The double exponential jump diffusion model for pricing European options under fuzzy environments

2012 ◽  
Vol 29 (3) ◽  
pp. 780-786 ◽  
Author(s):  
Li-Hua Zhang ◽  
Wei-Guo Zhang ◽  
Wei-Jun Xu ◽  
Wei-Lin Xiao
Keyword(s):  
Diffusion Model ◽  
Jump Diffusion ◽  
European Options ◽  
Double Exponential ◽  
Jump Diffusion Model

scholarly journals A Fast Fourier Transform Technique for Pricing European Options with Stochastic Volatility and Jump Risk

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Su-mei Zhang ◽  
Li-he Wang
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Stock Returns ◽  
Stochastic Volatility ◽  
Diffusion Model ◽  
Numerical Solutions ◽  
Jump Diffusion ◽  
European Options ◽  
Double Exponential ◽  
Jump Diffusion Model

We consider European options pricing with double jumps and stochastic volatility. We derived closed-form solutions for European call options in a double exponential jump-diffusion model with stochastic volatility (SVDEJD). We developed fast and accurate numerical solutions by using fast Fourier transform (FFT) technique. We compared the density of our model with those of other models, including the Black-Scholes model and the double exponential jump-diffusion model. At last, we analyzed several effects on option prices under the proposed model. Simulations show that the SVDEJD model is suitable for modelling the long-time real-market changes and stock returns are negatively correlated with volatility. The model and the proposed option pricing method are useful for empirical analysis of asset returns and managing the corporate credit risks.

PRICING OF FIRST TOUCH DIGITALS UNDER NORMAL INVERSE GAUSSIAN PROCESSES

2006 ◽  
Vol 09 (06) ◽  
pp. 915-949 ◽  
Author(s):  
OLEG KUDRYAVTSEV ◽  
SERGEI LEVENDORSKIǏ
Keyword(s):  
Diffusion Model ◽  
Diffusion Processes ◽  
Jump Diffusion ◽  
Spot Price ◽  
Inverse Gaussian ◽  
Jump Diffusion Processes ◽  
Double Exponential ◽  
Motion Approximation ◽  
Jump Diffusion Model ◽  
Normal Inverse Gaussian

We calculate prices of first touch digitals under normal inverse Gaussian (NIG) processes, and compare them to prices in the Brownian model and double exponential jump-diffusion model. Numerical results are produced to show that for typical parameters values, the relative error of the Brownian motion approximation to NIG price can be 2–3 dozen percent if the spot price is at the distance 0.05–0.2 from the barrier (normalized to one). A similar effect is observed for approximations by the double exponential jump-diffusion model, if the jump component of the approximation is significant. We show that two jump-diffusion processes can give approximately the same results for European options but essentially different results for first touch digitals and barrier options. A fast approximate pricing formula under NIG is derived.

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