# Carl ChiarellaUniversity of Technology Sydney | UTS · Finance Discipline Group

Carl Chiarella

BSc, MSc, MComm (Hons), PhD (Mathematics), PhD (Ec

## About

374

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## Publications

Publications (374)

The paper analyses from a disequilibrium perspective the role of banks’ “animal spirits” and collective behaviour in the creation of credit that, ultimately, determines the credit cycle. In particular, we propose a dynamic model to analyse how the transmission of waves of optimism and pessimism in the supply side of the credit market interacts with...

The main objective of the present paper is to investigate the role of the state of confidence in the macroeconomic dynamics of two interacting economies using the opinion dynamics approach by Weidlich and Haag (Concepts and models of a quantitative sociology. The dynamics of interacting populations. Springer, Berlin, 1983) and Lux (Econ J 105:881–8...

As mentioned in Chap. 1 following the events of the world-wide financial crisis over the periods 2007–2009, the risk profile of some assets changed drastically and many assets exhibited large losses. These events have reinforced thinking about proper portfolio models that not only avoid large losses, but also allow to impose some constraints. This...

This chapter studies intertemporal investment strategies under inflation risk by extending the dynamic programming we have used so far, to include a stochastic price index. The stochastic price index gives rise to a two-tier evaluation system: agents maximize their utility of consumption in real terms while investment activities and wealth evolutio...

In this chapter we provide an overview on forecasting asset returns and low frequency movements in asset returns. Saving and asset allocation decision, usually focus on low frequency movements in asset returns and how they are expected to behave in the future. Thus, the prevailing consensus in the context of portfolio theory, is of the view that th...

As discussed in Chap. 2 academic research on asset returns seems to converge toward the view that a proper formation of expected asset returns are essential for saving and asset allocation decisions. As also shown in Chap. 4 the use of time varying asset returns, following low frequency movements, appears to be quite suitable for the purpose of suc...

As mentioned, the transition of a continuous time model into a discrete time model is not an easy issue. We discuss here various discretization procedures to turn continuous time into discrete time models. There are many methods to convert continuous time models into discrete time variants. The main discretization methods are the Euler method, the...

Next we will include labor income into our asset accumulation and asset allocation decisions. This brings us to the problem of pension funds and retirement income. Academics, journalists and politicians have recently discussed in particular the issue of uncovered future retirement and pension fund liabilities. Many questions are being raised in thi...

In this chapter, we illustrate the use of dynamic programming (DP) and the HJB equation for a simple model. We focus on dynamic saving and asset allocation, formulated in continuous time. We first introduce a model with one asset and constant returns. Usually in the literature, the problem is formulated as consumption and asset allocation decision....

By incorporating behavioural sentiment in a model of a limit order market, we show that behavioural sentiment not only helps to replicate most of the stylized facts in limit order markets simultaneously, but it also plays a unique role in explaining those stylized facts that cannot be explained by noise trading, such as fat tails in the return dist...

This paper analyzes a term structure model that allows for both stochastic correlation between underlying factors and an extended market price of risk specification. We show that significant improvement in bond fitting and portfolio performance is obtained by the model. However, the restriction on market price of risk has a more negative impact on...

This book examines sustainable wealth formation and dynamic decision-making. The global economy experienced a veritable meltdown of asset markets in the years 2007-9, where many funds were overexposed to risky returns and suffered considerable losses. On the other hand, the long-term upswing in the stock market since 2010 has led to asset price boo...

This paper considers the American option pricing problem under regime-switching by using the method-of-lines (MOL) scheme. American option prices in each regime involve prices in all other regimes. We treat the prices from other regimes implicitly, thus guaranteeing consistency. Iterative procedures are required but very few iterative steps are nee...

This paper introduces a limit order market model of fast and slow traders with learning to examine the effect of high frequency trading (HFT) and learning on limit order markets. We demonstrate that informed HFT makes significant profit from trading with other traders and, more importantly, it is the learning and information advantage that plays mo...

By introducing a genetic algorithm learning with a classifier system into a limit order market, this paper provides a unified framework of microstructure and agent-based models of limit order markets that allows traders to determine their order submission endogenously according to market conditions. It examines how traders process and learn from ma...

By employing a continuous time multi-factor stochastic volatility model, the dynamic relation between returns and volatility in the commodity futures markets is analyzed. The model is estimated by using an extensive database of gold and crude oil futures and futures options. A positive relation in the gold futures market and a negative relation in...

The martingale approach is widely used in the literature on contingent claim analysis. Following the definition of a martingale process, we give some examples, including the Wiener process, stochastic integral, and exponential martingale. We then present the Girsanov’s theorem on a change of measure. As an application, we derive the Black–Scholes f...

