# Álvaro CarteaUniversity of Oxford | OX · Mathematical Institute

Álvaro Cartea

## About

106

Publications

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2,576

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Citations since 2016

Introduction

**Skills and Expertise**

Additional affiliations

January 2005 - December 2011

**Universidad Carlos III de Madrid**

## Publications

Publications (106)

Providing liquidity in over-the-counter markets is a challenging under-taking, in large part because a market maker does not observe where their competitors quote, nor do they typically know how many rivals they compete with or what the trader's overall liquidity demand is. Optimal pricing strategies can be derived in theory assuming full knowledge...

We propose a novel framework to solve risk-sensitive reinforcement learning (RL) problems where the agent optimises time-consistent dynamic spectral risk measures. Based on the notion of conditional elicitability, our methodology constructs (strictly consistent) scoring functions that are used as penalizers in the estimation procedure. Our contribu...

Linear multivariate Hawkes processes (MHP) are a fundamental class of point processes with self-excitation. When estimating parameters for these processes, a difficulty is that the two main error functionals, the log-likelihood and the least squares error (LSE), as well as the evaluation of their gradients, have a quadratic complexity in the number...

Latency (i.e. time delay) in electronic markets affects the efficacy of liquidity taking strategies. During the time liquidity, takers process information and send marketable limit orders (MLOs) to the exchange, the limit order book (LOB) might undergo updates, so there is no guarantee that MLOs are filled. We develop a latency-optimal trading stra...

We show how a market maker employs information about the momentum in the price of the asset (i.e. alpha signal) to make decisions in their liquidity provision strategy in an order-driven electronic market. The momentum in the midprice of the asset depends on the execution of liquidity taking orders and the arrival of news. Buy market orders (MOs) e...

We develop the optimal trading strategy for a foreign exchange (FX) broker who must liquidate a large position in an illiquid currency pair. To maximize revenues, the broker considers trading in a currency triplet which consists of the illiquid pair and two other liquid currency pairs. The liquid pairs in the triplet are chosen so that one of the p...

A risk‐averse agent hedges her exposure to a nontradable risk factor U using a correlated traded asset S and accounts for the impact of her trades on both factors. The effect of the agent's trades on U is referred to as cross‐impact. By solving the agent's stochastic control problem, we obtain a closed‐form expression for the optimal strategy when...

We model the trading strategy of an investor who spoofs the limit order book (LOB) to increase the revenue obtained from selling a position in a security. The strategy employs, in addition to sell limit orders (LOs) and sell market orders (MOs), a large number of spoof buy LOs to manipulate the volume imbalance of the LOB. Spoofing is illegal, so t...

We show there exists a profitable cross-border trading strategy for an agent who trades electricity in the European electricity network. Data of the European markets are employed to show how electricity prices in all locations of the network are affected by the flow of power between any two locations that trade power between them. The optimal cross...

Latency (i.e., time delay) in electronic markets affects the efficacy of liquidity taking strategies. During the time liquidity takers process information and send marketable limit orders (MLOs) to the exchange, the limit order book (LOB) might undergo updates, so there is no guarantee that MLOs are filled. We develop a latency-optimal trading stra...

A risk-averse agent hedges her exposure to a non-tradable risk factor $U$ using a correlated traded asset $S$ and accounts for the impact of her trades on both factors. The effect of the agent's trades on $U$ is referred to as cross-impact. By solving the agent's stochastic control problem, we obtain a closed-form expression for the optimal strateg...

We show how the supply of liquidity in order-driven markets is affected if limit orders (LOs) are forced to rest in the limit order book for a minimum resting time (MRT) before they can be cancelled. The bid-ask spread increases as the MRT increases because market makers (MMs) increase the depth of their LOs to protect them from being picked off by...

We examine the Foreign exchange (FX) spot price spreads with and without Last Look on the transaction. We assume that brokers are risk-neutral and they quote spreads so that losses to latency arbitrageurs are recovered from other traders in the FX market. These losses are reduced if the broker can reject, ex-post, loss-making trades by enforcing th...

We derive an investor's optimal trading strategy of electricity contracts traded in two locations joined by an interconnector. The investor employs a price model which includes the impact of her own trades. The investor's trades have a permanent impact on prices because her trading activity affects the demand of contracts in both locations. Additio...

We introduce a new approach for incorporating uncertainty in the decision to invest in a commodity reserve. An investment is an irreversible one-off capital expenditure, after which the investor receives a stream of cashflow from extracting the commodity and selling it on the spot market. The investor is exposed to price uncertainty as well as unce...

