Pricing vulnerable American put options under jump-diffusion processes when corporate liabilities are random

2021 ◽  
pp. 1-21
Author(s):  
Shengan Wang ◽  
Qing Zhou ◽  
Weilin Xiao
Keyword(s):  
Diffusion Processes ◽  
Jump Diffusion ◽  
Put Options ◽  
Jump Diffusion Processes ◽  
American Put Options ◽  
Corporate Liabilities ◽  
American Put

PRICING VULNERABLE AMERICAN PUT OPTIONS UNDER JUMP–DIFFUSION PROCESSES

2016 ◽  
Vol 31 (2) ◽  
pp. 121-138 ◽  
Author(s):  
Guanying Wang ◽  
Xingchun Wang ◽  
Zhongyi Liu
Keyword(s):  
Default Risk ◽  
Diffusion Processes ◽  
Compound Poisson Process ◽  
Jump Diffusion ◽  
Option Prices ◽  
Jump Diffusions ◽  
Put Options ◽  
Jump Diffusion Processes ◽  
American Put Options ◽  
American Put

This paper evaluates vulnerable American put options under jump–diffusion assumptions on the underlying asset and the assets of the counterparty. Sudden shocks on the asset prices are described as a compound Poisson process. Analytical pricing formulae of vulnerable European put options and vulnerable twice-exercisable European put options are derived. Employing the two-point Geske and Johnson method, we derive an approximate analytical pricing formula of vulnerable American put options under jump–diffusions. Numerical simulations are performed for investigating the impacts of jumps and default risk on option prices.

scholarly journals A Finite Difference Scheme for Pricing American Put Options under Kou's Jump-Diffusion Model

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Jian Huang ◽  
Zhongdi Cen ◽  
Anbo Le
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Diffusion Model ◽  
Finite Difference Scheme ◽  
Jump Diffusion ◽  
Uniform Mesh ◽  
Put Options ◽  
American Put Options ◽  
Jump Diffusion Model ◽  
American Put

We present a stable finite difference scheme on a piecewise uniform mesh along with a penalty method for pricing American put options under Kou's jump-diffusion model. By adding a penalty term, the partial integrodifferential complementarity problem arising from pricing American put options under Kou's jump-diffusion model is transformed into a nonlinear parabolic integro-differential equation. Then a finite difference scheme is proposed to solve the penalized integrodifferential equation, which combines a central difference scheme on a piecewise uniform mesh with respect to the spatial variable with an implicit-explicit time stepping technique. This leads to the solution of problems with a tridiagonal M-matrix. It is proved that the difference scheme satisfies the early exercise constraint. Furthermore, it is proved that the scheme is oscillation-free and is second-order convergent with respect to the spatial variable. The numerical results support the theoretical results.

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