Option Valuation in Jump-diffusion Models using the Exponential Runge-Kutta Methods

Option Pricing on Commodity Prices Using Jump Diffusion Models

In this paper, we aim at developing a model for option pricing to reduce the risks associated with Ethiopian commodity prices fluctuations. We used the daily closed Unwashed Lekempti grade 5 (ULK5) coffee and Whitish Wollega Sesame Seed Grade3 (WWSS3) prices obtained from Ethiopia commodity exchange (ECX) market to analyse the prices fluctuations.The natures of log-returns of the prices exhibit a...

Implicit–explicit Numerical Schemes for Jump–diffusion Processes

We study the numerical approximation of viscosity solutions for Parabolic Integro-Differential Equations (PIDE). Similar models arise in option pricing, to generalize the Black–Scholes equation, when the processes which generate the underlying stock returns may contain both a continuous part and jumps. Due to the non-local nature of the integral term, unconditionally stable implicit difference ...

Closed formulas for the price and sensitivities of European options under a double exponential jump diffusion model

We derive closed formulas for the prices of European options andtheir sensitivities when the underlying asset follows a double-exponentialjump diffusion model, as considered by S. Kou in 2002. This author hasderived the option price by making use of double series where each termrequires the computation of a sequence of special functions, such thatthe implementation remains difficult for a large...

Fast Communication Two-stage Stochastic Runge-kutta Methods for Stochastic Differential Equations with Jump Diffusion

Integrating-Factor-Based 2-Additive Runge–Kutta methods for Advection-Reaction-Diffusion Equations

There are three distinct processes that are predominant in models of flowing media with inter-acting components: advection, reaction, and diffusion. Collectively, these processes are typicallymodelled with partial differential equations (PDEs) known as advection-reaction-diffusion (ARD)equations.To solve most PDEs in practice, approximation methods known as numerical methods are...