Browsing by Author "Omar, Fathia"
Now showing 1 - 1 of 1
Results Per Page
Sort Options
Item EXPONENTIAL FINITE DIFFERENCE METHOD FOR NONLINEAR BLACK-SCHOLES EQUATION(2017-04-04) Omar, Fathia; Aksoy, Ümit; Aydın, AyhanIn this thesis, we investigate exponential finite difference method for nonlinear Black Scholes equation arising in an illiquid market. Chapter 1 is devoted to the literature survey with some basic definitions and terminology of the option pricing problem. In Chapter 2 we review the Black-Scholes model and finite difference methods for Black Scholes equation. In Chapter 3, an explicit finite difference method for a nonlinear Black-Scholes equation is studied with the monotonicity, stability and consistency re sults. In Chapter 4, we apply the exponential finite difference method to linear and nonlinear Black-Scholes equations. Moreover, we investigate consistency and con vergence of the method. Numerical experiments are performed to verify theoretical results. Exponential finite difference method is compared with an explicit finite dif ference method proposed for linear and nonlinear Black-Scholes equation. Numerical results show that exponential finite difference method exhibits better performance then explicit method. Finally, we give a brief conclusion in Chapter 5.