Optimal Limit Order Book Trading Strategies with Stochastic Volatility in the Underlying Asset

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Date

2022-1-01

Author

Aydoğan, Burcu
Uğur, Ömür
Aksoy, Ümit

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In quantitative finance, there have been numerous new aspects and developments related with the stochastic control and optimization problems which handle the controlled variables of performing the behavior of a dynamical system to achieve certain objectives. In this paper, we address the optimal trading strategies via price impact models using Heston stochastic volatility framework including jump processes either in price or in volatility of the price dynamics with the aim of maximizing expected return of the trader by controlling the inventories. Two types of utility functions are considered: quadratic and exponential. In both cases, the remaining inventories of the market maker are charged with a liquidation cost. In order to achieve the optimal quotes, we control the inventory risk and follow the influence of each parameter in the model to the best bid and ask prices. We show that the risk metrics including profit and loss distribution (PnL), standard deviation and Sharpe ratio play important roles for the trader to make decisions on the strategies. We apply finite differences and linear interpolation as well as extrapolation techniques to obtain a solution of the nonlinear Hamilton-Jacobi-Bellman (HJB) equation. Moreover, we consider different cases on the modeling to carry out the numerical simulations.

Subject Keywords

Market making, High-frequency trading, Limit order book, Stochastic control, Hamilton-Jacobi-Bellman equation, MARKET, Hamilton-Jacobi-Bellman equation, High-frequency trading, Limit order book, Market making, Stochastic control

URI

https://hdl.handle.net/11511/99677

Journal

Computational Economics

DOI

https://doi.org/10.1007/s10614-022-10272-4

Collections

Graduate School of Applied Mathematics, Article

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Citation Formats

B. Aydoğan, Ö. Uğur, and Ü. Aksoy, “Optimal Limit Order Book Trading Strategies with Stochastic Volatility in the Underlying Asset,” Computational Economics, pp. 0–0, 2022, Accessed: 00, 2022. [Online]. Available: https://hdl.handle.net/11511/99677.