This paper studies the intraday relationship between ultra-fast machine-driven activity (UFA) and market quality in automated equity markets. We find that higher UFA is associated with lower intraday market quality (greater quoted and effective spreads and lower depth). This effect is economically significant, and robust to different specifications...

Executing a basket of co‐integrated assets is an important task facing investors. Here, we show how to do this accounting for the informational advantage gained from assets within and outside the basket, as well as for the permanent price impact of market orders (MOs) from all market participants, and the temporary impact that the agent's MOs have...

Executing a basket of co-integrated assets is an important task facing investors. Here, we show how to do this accounting for the informational advantage gained from assets within and outside the basket, as well as for the permanent price impact of market orders (MOs) from all market participants, and the temporary impact that the agent's MOs have...

We develop a trading strategy that employs limit and market orders in a multiasset economy where the assets are not only correlated, but can also be structurally dependent. To model the structural dependence, the mid-price processes follow a multivariate reflected Brownian motion on the closure of a no-arbitrage region which is dictated by the bid–...

We use high-frequency data from the Nasdaq exchange to build a measure of volume imbalance in the limit order (LO) book. We show that our measure is a good predictor of the sign of the next market order (MO), i.e., buy or sell, and also helps to predict price changes immediately after the arrival of an MO. Based on these empirical findings, we intr...

We develop a high frequency (HF) trading strategy where the HF trader uses her superior speed to process information and to post limit sell and buy orders. By introducing a multifactor mutually exciting process, we allow for feedback effects in market buy and sell orders and the shape of the limit order book (LOB). Our model accounts for the arriva...

Real option valuation has traditionally been concerned with investment under project value uncertainty while assuming that the agent has perfect confidence in a specific model. However, agents do not generally have perfect confidence in their model and this ambiguity may affect their decisions. In addition, the value of real investments is not typi...

Algorithmic traders acknowledge that their models are incorrectly speci-ed, thus we allow for ambiguity in their choices to make their models robust to misspecification in (i) the arrival rate of market orders, (ii) the ffll probability of limit orders, and (iii) the dynamics of the midprice of the asset they deal. In the context of market making,...

We assume that the drift in the returns of asset prices consists of an idiosyncratic component and a common component given by a co-integration factor. We analyze the optimal investment strategy for an agent who maximizes expected utility of wealth by dynamically trading in these assets. The optimal solution is constructed explicitly in closed-form...

We provide an explicit closed-form strategy for an investor who executes a large order when market order-flow from all agents, including the investor’s own trades, has a permanent price impact. The strategy is found in closed-form when the permanent and temporary price impacts are linear in the market’s and investor’s rates of trading. We do this u...

We propose a model where an algorithmic trader takes a view on the distribution of prices at a future date and then decides how to trade in the direction of their predictions using the optimal mix of market and limit orders. As time goes by, the trader learns from changes in prices and updates their predictions to tweak their strategy. Compared to...

Shortcomings of continuous and static microstructure models are noted with motivation provided by data from the NASDAQ. The influence of order imbalance on microstructure dynamics is incorporated in to a model which allows the agent to adjust their strategy based on an easily observable quantity. The predictive power of order imbalance allows the a...

Agents who acknowledge that their models are incorrectly specified are said to be ambiguity averse, and this affects the prices they are willing to trade at. Models for prices of commodities attempt to capture three stylized features: seasonal trend, moderate deviations (a diffusive factor), and large deviations (a jump factor) both of which mean-r...

We provide two explicit closed-form optimal execution strategies to target volume weighted average price (VWAP). We do this under very general assumptions about the stochastic process followed by the volume traded in the market, and, unlike earlier studies, we account for permanent price impact stemming from order-flow of the agent and all other tr...

We derive an investor’s optimal trading strategy of electricity contracts traded in two locations joined by an interconnector. The investor employs a price model which includes the impact of her own trades. The investor’s trades have a permanent impact on prices because her trading activity affects the demand of contracts in both locations. Additio...

This book is not available from the author. If you wish to have a review copy please contact the publisher (Cambridge University Press) who will be happy to handle your request.

We develop an optimal execution policy for an investor seeking to execute a large order using limit and market orders. The investor solves the optimal policy considering different restrictions on volume of both types of orders and depth at which limit orders are posted. We show how the execution policies perform when targeting the volume schedule o...

