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

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 tra...

Full description

Saved in:
Bibliographic Details
Published in:Computational economics 2023-06, Vol.62 (1), p.289-324
Main Authors: Aydoğan, Burcu, Uğur, Ömür, Aksoy, Ümit
Format: Article
Language:English
Subjects:
Adverse selection
Analysis
Applied mathematics
Approximation
Bankruptcy
Behavioral/Experimental Economics
Computer Appl. in Social and Behavioral Sciences
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Economics and Finance
Electronic trading systems
Extrapolation
Finance
High frequency trading
Interpolation
Inventory
Investment analysis
Math Applications in Computer Science
Mathematical models
Numerical analysis
Operations Research/Decision Theory
Optimal control
Optimization
Optimization techniques
Prices
Profits
Random variables
Risk management
Stochastic control theory
Stochastic processes
Utility functions
Volatility
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0927-7099
1572-9974
DOI:10.1007/s10614-022-10272-4