scholarly journals Computation of time–dependent implied volatility from point observations for European options under jump–diffusion models

2019 ◽  
Author(s):  
Slavi G. Georgiev ◽  
Lubin G. Vulkov
Keyword(s):  
Implied Volatility ◽  
Jump Diffusion ◽  
Diffusion Models ◽  
Time Dependent ◽  
European Options

scholarly journals A combined compact difference scheme for option pricing in the exponential jump-diffusion models

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Rahman Akbari ◽  
Reza Mokhtari ◽  
Mohammad Taghi Jahandideh
Keyword(s):  
Diffusion Model ◽  
Jump Diffusion ◽  
Diffusion Models ◽  
Asset Market ◽  
European Options ◽  
Compact Difference Scheme ◽  
High Order Method ◽  
Compact Difference ◽  
Black Scholes ◽  
Jump Diffusion Model

AbstractIn the present paper, starting with the Black–Scholes equations, whose solutions are the values of European options, we describe the exponential jump-diffusion model of Levy process type. Here, a jump-diffusion model for a single-asset market is considered. Under this assumption the value of a European contingency claim satisfies a general “partial integro-differential equation” (PIDE). With a combined compact difference (CCD) scheme for the spatial discretization, a high-order method is proposed for solving exponential jump-diffusion models. The method is sixth-order accurate in space and second-order accurate in time. A known analytical solution to the model is used to evaluate the performance of the numerical scheme.

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