We develop a trading strategy which employs limit and market orders in a multi-asset economy where the assets are not only correlated, but can also be structurally dependent. To model the structural dependence, the midprice processes follow a multivariate reflected Brownian motion on the closure of a no-arbitrage region which is dictated by the ass...

We show how to execute a basket consisting of a subset of co-moving assets and demonstrate how the information carried in other traded assets, which are not in the basket, improves execution performance. Market orders (MOs) from all participants, including the agent's orders to execute her basket, have permanent price impact on the assets, i.e. exe...

Agents who acknowledge that their models are incorrectly specified are said to be ambiguity averse, and this affects the prices they are willing to trade at. Models for prices of commodities attempt to capture three stylized features: seasonal trend, moderate deviations (a diffusive factor), and large deviations (a jump factor) both of which mean-r...

We examine the Foreign Exchange (FX) spot price spreads with and without Last Look on the transaction. We assume that brokers are risk-neutral and they quote spreads so that losses to latency arbitrageurs (LAs) are recovered from other traders in the FX market. These losses are reduced if the broker can reject, ex-post, loss-making trades by enforc...

We assume that the drift in the returns of asset prices consists of an idiosyncratic component and a common component given by a co-integration factor. We analyze the optimal investment strategy for an agent who maximizes expected utility of wealth by dynamically trading in these assets. The optimal solution is constructed explicitly in closed-form...

We provide an explicit closed-form strategy for an investor who executes a large order when market order-flow from all agents, including the investor's own trades, has a permanent price impact. The strategy is found in closed-form when the permanent and temporary price impacts are linear in the market's and investor's rates of trading. We do this u...

We provide two explicit closed-form optimal execution strategies to target VWAP. We do this under very general assumptions about the stochastic process followed by the volume traded in the market, and, unlike earlier studies, we account for permanent price impact stemming from order-flow of the agent and all other traders. One of the strategies con...

Because algorithmic traders acknowledge that their models are incorrectly specified we allow for ambiguity in their choices to make their models robust to misspecification. We show how to include misspecification to: (i) the arrival rate of market orders (MOs), (ii) the fill probability of limit orders, and (iii) the dynamics of the midprice of the...

We propose a model where an algorithmic trader takes a view on the distribution of prices at a future date and then decides how to trade in the direction of their predictions using the optimal mix of market and limit orders. As time goes by, the trader learns from changes in prices and updates their predictions to tweak their strategy. Compared to...

I propose to model stock price tick-by-tick data via a non-explosive marked point process. The arrival of trades is driven by a counting process in which the waiting time between trades possesses a Mittag–Leffler survival function and price revisions have an infinitely divisible distribution. I show that the partial-integro-differential equation sa...

The liberalisation of energy markets entails the appearance of market risks which must be borne by market participants: producers, retailers, and final consumers. Some of these risks can be managed by participating in the forward markets and transferring it to other agents who are willing to bear it and command a compensation for it. Thus, forward...

We propose risk metrics to assess the performance of High Frequency (HF) trading strategies that seek to maximize profits from making the realized spread where the holding period is extremely short (fractions of a second, seconds or at most minutes). The HF trader maximizes expected terminal wealth and is constrained by both capital and the amount...

We test the performance of different volatility estimators that have recently been proposed in the literature and have been designed to deal with problems arising when ultra high-frequency data are employed: microstructure noise and price discontinuities. Our goal is to provide an extensive simulation analysis for different levels of noise and freq...

We analyze the impact of high frequency (HF) trading in financial markets based on a model with three types of traders: liquidity traders (LTs), professional traders (PTs), and high frequency traders (HFTs). Our four main findings are: i) The price impact of liquidity trades is higher in the presence of the HFTs and is increasing with the size of t...

We develop a High Frequency (HF) trading strategy where the HF trader uses her superior speed to process information and to post limit sell and buy orders. By introducing a multi-factor self-exciting process we allow for feedback effects in market buy and sell orders and the shape of the limit order book (LOB). Our model accounts for arrival of mar...

In this paper we show how to calculate European-style option prices when the log-stock and stock returns processes follow a symmetric Lévy-Stable process. We extend our results to price European-style options when the log-stock process follows a skewed Lévy-Stable process.

We analyze the impact of high frequency (HF) trading in financial markets based on a model with three types of traders: liquidity traders (LTs), professional traders (PTs), and high frequency traders (HFTs). Our four main findings are: i) The price impact of liquidity trades is higher in the presence of the HFTs and is increasing with the size of t...

