Fourth-order compact scheme with local mesh refinement for option pricing in jump-diffusion model

2011 ◽  
Vol 28 (3) ◽  
pp. 1079-1098 ◽  
Author(s):  
Spike T. Lee ◽  
Hai-Wei Sun
Keyword(s):  
Option Pricing ◽  
Diffusion Model ◽  
Fourth Order ◽  
Mesh Refinement ◽  
Jump Diffusion ◽  
Compact Scheme ◽  
Local Mesh Refinement ◽  
Jump Diffusion Model ◽  
Fourth Order Compact Scheme

FOURTH-ORDER COMPACT SCHEME FOR OPTION PRICING UNDER THE MERTON’S AND KOU’S JUMP-DIFFUSION MODELS

2018 ◽  
Vol 21 (04) ◽  
pp. 1850027 ◽  
Author(s):  
KULDIP SINGH PATEL ◽  
MANI MEHRA
Keyword(s):  
Fourth Order ◽  
Initial Conditions ◽  
Linear Equations ◽  
Jump Diffusion ◽  
Diffusion Models ◽  
Compact Scheme ◽  
Discrete Problem ◽  
Option Prices ◽  
Fully Discrete ◽  
Fourth Order Compact Scheme

In this paper, a compact scheme with three time levels is proposed to solve the partial integro-differential equation that governs the option prices in jump-diffusion models. In the proposed compact scheme, the second derivative approximation of the unknowns is approximated using the value of these unknowns and their first derivative approximations, thereby allowing us to obtain a tridiagonal system of linear equations for a fully discrete problem. Moreover, the consistency and stability of the proposed compact scheme are proved. Owing to the low regularity of typical initial conditions, a smoothing operator is employed to ensure the fourth-order convergence rate. Numerical illustrations concerning the pricing of European options under the Merton’s and Kou’s jump-diffusion models are presented to validate the theoretical results.

Option Pricing for a Jump-Diffusion Model with General Discrete Jump-Size Distributions

2017 ◽  
Vol 63 (11) ◽  
pp. 3961-3977 ◽  
Author(s):  
Michael C. Fu ◽  
Bingqing Li ◽  
Guozhen Li ◽  
Rongwen Wu
Keyword(s):  
Option Pricing ◽  
Diffusion Model ◽  
Jump Diffusion ◽  
Size Distributions ◽  
Jump Size ◽  
Jump Diffusion Model

scholarly journals Equilibrium Asset and Option Pricing under Jump-Diffusion Model with Stochastic Volatility

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Xinfeng Ruan ◽  
Wenli Zhu ◽  
Shuang Li ◽  
Jiexiang Huang
Keyword(s):  
Option Pricing ◽  
Stochastic Volatility ◽  
Diffusion Model ◽  
Jump Diffusion ◽  
Transformation Method ◽  
Exact Expression ◽  
Risk Neutral ◽  
Jump Diffusion Model ◽  
Fourier Transformation Method ◽  
Relationship Of

We study the equity premium and option pricing under jump-diffusion model with stochastic volatility based on the model in Zhang et al. 2012. We obtain the pricing kernel which acts like the physical and risk-neutral densities and the moments in the economy. Moreover, the exact expression of option valuation is derived by the Fourier transformation method. We also discuss the relationship of central moments between the physical measure and the risk-neutral measure. Our numerical results show that our model is more realistic than the previous model.

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