Valuing Credit Default Swap under a double exponential jump diffusion model

2014 ◽  
Vol 29 (1) ◽  
pp. 36-43 ◽  
Author(s):  
Rui-cheng Yang ◽  
Mao-xiu Pang ◽  
Zhuang Jin
Keyword(s):  
Diffusion Model ◽  
Credit Default Swap ◽  
Jump Diffusion ◽  
Double Exponential ◽  
Credit Default ◽  
Jump Diffusion Model ◽  
Default Swap

CREDIT MODELING UNDER JUMP DIFFUSIONS WITH EXPONENTIALLY DISTRIBUTED JUMPS — STABLE CALIBRATION, DYNAMICS AND GAP RISK

2013 ◽  
Vol 16 (04) ◽  
pp. 1350021 ◽  
Author(s):  
MARTIN HELLMICH ◽  
STEFAN KASSBERGER ◽  
WOLFGANG M. SCHMIDT
Keyword(s):  
Credit Default Swap ◽  
Jump Diffusion ◽  
Credit Spreads ◽  
Jump Diffusions ◽  
Time Dynamics ◽  
Credit Default ◽  
Gap Risk ◽  
Default Swap ◽  
Swap Spreads ◽  
Quantities Of Interest

This paper investigates a structural credit default model that is based on a hyper-exponential jump diffusion process for the value of the firm. For credit default swap prices and other quantities of interest, explicit expressions for the corresponding Laplace transforms are derived. The time-dynamics of the model are studied, particularly the jumps in credit spreads, the understanding of which is crucial e.g. for the pricing of gap risk. As an application of our findings, the model is calibrated to credit default swap spreads observed in the market.

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.

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
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