Dr. Burcu Aydogan Ph.D.
|18/07/2022 - 29/07/2022||Optimal Market Making with Real Data Applications||Tirana, Albania|
|15/05/2022 - 28/05/2022||Optimal Market Making with Mean-Reversion and Stochastic Volatility Price Process||King Abdullah University of Science and Technology, Saudi Arabia (Hybrid)|
|11/07/2021 - 14/07/2021||An Optimal Market Making Model where the Price Dynamics Follows a Mean-reverting Process with Stochastic Volatility||Online|
|28/06/2021 - 29/06/2021||Optimal Market Making Models with Stochastic Volatility for High-Frequency Trading||Online|
Monday, July 18, 2022
Optimal Market Making with Real Data Applications
Event: CIMPA Summer School: Mathematical Methods in Data Analysis
Description: We develop optimal market making models for high-frequency trading (HFT) in a limit order book (LOB) considering stock price processes with stochastic volatility which consist jumps either in price or volatility. By adding the jump processes, we measure the effect of the arrival of each marker orders on stock price. By such models, we obtain the optimal trading strategies via stochastic optimal control theory deciding for the best bid and ask prices that a market maker sets up. We write the related Hamilton-Jacobi-Bellman (HJB) equation for each control problem and then apply finite differences and interpolation/extrapolation methods after proposing a solution for each HJB equation in order to obtain the optimal policies. The results are performed on Borsa Istanbul Stock Exchange Market (BIST) high-frequency data by estimating the model parameters besides the artificial data applications. Further, we provide the applications of the models on some stocks traded in global markets and we get the result of that the strategies are profitable and meaningful even traded on global stocks besides the developing markets.
Sunday, May 15, 2022
Optimal Market Making with Mean-Reversion and Stochastic Volatility Price Process
Event: Stochastic Numerics and Statistical Learning: Theory and Applications Workshop
Description: In this work, we develop an optimal market making model for high-frequency trading in a limit order book (LOB) considering a stock price process with mean-reversion and stochastic volatility effects. Moreover, we build the model including jump processes in price to measure the effect of the market impact by the amount and type of the orders. Here, we only provide the numerical results in case that there are no jumps in the price. Our goal is to investigate the optimal trading strategies by maximizing the expected return of the trader at the end of the trade session with the control of the inventories during the entire duration. In order to obtain the optimal prices, we propose a solution for the related Hamilton-Jacobi-Bellman (HJB) equation of the control problem and apply the finite differences method. We show the results for the optimal spreads derived by the optimal prices. Furthermore, we handle some comparisons with a model without a mean-reversion effect and for different levels of mean-reverting rate.
Sunday, July 11, 2021
An Optimal Market Making Model where the Price Dynamics Follows a Mean-reverting Process with Stochastic Volatility
Event: EURO 2021, 31st European Conference on Operational Research
Description: In this study, we intend to develop optimal market making strategies for high-frequency trading in a limit order book where the stock price is generated by a mean-reverting process with stochastic volatility. In this model, we further assume that the price changes with the adverse selection effects including the jump components. We suppose that the trader is risk-neutral and the objective function of the trader is to maximize her terminal wealth with a control of the inventories. Our aim is to get the optimal bid and ask prices by these assumptions and modelling. For this purpose, we write the corresponding Hamilton-JacobiBellman (HJB) equation of the stochastic control problem. Then, we reduce the HJB equation in a PDE system which gives us the optimal prices. The PDE system is solved by applying the finite difference method and linear interpolation and extrapolation techniques. Then, we provide our numerical illustrations and optimal behaviours of the trader with this stock price modelling.
Sunday, July 11, 2021
Optimal Market Making Models with Stochastic Volatility for High-Frequency Trading
Event: EPCO 2021, Portuguese Meeting on Optimal Control
Description: In this study, we develop optimal market making strategies for high-frequency trading with the help of stochastic control theory. We first assume that the underlying asset follows the Heston stochastic volatility model including jump parts in price dynamics to see the effect of the arrival of the market orders. We use two types of utility functions in order to arrive at the goal of the market maker which is maximizing the terminal wealth: quadratic and exponential with a risk aversion degree. Then, we set up a model with the stochastic volatility stock price dynamics where the jump parts occur in the volatility. We obtain the optimal prices for both models by writing and solving the related Hamilton-Jacobi-Bellman (HJB) equations. For the numerical solutions, we apply finite differences and linear interpolation as well as extrapolation methods on the HJB equations. In the applications, we show the risk metrics of the models such as profit and loss distribution (PnL), standard deviation of PnL and Sharpe ratio to make decisions on the strategies. Then, we examine the behaviour of the optimal prices for each inventory level of the trader. Moreover, we compare our strategies with the existing ones in the literature. Lastly, we apply our models on a real high-frequency data of an emerging market and explore the results.