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We propose risk measures 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 is risk-neutral and maximizes expected terminal wealth but is constrained by both capital and the amount of inventory that she can hold at any time. The risk measures enable the HF trader to fine tune her strategies by trading off different measures 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).
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. We introduce a multi-factor self-exciting process which allows for feedback effects in market buy and sell orders and the shape of the limit order book (LOB). The model accounts for arrival of market orders that influence activity, trigger one-sided and two-sided clustering of trades, and induce temporary changes in the shape of the LOB. The resulting strategy outperforms the Poisson strategy where the trader does not distinguish between influential and non-influential events.
In this paper we solve an optimal portfolio choice problem in real terms in order to measure what benefits do Treasury Inflation Indexed Securities (TIPS) provide to investors. We show analytically that this approach should be used when there is uncertainty about future inflation rates and there is a riskless asset in real terms, or when there is uncertainty about future inflation rates and assets in the investment opportunity set covary with inflation. We differentiate the types of investors according to their investment horizon, short-term and long-term, and according to their degree of risk aversion. Then, we measure the historical benefits that TIPS provide to the two types of investor in the presence of different asset classes such as equity, commodities, and real estate. We find that while buy-and-hold long-term investors can take advantage of the diversification effects they provide, as well as serving as the safe asset, short-term investors may find TIPS useful to improve the investment opportunity set in real terms. 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 to develop trading strategies at ultra-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 intra-day states with shortest average durations were also the ones with very few trades, in February 2008 the vast majority of trades took place in the states with shortest average durations. Moreover, in 2008 the fastest states have the smallest price impact as measured by the volatility of price innovations. Abstract:
We analyze the impact of high frequency trading in financial markets based on a model with three types of traders: liquidity traders, market makers, and high frequency traders. Our four main findings are: i) The price impact of the liquidity trades is higher in the presence of the high frequency trader. In particular, we show that the high frequency trader reduces (increases) the prices that liquidity traders receive when selling (buying) their equity holdings. ii) Although market makers also lose revenue to the high frequency trader in every trade, they are compensated for these losses by a higher liquidity premium. iii) High frequency trading increases the volatility of prices. iv) The volume of trades doubles as the high frequency trader intermediates all trades between the liquidity traders and market makers. This additional volume is a consequence of trades which are carefully tailored for surplus extraction and are neither driven by fundamentals nor is it noise trading.
Abstract:
The contribution of this paper is two-fold. First we show how to estimate the volatility of high requency log-returns where the estimates are not affected by microstructure noise and the presence of Lévy-type jumps in prices. The second contribution focuses on the relationship between the number of jumps and the volatility of log-returns of the SPY, which is the fund that tracks the S&P 500. We employ SPY high frequency data (minute-by-minute) to obtain estimates of the volatility of the SPY log-returns to show that: (i) The number of jumps in the SPY is an important variable in explaining the daily volatility of the SPY log-returns; (ii) The number of jumps in the SPY prices has more explanatory power with respect to daily volatility than other variables based on: volume, number of trades, open and close, and other jump activity measures based on Bipower Variation; (iii) The number of jumps in the SPY prices has a similar explanatory power to that of the VIX, and slightly less explanatory power than measures based on high and low prices, when it comes to explaining volatility; (iv) Forecasts of the average number of jumps are important variables when producing monthly volatility forecasts and, furthermore, they contain information that is not impounded in the VIX. Abstract:
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