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Decisions in Economics and Finance

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10-03-2020

Trading strategy with stochastic volatility in a limit order book market

Authors: Qing-Qing Yang, Wai-Ki Ching, Jiawen Gu, Tak-Kuen Siu

Published in: Decisions in Economics and Finance | Issue 1/2020

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Abstract

In this paper, we employ the Heston stochastic volatility model to describe the stock’s volatility and apply the model to derive and analyze trading strategies for dealers in a security market with price discovery. The problem is formulated as a stochastic optimal control problem, and the controlled state process is the dealer’s mark-to-market wealth. Dealers in the security market can optimally determine their ask and bid quotes on the underlying stocks continuously over time. Their objective is to maximize an expected profit from transactions with a penalty proportional to the variance of cumulative inventory cost. We provide an approximate, analytically tractable solution to the stochastic control problem. Numerical experiments are given to illustrate the effects of various parameters on the performances of trading strategies.

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Heston’s model stands out from other stochastic volatility models here because there exists an analytical solution for European options that take the correlation between stock price and volatility into consideration (Heston 1993).

The value of \(\eta \) is relatively small when compared with the stock price \(S_t\). The parameter for NASDAQ stock FARO in 2013 is \(1.41\times 10^{-4}\), SMH, \(5.45\times 10^{-6}\) and INTC, \(6.15\times 10^{-7}\) (see Cartea et al. 2015, Chap. 4). However, such a small number will have a great influence on the profitability of a high-frequency trading (HFT) strategy, e.g., market-making strategies in a LOB (see, for instance Rishi Narang 2013, for more on this).

The concept of the adverse selection risk was first introduced by Bagehot (1971) and formalized by Copeland and Galai (1983), Glosten and Milgrom (1985) and others. Adverse selection in the sense that applies to capital markets is defined as a situation in which there is a tendency for bad outcomes to occur, due to asymmetric information between a buyer and a seller.

The set of baseline parameters is the same with that for European call options with maturity 2014-05-16, but on daily basis.

Price impact adjustment here refers to whether the dealer’s model takes the price impact phenomena into consideration.

In our experiment, dealers are committed to, respectively, buy/sell one share of stock at their quoting prices.

The right-hand-side term of Eq. (4.2) is integrable.

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Title: Trading strategy with stochastic volatility in a limit order book market
Authors: Qing-Qing Yang
Wai-Ki Ching
Jiawen Gu
Tak-Kuen Siu
Publication date: 10-03-2020
Publisher: Springer International Publishing
Published in: Decisions in Economics and Finance / Issue 1/2020
Print ISSN: 1593-8883
Electronic ISSN: 1129-6569
DOI: https://doi.org/10.1007/s10203-020-00278-8

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