrates the importance of a flexible regulatory framework that achieves the desired level of stability while allowing the mix of risk controls applied by each CCP to vary according to its particular incentives and operating environment. The chapter goes on to discuss the emerging trends towards competition and interoperability between CCPs and cross-border provision of clearing services, and consider the implications for CCPs' risk management choices. © 2016, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited.

Using Japanese long sample (1977–2010) market data, we examine whether margin buying is informed trades about future stock returns and whether they are related to undervaluation of the market. We find that margin buying increases when temporary returns are higher contemporaneously. We do not find that Japanese margin buying is well-informed in predicting future permanent changes in stock returns. Further, we find that margin buying is not related to the undervaluation of stock market prices.

This study examines the consistence of the futures margin levels of different commodities and combinations in the CME group by Extreme Value Copula (EVC).We find that if we ignore the co-movements of the commodities, the margins become consistent with each other, and the margin violation rates hover around 0.5%. However, if we consider the co-movement of the related commodities using EVC, the margin levels are found to be not consistent anymore, especially in the combinations of strongly related commodities which are in the same category. Therefore, we suggest that the CME group should try to harmonize the margins policy with respect to the dependence between the futures in the future. © 2014 by the Mathematical Association of Thailand. All rights reserved.

Clearing forms the core part of a smooth and efficiently functioning financial market infrastructure. Traditionally, it has been provided by clearing houses, most of which today act as a 'central counterparty' (CCP) between the two sides of a trade. The rapid growth of cross-border trading has sparked discussion on the most efficient industry structure - particularly in Europe and the US. At the heart of this discussion lies the question of whether the implementation of a single clearing house creates greater benefits than a more competitive but interlinked market structure. This is the starting point for this book, which analyses the efficiency of clearing and clearing industry structure. Along with clear-cut definitions and a concise characterisation and descriptive analysis of the clearing industry, the book determines the efficiency impact of various cross-border integration and harmonisation initiatives between CCPs. This serves to identify the most preferable future structure for the clearing industry. © Tina P. Hasenpusch 2009 and Cambridge University Press, 2010.

We review selectively some recent advances in the commodity futures literature. First, we discuss the literature on the diversification benefits of commodity futures and highlight some common misconceptions. Next, we survey the commodity futures asset pricing literature. We explain why it is hard to find a model to explain the cross-sectional variation of the commodity futures expected returns. Finally, we revisit the debate about whether the commodity futures margins should be regulated. These topics are of interest to academics, practitioners, and policymakers, and they are challenging because they raise a number of questions still to be answered.

This article proposes a theoretical framework that is built upon extreme value theory to study three instruments (i.e. margin, capital requirement and price limits) for managing default risk in futures markets. Specifically, the exceedances over a price threshold are modeled using a generalized Pareto distribution, and the models are static (one-period). We incorporate the risk attitudes of clearing firms into the framework to investigate the efficacy of these instruments under several risk measures, including value-at-risk measures, expected-shortfall measures and spectral risk measures. An empirical study on the VIX futures (or VX) data shows that the effectiveness of these market instruments rests not only on clearing firms' risk attitudes, but also on the tail fatness of the futures price distribution. Moreover, the shift in the risk attitudes of clearing firms may cause interactions among these instruments, which casts new light on the economic rationale of price limits.

The optimal clearing margin levels are crucial for default risk management system of a clearing house. The margin levels must be conservatively high enough to provide financial protection in the default loss event, but not too high to cause market liquidity problem. A static margin setting can result in a margin level which is too high. This paper proposes a dynamic margin setting model and methodology based on value-at-risk with simulated exponentially weighted moving average (EWMA) volatilities. The EWMA model gives the largest weight to the most recent innovation, which makes the dynamic setting of the margin levels more plausible. Based on the worst-case-scenario approach, the optimal margin levels can be set by choosing the model parameters as their maximum values from across different historical periods. The back test shows that the margin setting model is not sensitive to any chosen sample period. Both optimal margin level and back test can be run on a daily basis.