It is commonly observed across many underlying assets that the implied volatility of the Black Scholes model varies across exercise price and time-to-maturity and has a pattern known as the volatility smile. In this chapter, we first address the volatility smile using the stochastic volatility models which may underestimate the size of the smile. W...

This chapter outlines the paradigm problem of option pricing and motivates key concepts and techniques that we will develop in Part I when the risk-free rate is deterministic.

Many computational applications of derivative pricing models such as the determination of derivative prices by simulation or the estimation of derivative pricing models can be significantly simplified by a change of numeraire. In this chapter we discuss the main idea behind the change of numeraire technique and the formation of equivalent probabili...

This chapter extends the hedging argument of option pricing developed for continuous diffusion processes previously to the situations when the underlying asset price is driven by the jump-diffusion stochastic differential equations. By constructing hedging portfolios and employing the capital asset pricing model, we provide an option pricing integr...

This chapter considers jump-diffusion processes to allow for price fluctuations to have two components, one consisting of the usual increments of a Wiener process, the second allows for “large” jumps from time-to-time. We introduce Poisson jump process with either absolute or proportional jump sizes through the stochastic integrals and provide solu...

The discussion in Chaps. 12 and 15 considered a relaxation of one of the key assumptions of the Black–Scholes framework, namely that the asset price changes follow a geometric Brownian motion. Another crucial assumption is the assumption of a constant interest rate over the life of the option. In this chapter we consider the specific case of stock...

This chapter applies the general pricing framework developed in Chap. 10 to some standard one factor examples including stock options, currency options, futures options and a two factor model of exchange option.

The Partial Differential Equation (PDE) Approach is one of the techniques in solving the pricing equations for financial instruments. The solution technique of the PDE approach is the Fourier transform, which reduces the problem of solving the PDE to one of solving an ordinary differential equation (ODE). The Fourier transform provides quite a gene...

In this chapter we consider the solution of the integro-partial differential equation that determines derivative security prices when the underlying asset price is driven by a jump-diffusion process. We take the analysis as far as we can for the case of a European option with a general pay-off and the jump-size distribution is left unspecified. We...

To develop the hedging argument of Black and Scholes, this chapter introduces stochastic differential equations to model the evolution of the price path itself and the statistical properties of small price changes over small changes in time. We then consider the stochastic differential equations for the Wiener process, Ornstein–Uhlenbeck process an...

In this chapter, we establish the fundamental relationships between interest rates, bond prices and forward rates. We further discuss the modelling of interest rates and analyse typical models for the spot interest rate and the forward rates. As we desire interest rates to be non-negative, we seek stochastic processes with this feature such as the...

To
understand the problems and techniques of pricing the American feature of an option, this chapter introduces the American option pricing problem from the conventional approach based on compound options and the free boundary value problem which can be solved by using either the Fourier transform technique or a simple approximation procedure. The...

This chapter presents the binomial tree approach to the option pricing problem. We first illustrate the basic ideas of option pricing by considering the one-period binomial tree model and then extend to a multi-period binomial tree model. We then show that, by taking limits in an appropriate way, the binomial expression for the option price converg...

In this chapter we develop a framework for term structure modelling that allows factors other than the instantaneous spot rate itself to influence the evolution of the term structure of interest rates. The framework allows for multi-factor generalisations of the Hull–White model as well as of the CIR model. First we present a two-factor extension o...

This chapter uses the concepts developed in Chap. 2 to illustrate the problem of option pricing as a discounted expected option payoff. By assuming that investors are risk neutral and using the Kolmogorov equation for the conditional probability, we demonstrate how the Black–Scholes option formula can be arrived. We also illustrate how the option p...

This chapter gives an intuitive appreciation and review of many important aspects of the stochastic processes that have been used to model asset price processes. We will be interested in a probabilistic description of the time evolution of asset prices. After imposing some structure on the stochastic process for the return on the asset, this chapte...

Interest rate modelling can also be performed by starting from the dynamics of the instantaneous forward rate. As we shall see the dynamics of all other quantities of interest can then be derived from it. This approach has its origin in
Ho and Lee (J Finance XLI:1011–1029, 1986) but was most clearly articulated in Heath et al. (Econometrica 60(1):7...

Many of the calculations of derivative security pricing involve formal manipulations of stochastic differential equations and stochastic integrals. This chapter derives those that are most frequently used. We also consider transformation of correlated Wiener processes to uncorrelated Wiener processes for higher dimensional stochastic differential e...

