Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/310013 
Year of Publication: 
2022
Citation: 
[Journal:] Computational Economics [ISSN:] 1572-9974 [Volume:] 62 [Issue:] 1 [Publisher:] Springer US [Place:] New York, NY [Year:] 2022 [Pages:] 289-324
Publisher: 
Springer US, New York, NY
Abstract: 
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.
Subjects: 
Market making
High-frequency trading
Limit order book
Stochastic control
Hamilton-Jacobi-Bellman equation
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version

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