scholarly journals Numerical pricing of American options under two stochastic factor models with jumps using a meshless local Petrov–Galerkin method

2017 ◽  
Vol 115 ◽  
pp. 252-274 ◽  
Author(s):  
Jamal Amani Rad ◽  
Kourosh Parand
Keyword(s):  
Galerkin Method ◽  
American Options ◽  
Factor Models ◽  
Stochastic Factor

A Discontinuous Galerkin Method for Pricing American Options Under the Constant Elasticity of Variance Model

2015 ◽  
Vol 17 (3) ◽  
pp. 761-778 ◽  
Author(s):  
David P. Nicholls ◽  
Andrew Sward
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
American Options ◽  
Mathematical Finance ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Early Exercise ◽  
Black Scholes ◽  
Cev Process

AbstractThe pricing of option contracts is one of the classical problems in Mathematical Finance. While useful exact solution formulas exist for simple contracts, typically numerical simulations are mandated due to the fact that standard features, such as early-exercise, preclude the existence of such solutions. In this paper we consider derivatives which generalize the classical Black-Scholes setting by not only admitting the early-exercise feature, but also considering assets which evolve by the Constant Elasticity of Variance (CEV) process (which includes the Geometric Brownian Motion of Black-Scholes as a special case). In this paper we investigate a Discontinuous Galerkin method for valuing European and American options on assets evolving under the CEV process which has a number of advantages over existing approaches including adaptability, accuracy, and ease of parallelization.

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