There are a number of instruments in interest rate markets that are equivalent to an option on an interest rate or an option on a bond. In this chapter we focus on the interest rate caps, which are call options on an interest rate. We show that they can be interpreted as a put option on a bond. The problem of pricing such bonds, and hence the inter...

The modifications to the Heath-Jarrow-Morton framework to cater for market quoted rates such as LIBOR rates were carried out by Brace and Musiela (Math Finance 4(3):259–283, 1994)
(henceforth BM). In this chapter, we first describe the BM parameterisation of the Heath–Jarrow–Morton model, and then we outline the choice of volatility functions that...

This chapter extends the hedging argument developed in Chap. 7 and the martingale approach developed in Chap. 8 by allowing derivative securities to depend on multiple sources of risks and multiple underlying factors, some are tradable and some are not tradable. It provides a general PDE and martingale approaches to pricing derivative securities.

This chapter develops a continuous hedging argument for derivative security pricing. Following fairly closely the original Black and Scholes (1973)
article, we make use of Ito’s lemma to derive the expression for the option value and exploit the idea of creating a hedged position by going long in one security, say the stock, and short in the other...

In this chapter we survey models of interest rate derivatives which take the instantaneous spot interest rate as the underlying factor. The continuous hedging argument is extended so as to model the term structure of interest rates and other interest rate derivative securities. This basic approach is due to Vasicek (J Financ Econ 5:177–188, 1977)
a...

This chapter introduces Ito’s lemma, which is one of the most important tools of stochastic analysis in finance. It relates the change in the price of the derivative security to the change in the price of the underlying asset. Applications of Ito’s lemma to geometric Brownian motion asset price process, the Ornstein–Uhlenbeck process, and Brownian...

Empirical studies show that the volatility of asset returns are not constant and the returns are more peaked around the mean and have fatter tails than implied by the normal distribution. These empirical observations have led to models in which the volatility of returns follows a diffusion process. In this chapter, we introduce some stochastic vola...

By employing a continuous time multi‐factor stochastic volatility model, the dynamic relation between returns and volatility in the commodity futures markets is analyzed. The model is estimated by using an extensive database of gold and crude oil futures and futures options. A positive relation in the gold futures market and a negative relation in...

The book presents applications of stochastic calculus to derivative security pricing and interest rate modelling. By focusing more on the financial intuition of the applications rather than the mathematical formalities, the book provides the essential knowledge and understanding of fundamental concepts of stochastic finance, and how to implement th...

This paper proposes a model for credit default swap (CDS) spreads under heterogeneous expectations to explain the escalation in sovereign European CDS spreads and the widening variations across European sovereigns following the Global Financial Crisis (GFC). In our model, investors believe that sovereign CDS spreads are determined by country-specif...

The early exercise opportunity of an American option makes it challenging to price and an array of approaches have been proposed in the vast literature on this topic. In The Numerical Solution of the American Option Pricing Problem, Carl Chiarella, Boda Kang and Gunter Meyer focus on two numerical approaches that have proved useful for finding all...

The primary purpose of this paper is to provide an in-depth analysis of a number of structurally different methods to numerically evaluate European compound option prices under Heston’s stochastic volatility dynamics. Therefore, we first outline several approaches that can be used to price these type of options in the Heston model: a modified spars...

In this paper we consider various computational methods for pricing American style derivatives. We do so under both jump diffusion and stochastic volatility processes. We consider integral transform methods, the method of lines, operator-splitting, and the Crank-Nicolson scheme, the latter being used to generate the benchmark solution. Overall, we...

In this paper we consider the pricing of an American call option whose underlying asset dynamics evolve under the influence of two independent stochastic volatility processes as proposed in Christoffersen, Heston and Jacobs (2009) [13]. We consider the associated partial differential equation (PDE) for the option price and its solution. An integral...

A compound option (the mother option) gives the holder the right, but not the obligation, to buy (long) or sell (short) the underlying option (the daughter option). In this paper, we consider the problem of pricing American-type compound options when the underlying dynamics follow Heston’s stochastic volatility and with stochastic interest rate dri...

This chapter extends the dynamic leverage ratio model of of Hui et al. to the two-firm case so as to study the implications for default correlations and joint survival probabilities. The two-firm model has been proposed by Zhou, who extends the one-firm model of Black and Cox to the two-firm situation. The chapter reviews the techniques used by the...

This paper extends the integral transform approach of McKean (1965) and Chiarella and Ziogas (2005) to the pricing of American options written on more than one underlying asset under the Black and Scholes (1973) framework. A bivariate transition density function of the two underlying stochastic processes is derived by solving the associated backwar...