In this paper, we solve an optimal portfolio choice problem to measure the benefits of Treasury Inflation Indexed Securities (TIPS) to investors concerned with maximizing real wealth. We show how the introduction of a real riskless asset completes the investor asset space, by contrasting optimal portfolio allocations with and without such assets. W...

Algorithmic Trading (AT) and High Frequency (HF) trading, which are responsible for over 70\% of US stocks trading volume, have greatly changed the microstructure dynamics of tick-by-tick stock data. In this paper we employ a hidden Markov model to examine how the intra-day dynamics of the stock market have changed, and how to use this information...

I propose to model stock price tick-by-tick data via a non-explosive marked point process. The arrival of trades is driven by a counting process in which the waiting time between trades possesses a Mittag--Leffler survival function and price revisions have an infinitely divisible distribution. I show that the partial-integro-differential equation s...

An interconnector is an asset that gives the owner the option to transmit electricity between two locations. In financial terms, the value of an interconnector is the same as a strip of real options written on the spread between power prices in two markets. We model the spread based on a: seasonal trend, mean-reverting Gaussian process, and mean-re...

I propose to model stock price tick-by-tick data via a non-explosive marked point process. The arrival of trades is driven by a counting process in which the waiting-time between trades possesses a Mittag-Leffler survival function and price revisions have an infinitely divisible distribution. I show that the partial-integro-differential equation sa...

This paper provides an introduction to alternative models of uncertain commodity prices. A model of commodity price movements is the engine around which any valuation methodology for commodity production projects is built, whether discounted cash flow (DCF) models or the recently developed modern asset pricing (MAP) methods. The accuracy of the val...

Using high frequency data for the price dynamics of equities we measure the impact that market microstructure noise has on estimates of the: (i) volatility of returns; and (ii) variance-covariance matrix of n assets. We propose a Kalman-filter-based methodology that allows us to deconstruct price series into the true efficient price and the microst...

The understanding of joint asset return distributions is an important ingredient for managing risks of portfolios. While this is a well-discussed issue in fixed income and equity markets, it is a challenge for energy commodities. In this paper we are concerned with describing the joint return distribution of energy related commodities futures, name...

We employ the Schwartz and Smith [Schwartz, E., and J. Smith, 2000, Short-term variations and long-term dynamics in commodity prices, Management Science 46, 893–911.] model to explore the dynamics of the UK gas markets. We discuss in detail the short-term and long-term market prices of risk borne by the market players and how deviations from expect...

We present a spot price model for wholesale electricity prices which incorporates forward looking information that is available to all market players. We focus on information that measures the extent to which the capacity of the England and Wales generation park will be constrained over the next 52 weeks. We propose a measure of ‘tight market condi...

We propose a model where wholesale electricity prices are explained by two state variables: demand and capacity. We derive analytical expressions to price forward contracts and to calculate the forward premium. We apply our model to the PJM, England and Wales, and Nord Pool markets. Our empirical findings indicate that volatility of demand is seaso...

We propose a model for stock price dynamics that explicitly incorporates random waiting times between trades, also known as duration, and show how option prices can be calculated using this model. We use ultra-high-frequency data for blue-chip companies to motivate a particular choice of waiting-time distribution and then calibrate risk-neutral par...

We propose a model where wholesale electricity prices are explained by two state variables: demand and capacity. We derive analytical expressions to price forward contracts and to calculate the forward premium. We apply our model to the PJM, England and Wales, and Nord Pool markets. Our empirical findings indicate that volatility of demand is seaso...

We propose a model for stock price dynamics that explicitly incorporates random waiting times between trades, also known as
duration, and show how option prices can be calculated using this model. We use ultra-high-frequency data for blue-chip companies
to motivate a particular choice of waiting-time distribution and then calibrate risk-neutral par...

The understanding of joint asset return distributions is an important ingredient for managing risks of portfolios. While this is a well-discussed issue in fixed income and equity markets, it is a challenge for energy commodities. In this paper we are concerned with describing the joint return distribution of energy related commodities futures, name...

The continuous time random walk (CTRW) is a natural generalization of the Brownian random walk that allows the incorporation of waiting time distributions psi(t) and general jump distribution functions eta(x). There are two well-known fluid limits of this model in the uncoupled case. For exponential decaying waiting times and Gaussian jump distribu...