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

Download

index.pdf

Date

2022-1-01

Author

Aydoğan, Burcu
Uğur, Ömür
Aksoy, Ümit

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

297
views

83
downloads

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

Suggestions

OpenMETU
Core

Optimal market making models in high-frequency trading Aydoğan, Burcu; Uğur, Ömür; Aksoy, Ümit; Department of Financial Mathematics (2021-4-08) In this thesis, we aim to develop optimal trading strategies in a limit order book for high-frequency trading by stochastic control theory. First, we address for evolving optimal prices where the underlying asset follows the Heston stochastic volatility model including jump components to explore the effect of the arrival of the orders. The goal of the market maker is to maximize her expected return while controlling the inventories where the remaining is charged with a liquidation cost. Two types of ...
Stochastic volatility and stochastic interest rate model with jump and its application on General Electric data Celep, Betül; Hayfavi, Azize; Department of Financial Mathematics (2011) In this thesis, we present two different approaches for the stochastic volatility and stochastic interest rate model with jump and analyze the performance of four alternative models. In the first approach, suggested by Scott, the closed form solution for prices on European call stock options are developed by deriving characteristic functions with the help of martingale methods. Here, we study the asset price process and give in detail the derivation of the European call option price process. The second appr...
Advances in optimal control of markov regime-switching models with applications in finance and economics Savku, Emel; Weber, Gerhard Wilhelm; Department of Financial Mathematics (2017) We study stochastic optimal control problems of finance and economics in a Markov regime-switching jump-diffusion market with and without delay component in the dynamics of our model. We formulate portfolio optimization problems as a two player zero-sum and a two player nonzero-sum stochastic differential games. We provide an extension of Dynkin formula to present the Hamilton-Jacobi-Bellman-Isaacs equations in such a more general setting. We illustrate our results for a nonzero-sum stochastic differential ...
Optimal lot-sizing/vehicle-dispatching policies under stochastic lead times and stepwise fixed costs Alp, O; Erkip, NK; Gullu, R (Institute for Operations Research and the Management Sciences (INFORMS), 2003-01-01) We characterize optimal policies of a dynamic lot-sizing/vehicle-dispatching problem under dynamic deterministic demands and stochastic lead times. An essential feature of the problem is the structure of the ordering cost, where a fixed cost is incurred every time a batch is initiated (or a vehicle is hired) regardless of the portion of the batch (or vehicle) utilized. Moreover, for every unit of demand not satisfied on time, holding and backorder costs are incurred. Under mild assumptions we show that the ...
Optimal control of stochastic hybrid system with jumps: A numerical approximation Temoçin, Büşra Zeynep; Weber, Gerhard Wilhelm (2014-03-15) The generalized class of stochastic hybrid systems consists of models with regime changes including the occurrence of impulsive behavior. In this paper, the stochastic hybrid processes with jumps are approximated by locally consistent Markov decision processes that preserve local mean and covariance. We further apply a randomized switching policy for approximating the dynamics on the switching boundaries. To investigate the validity of the approximation, we study a stochastic optimal control problem. On the...

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.