Numerical solutions to an integro-differential parabolic problem arising in the pricing of financial options in a Levy market

Abstract

We study the numerical solutions for an integro-differential parabolic problem modeling a process with jumps and stochastic volatility in financial mathematics. We present two general algorithms to calculate numerical solutions. The algorithms are implemented in PDE2D, a general-purpose, partial differential equation solver.

Numerical methods applied to option pricing models with transaction costs and stochastic volatility

“…We do not consider jumps in this work as they will lead to nonlinear PDE's with an integral term, which are very hard to work with. For detailed explanation of why such equations will arise, we refer to our previous work (Mariani et al 2009, Florescu andMariani 2010) which considers jumps but not transaction costs.…”

Numerical Solutions for Option Pricing Models Including Transaction Costs and Stochastic Volatility

“…Any model where the volatility is random is called a stochastic volatility model. An alternative approach where the asset price is modeled using jump diffusion processes as well as Lévy processes has been considered in [3,12,13] (without considering the impact of transaction costs).…”

Solutions to Integro‐Differential Parabolic Problem Arising on Financial Mathematics

“…The necessity of taking into account the large market movements, and a great amount of information arriving suddenly (i.e., a jump) has led to the study of PIDE in which the integral term is modeling the jump [1,7]. The necessity of taking into account the large market movements, and a great amount of information arriving suddenly (i.e., a jump) has led to the study of PIDE in which the integral term is modeling the jump [1,7].…”