2 To ensure that central counterparties (" CCPs ") are safe in all market conditions the European Union (EU) has adopted legislation , commonly known as the European Market Infrastructure Regulation (" EMIR ") that deal with their organisational requirements including prudential requirements in relations to margins and the waterfall and default funds. It has published in a single Regulation (EU) No 153 / 2013 , the technical standards required to be adopted by all CCPs operating in the EU. EMIR requires a mandatory clearing of certain standardised OTC (i. e. over-the-counter) derivatives transactions through central counterparties. A risk methodology that can meet some of the most challenging technical requirements , such as sensitivity testing , estimating the probability of joint member defaults and reverse stress testing is the Filtered Historical Simulation (FHS). In this study we extend the use of Filtered Historical Simulation in estimating the potential losses the CCP would face from a multiple default. The proposed methodology provides a probabilistic estimation of defaulting of named members , the expected size of losses , i. e. the joint expected shortfall (JES) , and confidence intervals around the JES. This in turn provides an estimate of CCPs need of financial resources to absorb multiple defaults. Our methodology is carrying a full re-pricing of all instruments in the portfolio and takes into account positions that expire before the profits and losses (P&L) horizon. Order statistics tell us that estimates on the tails is unreliable. To handle this risk we carry out a bootstrapping of 5 , 000 , 000 simulation trials. The bootstrapping of 5 , 000 , 000 trials is repeated 5 , 000 times to generated the density of the JES. . Central counterparty risk management , filtered historical simulation , tail dependency .

Margin regulation raises two policy concerns. First, an alignment of margins to volatility can amplify procyclicality, leading to a build-up of excess leverage in good times and a forced deleverage in bad times. Second, competition among central counterparties (CCPs) can result in lower margin levels in order to attract more trading volume, which is referred to as a “race to the bottom.” Motivated by these issues, we empirically analyze the determinants of margin changes by using a data set of various futures margins from Chicago Mercantile Exchange (CME) Group. We first find that CME Group raises margins quickly following volatility spikes but does not immediately lower margins following volatility declines, implying that margin-induced procyclicality is more of a concern in recessions than in expansions. In addition, we find some evidence that the margin difference between CME Group and its competitor, Intercontinental Exchange (ICE), is an important driver of margin changes after changes in other margin determinants are controlled for, implying that competition may be factored into margin setting.

Ryzyko inwestowania na rynku kontraktów terminowych futures jest nieporównywalnie wyższe niż na tradycyjnych rynkach akcji czy obligacji. Stopa zwrotu z inwestycji w kontrakty terminowe jest wypadkową dwóch czynników: zmiany kursu terminowego i wysokości depozytu zabezpieczającego.
W niniejszej monografii zostały przedstawione badania dotyczące ryzyka ekstremalnego jakiego doświadczają inwestorzy na rynku kontraktów futures notowanych na Giełdzie Papierów Wartościowych w Warszawie. Po raz pierwszy w literaturze do analizy ryzyka wykorzystany został rzeczywisty rozkład zysków i strat z inwestycji w kontrakty terminowe. Wyniki przedstawionych badań będą stanowić dla inwestorów i badaczy źródło lepszego poznania mechanizmów rządzących rynkiem terminowym.

The method of pair copula constructions of multiple dependence was used to set dynamic futures portfolio margin level based on the theory of risk-based margin. The proposed model, fully reflects the characteristics of risk hedging and can flexibly capture the tail dependent features pair wise between different futures contracts, providing accurate measurement about the occurrence of market extreme events. Empirical results indicate that set by the futures exchanges margin level currently is obviously somewhat too high, while the proposed model can reflect the changes of market risk much better, there by ensuring a reasonable daily margin level.

Taking daily price limits into account and supposing that the information is asymmetric on China's futures markets, this paper constructs a Two-limit Tobit-GJR-GARCH model, and carries out Bayesian analysis by means of Monte Carlo simulation to evaluate the VaR and CVaR of the active trading commodities (e.g. soybean oil, copper and sugar) on China's futures markets. Empirical evidence indicates that daily price limits have important impacts on the risk measure and the theoretical margin of commodities with larger volatility. It is easy to underestimate the risk without regard to the impact of price limits, and the theoretical margin may not be able to cover the market risk. It will be more reliable to measure the risk and determine the theoretical margin based on the Tobit-GJR-Garch model which considers the impact of price limits, and the method provided in the paper accord with the actual situation and may be applied to the risk management of China's futures markets.

Since the CSI 300 index futures launched by the China Financial Futures Exchange in 2010, stock index trading has become another central issue in domestic financial research. This study determined the theoretical relationship between the margin level and market trading volume by using the definition of margin liquidity cost in a mathematical analysis model, and derived the general conclusions about the connection of market margin and market liquidity and volatility on the theoretical point. Furthermore, the study verified the validity of the theoretical conclusions by using the real trading data of S&P500 index futures contracts. At last, this article concludes: stock index futures margin level has a positive impact on the liquidity of the stock index futures market, and a reverse impact on market volatility.

