Optimal market making models in high-frequency trading

Download
iam_thesis.pdf
2021-4-08
Aydoğan, Burcu
Show full item record
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
977
views
1918
downloads
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 utility functions are considered: quadratic and exponential with a risk averse degree. Then, we study on a model considering an underlying asset with jumps in stochastic volatility. We derive the optimal quotes for both models under the assumptions. For numerical simulations, we apply finite differences and linear interpolation as well as extrapolation methods to obtain a solution of the related Hamilton-Jacobi-Bellman (HJB) equation. We demonstrate the risk metrics of the models including profit and loss distribution (PnL), standard deviation of PnL and Sharpe ratio which play important roles for the trader to make decisions on the strategies in high-frequency trading. Moreover, we provide the comparisons of the strategies with the existing ones. As a real data application, we conduct our simulations for the developed strategies in this thesis on a high-frequency data of Borsa Istanbul (BIST). For this purpose, we first estimate the parameters of each model and then perform the numerical experiments on the optimal quotes. Furthermore, we provide the applications on global stocks in order to see that the models are applicable, reasonable, and profitable also for the developed markets. Lastly, we take into account of the optimal market making models with stochastic latency impact. We contribute to this study by providing the numerical experiments with an artificial data. Finally, the thesis ends up with a conclusion and future research directions.
Market making, Limit order book, High-frequency trading, Stochastic control, Hamilton-Jacobi-Bellman equation, Emerging market
https://hdl.handle.net/11511/89734
Graduate School of Applied Mathematics, Thesis

Suggestions

Optimal Limit Order Book Trading Strategies with Stochastic Volatility in the Underlying Asset
Aydoğan, Burcu; Uğur, Ömür; Aksoy, Ümit (2022-1-01)
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 t...
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 ...
Analysis of volatility feedback and leverage effects on the ISE30 index using high frequency data
Inkaya, A.; Okur, Y. Yolcu (Elsevier BV, 2014-03-15)
In this study, we employ the techniques of Malliavin calculus to analyze the volatility feedback and leverage effects for a better understanding of financial market dynamics. We estimate both effects for a general semimartingale model applying Fourier analysis developed in Malliavin and Mancino (2002) [10]. We further investigate their joint behaviour using 5 min data of the ISE30 index. On the basis of these estimations, we look for the evidence that volatility feedback effect rate can be employed in the s...
The role of trading volume, open interest and trader positions on volatility transmission between spot and futures markets
Ordu-Akkaya, Beyza Mina; Ugurlu-Yildirim, Ecenur; Soytaş, Uğur (2019-06-01)
In this paper, we investigate the role of open interest, trading volume and trading positions of trader groups on volatility spillover between futures and spot markets of two major commodities; oil and gold during the last two decades. The initial analysis including only spot and futures markets imply that the relationship is bi-directional for crude oil, and uni-directional for gold. Though, including open interest and trading volume enrich our results indicating open interest and spot markets are closely ...
Citation Formats
B. Aydoğan, “Optimal market making models in high-frequency trading,” Ph.D. - Doctoral Program, Middle East Technical University, 2021.
METU IIS - Integrated Information Service open@metu.edu.tr