Implicit-Explicit Method for American Options in Jump-Diffusion Models with Stochastic Volatility

2008 ◽  
Author(s):  
Svetlana I. Boyarchenko ◽  
Sergei Z. Levendorskii
Keyword(s):  
Stochastic Volatility ◽  
American Options ◽  
Jump Diffusion ◽  
Diffusion Models ◽  
Explicit Method

scholarly journals An RBF–FD method for pricing American options under jump–diffusion models

2018 ◽  
Vol 76 (10) ◽  
pp. 2434-2459 ◽  
Author(s):  
Majid Haghi ◽  
Reza Mollapourasl ◽  
Michèle Vanmaele
Keyword(s):  
American Options ◽  
Jump Diffusion ◽  
Diffusion Models

Finite Volume Method for Pricing European and American Options under Jump-Diffusion Models

2017 ◽  
Vol 7 (2) ◽  
pp. 227-247 ◽  
Author(s):  
Xiao-Ting Gan ◽  
Jun-Feng Yin ◽  
Yun-Xiang Guo
Keyword(s):  
Finite Volume ◽  
American Options ◽  
Linear Complementarity Problems ◽  
Jump Diffusion ◽  
Linear Interpolation ◽  
Finite Volume Methods ◽  
Diffusion Models ◽  
System Matrix ◽  
Element Space ◽  
European Option Pricing

AbstractA class of finite volume methods is developed for pricing either European or American options under jump-diffusion models based on a linear finite element space. An easy to implement linear interpolation technique is derived to evaluate the integral term involved, and numerical analyses show that the full discrete system matrices are M-matrices. For European option pricing, the resulting dense linear systems are solved by the generalised minimal residual (GMRES) method; while for American options the resulting linear complementarity problems (LCP) are solved using the modulus-based successive overrelaxation (MSOR) method, where the H+-matrix property of the system matrix guarantees convergence. Numerical results are presented to demonstrate the accuracy, efficiency and robustness of these methods.

scholarly journals Pricing of American Put Option under a Jump Diffusion Process with Stochastic Volatility in an Incomplete Market

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Shuang Li ◽  
Yanli Zhou ◽  
Xinfeng Ruan ◽  
B. Wiwatanapataphee
Keyword(s):  
Diffusion Process ◽  
Stochastic Volatility ◽  
American Options ◽  
Option Price ◽  
Jump Diffusion ◽  
Incomplete Market ◽  
American Put Option ◽  
Put Option ◽  
Jump Diffusion Process ◽  
American Put

We study the pricing of American options in an incomplete market in which the dynamics of the underlying risky asset is driven by a jump diffusion process with stochastic volatility. By employing a risk-minimization criterion, we obtain the Radon-Nikodym derivative for the minimal martingale measure and consequently a linear complementarity problem (LCP) for American option price. An iterative method is then established to solve the LCP problem for American put option price. Our numerical results show that the model and numerical scheme are robust in capturing the feature of incomplete finance market, particularly the influence of market volatility on the price of American options.

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