Both in practice and in the academic literature, models for setting margin requirements in futures markets use daily closing price changes. However, financial markets have recently shown high intraday volatility, which could bring more risk than expected. Such a phenomenon is well documented in the literature on high-frequency data and has prompted some exchanges to set intraday margin requirements and ask intraday margin calls. This article proposes to set margin requirements by taking into account the intraday dynamics of market prices. Daily margin levels are obtained in two ways: first, by using daily price changes defined with different time-intervals (say from 3 pm to 3 pm on the following trading day instead of traditional closing times); second, by using 5-minute and 1-hour price changes and scaling the results to one day. An application to the FTSE 100 futures contract traded on LIFFE demonstrates the usefulness of this new approach.

In this paper, we study the margin of Chinese Stock Index Futures using GARCH-VaR model and Monte Carlo simulation respectively. The result of the empirical study shows that the model of GARCH-VaR is more precise in describing the proper margin level. Furthermore, the average margin level of the long is higher than the short, which means the long is exposed to more risks than the short Moreover, we find that the level of the margin is lower than current domestic stock index futures security level at both 99% and 95% confidence level . Keywords-Stock Index Futures; Margin ; Value at Risk; GARCH model ; Monte Carlo simulation

Let {W(t), 0 ≦ t < ∞} be the standard Wiener process. The probabilities of the type P[sup0≦t ≦ T
W(t) − f(t) ≧ 0] have been extensively studied when f(t) is a deterministic function. This paper discusses the probabilities of the type P{sup0≦t ≦ T
W(t) − [f(t) + X(t)] ≧ 0} when X(t) is a stochastic process. By taking compound Poisson processes as X(t), the paper gives procedures for finding such probabilities.

Let left brace W(t), 0 less than equivalent to t less than infinity right brace be the standard Wiener process. The probabilities of the type P left bracket sup//0// less than equivalent to t// less than equivalent to //TW(t) minus f(t) greater than equivalent to 0 right bracket have been extensively studied when f(t) is a deterministic function. The probabilities of the type P left brace sup//0 less than equivalent to t less than equivalent to TW(t) minus left bracket f(t) plus X(t) right bracket greater than equivalent to 0 right brace when X(t) is a stochastic process are discussed. By taking compound Poisson processes as X(t), procedures for finding such probabilities are given.

The calculation of margin for investor's option accounts is a complex and costly problem for brokerage houses. The existing procedures usually involve a heuristic requiring sequential computations. These are shown to be inefficient and suboptimal. A simple transportation formulation is presented which permits a direct computation of minimum margin and shows considerable savings when compared with existing heuristic procedures.

The sequential probability ratio test is constructed as a sequential test of one simple hypothesis against another. In many instances a parametric form is assumed for the density or (discrete) probability function, and the two simple hypotheses are specified by two values of the parameter. The sequential probability ratio test has an optimum property for these two hypotheses, namely, given such a test there is no other test with at least as low probabilities of Type I and Type II errors and with smaller expected sample sizes under either or both of the two hypotheses. Usually, however, one is interested in the performance of the procedure for more values of the parameter than these two. A disadvantage of the sequential probability ratio test is that in general the expected sample size is relatively large for values of the parameter between the two specified ones; that is, in cases in which one does not care greatly which decision is taken, a large number of observations is expected. The question is how to reduce the expected sample size for values of the parameter when this tends to be large. In this paper we consider a special case of the problem, when the distribution is normal with known variance and the parameter of interest is the mean. The sequential probability ratio test in this case consists in taking observations sequentially and after each observation is taken comparing the sum of the observations (referred to a suitable origin) with two constants. In this study the two constants are replaced by two linear functions of the number of observations taken, and the taking of observations is truncated (Section 2). Approximations to the operating characteristic (or power function) and the average sample size number are given (Section 4 and 5). Computations for two cases of special interest show a considerable decrease in average sample size at parameter values between the two specified ones (Section 3). The problem is studied by replacing the sum of observations by the Wiener stochastic process (of a continuous time parameter); this can be thought of intuitively as interpolating between observations in a manner consistent with the addition of independent random variables. For this procedure we calculate exactly the operating characteristic, the distribution of observation time, the expected observation time, and related probabilities.

