Álvaro Cartea

Modelling Asset Prices for Algorithmic and High-Frequency Trading

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 article, we employ a hidden Markov model to examine how the intraday dynamics of the stock market have changed and how to use this information to develop trading strategies at high frequencies. In particular, we show how to employ our model to submit limit orders to profit from the bid-ask spread, and we also provide evidence of how HF traders may profit from liquidity incentives (liquidity rebates). We use data from February 2001 and February 2008 to show that while in 2001 the intraday states with the shortest average durations (waiting time between trades) were also the ones with very few trades, in 2008 the vast majority of trades took place in the states with the shortest average durations. Moreover, in 2008, the states with the shortest durations have the smallest price impact as measured by the volatility of price innovations.

Risk Metrics and Fine Tuning of High Frequency Trading Strategies

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 of inventory that she can hold at any time. The risk metrics enable the HF trader to fine tune her strategies by trading off different metrics of inventory risk, which also proxy for capital risk, against expected profits. The dynamics of the midprice of the asset are driven by information flows which are impounded in the midprice by market participants who update their quotes in the limit order book. Furthermore, the midprice also exhibits stochastic jumps as a consequence of the arrival of market orders that have an impact on prices which can give rise to market momentum (expected prices to trend up or down). The HF traders optimal strategy incorporates a buffer to cover adverse selection costs and manages inventories to maximize the expected gains from market momentum.

An Analysis of the Main Determinants of Electricity Forward Prices and Forward Risk Premia

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 prices are made up of two components: the expected spot price at a future date and the forward risk premium. In this chapter we analyse the factors influencing the evolution of electricity forward prices in Spain. These factors include the forward prices for natural gas and CO2 emission rights, as well as the electricity forward prices in Germany and in France and spot prices in Spain. We also analyse the behaviour of the ex-post electricity forward risk premia in Germany, France and Spain, and in particular we find a positive correlation between ex-post electricity risk premia in these three countries as well as between risk premia for electricity and natural gas futures prices.

A Closed-Form Execution Strategy to Target VWAP

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 consists of TWAP adjusted upward by a fraction of instantaneous order-flow and adjusted downward by the average order-flow that is expected over the remaining life of the strategy. The other strategy consists of the Almgren-Chriss execution strategy adjusted by the expected volume and net order-flow during the remaining life of the strategy. We calibrate model parameters to five stocks traded in Nasdaq (FARO, SMH, NTAP, ORCL, INTC) and use simulations to show that the strategies target VWAP very closely and on average outperform the target by between 0.10 and 8 basis points.

Assessing the Performance of Different Volatility Estimators: A Monte Carlo Analysis

Abstract 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 frequency of jumps to compare the performance of the proposed volatility estimators. We conclude that the maximum likelihood estimator filter (MLE-F), a two-step parametric volatility estimator proposed by Cartea and Karyampas (2011a; The relationship between the volatility returns and the number of jumps in financial markets, SSRN eLibrary, Working Paper Series, SSRN), outperforms most of the well-known high-frequency volatility estimators when different assumptions about the path properties of stock dynamics are used.

Hedging Non-Tradable Risks with Transaction Costs and Price Impact

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 agents trades on U is referred to as cross-impact. By solving the agents stochastic control problem, we obtain a closed-form expression for the optimal strategy when the agent holds a linear position in U. When the exposure to the non-tradable risk factor is non-linear, we provide an approximation to the optimal strategy in closed-form, and prove that the value function is correctly approximated by this strategy when cross-impact and risk-aversion are small. We further prove that when exposure to U is non-linear, the approximate optimal strategy can be written in terms of the optimal strategy for a linear exposure with the size of the position changing dynamically according to the exposures Delta under a particular probability measure.

Volume Imbalance and Market Making

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 agent to decide when they should trade more agressively to take advantage of beneficial price movements, and when they should trade more conservatively to protect against adverse selection effects. High imbalance results in a stronger inclination to place limit buy orders with the opposite effect on limit sell orders.