Browsing by Author "Ugur, Omur"

Filter results by typing the first few letters
Now showing 1 - 2 of 2
  • Thumbnail Image
    Conference Object
    Citation - WoS: 1
    Citation - Scopus: 1
    On the Methods of Pricing American Options: Case Study
    (Springer, 2018) Aydogan, Burcu; Aksoy, Umit; Ugur, Omur
    In this study, a comparative analysis of numerical and approximation methods for pricing American options is performed. Binomial and finite difference approximations are discussed; furthermore, Roll-Geske-Whaley, Barone-Adesi and Whaley and Bjerksund-Stensland analytical approximations as well as the least-squares Monte Carlo method of Longstaff and Schwartz are presented. Applicability and efficiency in almost all circumstances, numerical solutions of the corresponding free boundary problem is emphasized. Methods used in pricing American options are also compared on dividend and non-dividend paying assets; and their pros and cons are discussed along with numerical experiments.
  • Thumbnail Image
    Article
    Citation - WoS: 2
    Citation - Scopus: 2
    Optimal Limit Order Book Trading Strategies With Stochastic Volatility in the Underlying Asset
    (Springer, 2023) Aydogan, Burcu; Ugur, Omur; Aksoy, Umit
    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.