Single-product oligopolies are examined with uncertain isoelastic price functions and linear cost functions. Each firm wants to maximize its expected profit and also wants to minimize its uncertainty by minimizing the variance. This multiobjective optimization problem is solved by the weighting method, where the utility function of each firm is a l...

The essays in this special volume survey some of the most recent advances in the global analysis of dynamic models for economics, finance and the social sciences. They deal in particular with a range of topics from mathematical methods as well as numerous applications including recent developments on asset pricing, heterogeneous beliefs, global bif...

The primary purpose of this paper is to provide an in-depth analysis of a number of structurally different methods to numerically evaluate European compound option prices under Heston’s stochastic volatility dynamics. Therefore, we first outline several approaches that can be used to price these type of options in the Heston model: a modified spars...

A continuously distributed time lag is considered in a monopoly where the time window of past data is bounded from below and its length is fixed. The dynamic behavior of the resulting system is described by a special delayed differential equation with infinite spectrum. The location of the stability switch is determined and a simple rule is develop...

The paper presents a survey of the literature that has grown out of the work of Hyman Minsky and, in particular, of the main models which have mathematically formalized the cyclical dynamics of a capitalist economy implied by the Financial Fragility Hypothesis. We identify some of the issues that the existing literature has left unresolved. We then...

The paper presents an agent-based model to study the possible effects of different fiscal and monetary policies in the context of debt deflation. We introduce a modified Taylor rule that includes the financial position of firms as a target. Monte Carlo simulations provide a representation of the complex feedback effects generated by the interaction...

This paper proposes a model for credit default swap (CDS) spreads under heterogeneous expectations to explain the escalation in sovereign European CDS spreads and the widening variations across European sovereigns following the Global Financial Crisis (GFC). In our model, investors believe that sovereign CDS spreads are determined by country-specif...

We investigate the partial differential equation (PDE) for pricing interest derivatives in the multi-factor Cheyette Model, which involves time-dependent volatility functions with a special structure. The high dimensional parabolic PDE that results is solved numerically via a modified sparse grid approach, that turns out to be accurate and efficien...

This paper presents an agent based model that investigates the possible outcomes of different fiscal and regulatory policies in a financially fragile economy. We analyse the consequences of the attempt by the government to counteract a downturn ignoring the debt dynamics as modelled by Fisher and Minsky. In particular we formulate an educated guess...

Heterogeneity and evolutionary behaviour of investors are two of the most important characteristics of financial markets. This papers incorporates the adaptive behavior of agents with heterogeneous beliefs and establishes an evolutionary capital asset pricing model (ECAPM) within the mean-variance framework. We show that the rational behavior of ag...

In this paper we study the implications of the present broad banking system for macroeconomic stability. We show that when commercial banks are allowed to trade in financial assets (here equities) as a substitute for traditional lending, the macroeconomic system is likely to be an unstable one. We then consider a narrow banking system defined by a...

This paper analyzes the volatility structure of commodity derivatives markets. The model encompasses stochastic volatility that may be unspanned by futures contracts. A generalized hump-shaped volatility specification is assumed that entails a finite-dimensional affine model for the commodity futures curve and quasi-analytical prices for options on...

This paper analyzes the volatility structure of the commodity derivatives markets. The model encompasses stochastic volatility that may be unspanned by the futures contracts. A generalized hump-shaped volatility specification is assumed that entails a finite-dimensional affine model for the commodity futures curve and quasi-analytical prices for op...

We consider the evaluation of American options on dividend paying stocks in the case where the underlying asset price evolves according to Heston’s stochastic volatility model in (Heston, Rev. Financ. Stud. 6:327–343, 1993). We solve the Kolmogorov partial differential equation associated with the driving stochastic processes using a combination of...

This article provides a generalized two-firm model of default correlation, based on the structural approach that incorporates interest rate risk. In most structural models default is driven by the firms' asset dynamics. In this article, a two-firm model of default is instead driven by the dynamic leverage ratios, which combines the measure of risks...

Many monetary and fiscal policy measures have aimed at mitigating the effects of the financial market meltdown that started in the U.S. subprime sector in 2008 and has subsequently spread world wide as a great recession. Slowly some recovery appears to be on the horizon, yet it is worthwhile exploring the fragility and potentially destabilizing fee...

A typical gas swing contract is an agreement between a supplier and a purchaser for the delivery of variable daily quantities of gas, between specified minimum and maximum daily limits, over a certain period at a specified set of contract prices. The main constraint of such an agreement that makes them difficult to value are that there is a minimum...

A numerical technique for the evaluation of American spread call options where the underlying asset dynamics evolve under the influence of a single stochastic variance process of the Heston (1993) type is presented. The numerical algorithm involves extending to the multi-dimensional setting the method of lines approach first presented in the option...