"Stimulating, provocative, often infuriating, but well worth reading."âPeter Newman, Economica "His critical blast blows like a north wind against the more pretentious erections of modern economics. It is however a healthy and invigorating blast, without malice and with a sincere regard for scientific objectivity."âK.E. Boulding, Political Science Quarterly "Certainly one of the most engrossing volumes that has appeared recently in economic theory."âWilliam J. Baumol, Review of Economics and Statistics

If options are correctly priced in the market, it should not be possible to make sure profits by creating portfolios of long and short positions in options and their underlying stocks. Using this principle, a theoretical valuation formula for options is derived. Since almost all corporate liabilities can be viewed as combinations of options, the formula and the analysis that led to it are also applicable to corporate liabilities such as common stock, corporate bonds, and warrants. In particular, the formula can be used to derive the discount that should be applied to a corporate bond because of the possibility of default.

The relationship between Federal Reserve margin requirements and the behavior of stock prices has long been of interest to academicians and investors. This paper reports the results of a study of price movements around times when margins were changed. Using data from the 1933-69 period, the study concludes that increases in margin appear, at most, to have a trivial depressing influence on stock prices, which takes place over a number of days following the announcement of increases. Margin decreases, on the other hand, do not seem to have any significant impact on price behavior.

The contract price on a forward contract stays fixed for the life of the contract, while a futures contract is rewritten every day. The value of a futures contract is zero at the start of each day. The expected change in the futures price satisfies a formula like the capital asset pricing model. If changes in the futures price are independent of the return on the market, the futures price is the expected spot price. The futures market is not unique in its ability to shift risk, since corporations can do that too. The futures market is unique in the guidance it provides for producers, distributors, and users of commodities. Using assumptions like those used in deriving the original option formula, we find formulas for the values of forward contracts and commodity options in terms of the futures price and other variables.

This paper presents empirical tests of a model of intraday transaction price walks haveior events both the existence of price reversal's in transaction price sequence with random, New York daily. and longer different intervlas. In genral, we find that trasaction of independ events both with respect to their time execution and the siem and (bid or ask) or whick thaye are executed. Over very short intervals times, however, transapction tend to cluster in time and on a particular side of the market. We conjecture that this latter phenomenon is a consequence of market procedures on the New York Stock Exchange.

ABSTRACTA portfolio‐theoretic model of the optimal margin account is developed. It is argued that the Federal Reserve's goal in setting the margin requirement is to influence investor equity ratios. Using the average equity ratio as the dependent variable and the arguments of the model as independent variables, an empirical model is estimated. It is concluded that the margin requirement is an effective regulatory tool.

Satisfied as we may be with the overall efficiency of the market system and with the tenets of the perfect market model, we all viscerally know that were we down on the market floor we would certainly react to a multitude of apparent price discrepancies. Indeed, it is intuitively inconceivable that a man‐made institution (such as the market) could be so mechanically perfect that all such discrepancies would be totally annihilated before they can be observed. Accordingly, we would expect floor traders and other professionals to be speculating abundantly on what they perceive to be the direction in which the market is going. Almost surely, such behavior has an effect on the dynamics of stock prices. A financial theory that cavalierly ignores this component in the determination of prices would be regrettably deficient.

Al) holds for all values On the Dynamic Behavior of Prices in The Pricing of Commodity Contracts The Pricing of Options and Corporate Liabilities

- Beja
- A Goldman
- B Black
- F Scholes

26A more general theorem, proved in Anderson (1960), can be used to show that the restriction on the signs of a and b is unnecessary, and Eq. (Al) holds for all values. 414 / FICLEWSKI Beja, A., and Goldman, B., (1980): " On the Dynamic Behavior of Prices in Disequili-Black, F. (1976): " The Pricing of Commodity Contracts, " Journal of Financial Economics, Black, F., and Scholes, M. J. (1973): " The Pricing of Options and Corporate Liabilities, " Journal of Political Economy, 81(3): 637-654. Chicago Board of Trade, Chicago Mercantile Exchange, Coffee, Sugar and Cocoa Ex-change, Commodity Exchange, Midamerica Commodity Exchange, New York Futures Exchange (1983, May 27): " Re: Options on Futures; Margins, " Document submitted to CFTC.

Margins: A Review of the Literature

- Kuhn

December): Margins, Speculation, and Prices in Grain Futures Markets

- Inc Associates
- Nathan

The Structure of Margin Credit

- Ulrey