Trading Strategy with Stochastic Volatility in a Limit Order Book Market

TL;DR

This paper develops optimal trading strategies for dealers in stock and option markets using the Heston stochastic volatility model, formulating the problem as a stochastic control to maximize profit while managing inventory risk.

Contribution

It introduces a novel application of the Heston model to derive continuous-time optimal trading strategies for both stock and option market making.

Findings

Derives explicit optimal bid and ask quotes under stochastic volatility.

Demonstrates the effectiveness of the strategies through theoretical analysis.

Extends the framework to option market making with stochastic volatility considerations.

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 the optimal trading strategies for dealers in a security market. We also extend our study to option market making for options written on stocks in the presence of stochastic volatility. Mathematically, 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 or options continuously over time. Their objective is to maximize an expected profit from transactions with a penalty proportional to the variance of cumulative inventory cost.