Research on the Heath-Jarrow-Morton (1992) term structure models so far has focused on the class having time-deterministic instantaneous forward rate volatility. In this case the forward rate process is Markovian, even if the spot rate process is not. However, this Markovian feature can only be used under the historical measure, involving two unsat...

Long-run analyses usually stress the leading role of aggregate supply. As a result, aggregate demand is supposed to adjust in order to accommodate supply changes. In a medium-run perspective, however, both aggregate demand and supply forces must be taken ...

This article extends the exchange option model of Margrabe, where the distributions of both stock prices are log-normal with correlated Wiener components, to allow the underlying assets to be driven by jump-diffusion processes of the type originally introduced by Merton. We introduce the Radon–Nikodým derivative process that induces the change of m...

This paper considers the problem of pricing American options when the dynamics of the underlying are driven by both stochastic volatility following a square-root process as used by Heston [Rev. Financial Stud., 1993, 6, 327–343], and by a Poisson jump process as introduced by Merton [J. Financial Econ., 1976, 3, 125–144]. Probability arguments are...

This study examines the interrelation between small traders' open interest and large hedging and speculation in the Canadian dollar, Swiss franc, British pound, and Japanese yen futures markets. The results, based on Granger-causality tests and vector autoregressive models, suggest that small traders' open interest is closely related to large specu...

In this paper we model a financial market composed of agents with heterogeneous beliefs who change their strategy over time. We propose two different solution methods which lead to two different types of endogenous dynamics. The first makes use of the maximum entropy approach to obtain an exponential type probability function for strategies, analog...

In a basic model of monetary dynamics we allow inflationary expectations to be formed as a weighted average of fundamentalist
and chartists expectations. The fundamentalists form inflationary expectations rationally in the traditional sense in that
they have full knowledge of the economic environment. The chartists form expectations by using standa...

This paper proposes a framework for pricing credit derivatives within the defaultable Markovian HJM framework featuring unspanned stochastic volatility. Motivated by empirical evidence, hump-shaped level dependent stochastic volatility specifications are proposed, such that the model admits finite dimensional Markovian structures. The model also ac...

Financial markets are typically characterized by high (low) price level and low (high) volatility during boom (bust) periods, suggesting that price and volatility tend to move together with different market conditions/states. By proposing a simple heterogeneous agent model of fundamentalists and chartists with Markov chain regime-dependent expectat...

This paper proposes and analyses a term structure model that allows for both stochastic correlation between underlying factors and an extended market price of risk specification. The issues of invariant transformation and different normalization are then considered so that a comparison between different restrictions can be made. We show that signi?...

It is believed that diversity is good for our society, but is it good for financial markets? In particular, does the diversity with respect to beliefs among investors reduce the market risk of risky assets? The current paper aims to answer this question. Within the standard mean-variance framework, we introduce heterogeneous beliefs not only in ris...

A typical gas sales agreement (GSA) also called a gas swing contract, is an agreement between a supplier and a purchaser for the delivery of variable daily quantities of gas, between speci?ed minimum and maximum daily limits, over a certain number of years at a speci?ed set of contract prices. The main constraint of such an agreement that makes the...

Heterogeneous agent models (HAMs) in finance and economics are often characterised by high dimensional nonlinear stochastic differential or difference systems. Because of the complexity of the interaction between the nonlinearities and noise, a commonly used, often called indirect, approach to the study of HAMs combines theoretical analysis of the...

Merton has provided a formula for the price of a European call option on a single stock where the stock price process contains a continuous Poisson jump component, in addition to a continuous log-normally distributed component. In Merton's analysis, the jump-risk is not priced. Thus the distribution of the jump-arrivals and the jump-sizes do not ch...

In this paper a simulation approach for defaultable yield curves is developed within the Heath et al. (1992) framework. The default event is modelled using the Cox process where the stochastic intensity represents the credit spread. The forward credit spread volatility function is affected by the entire credit spread term structure. The paper provi...

IntroductionMacroeconomic Portfolio Choice and Keynesian Business Cycle Theory; the KMGTModelLong-Term Bonds, Not Money, as the Primary Financing Instrument of the GovernmentIntensive Form of the ModelKeynesian Fiscal Policy Rules and Stability of Balanced GrowthConclusions
NotesReferences

This article surveys boundedly rational heterogeneous agent (BRHA) models of financial markets. We give particular emphasis to the role of the market clearing mechanism used, the utility function of the investors, the interaction of price and wealth dynamics, and calibration of this class of models. Due to agents' behavioural features and market no...