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.

scholarly journals A jump-diffusion model for pricing electricity under price-cap regulation

2019 ◽  
Vol 13 (4) ◽  
pp. 395-405
Author(s):  
M. Kegnenlezom ◽  
P. Takam Soh ◽  
M. L. D. Mbele Bidima ◽  
Y. Emvudu Wono
Keyword(s):  
Diffusion Model ◽  
Jump Diffusion ◽  
Exact Formula ◽  
Martingale Measure ◽  
Spot Price ◽  
Price Cap Regulation ◽  
Price Cap ◽  
Electricity Spot Price ◽  
Jump Diffusion Model ◽  
Equivalent Martingale

Abstract In this paper, we derive a new jump-diffusion model for electricity spot price from the “Price-Cap” principle. Next, we show that the model has a non-classical mean-reverting linear drift. Moreover, using this model, we compute a new exact formula for the price of forward contract under an equivalent martingale measure and we compare it to Cartea et al. (Appl Math Finance 12(4):313–335, 2005) formula.

First passage times of a jump diffusion process

2003 ◽  
Vol 35 (2) ◽  
pp. 504-531 ◽  
Author(s):  
S. G. Kou ◽  
Hui Wang
Keyword(s):  
Diffusion Process ◽  
Diffusion Processes ◽  
Jump Diffusion ◽  
First Passage Times ◽  
First Passage ◽  
Jump Diffusion Processes ◽  
Lookback Options ◽  
Double Exponential ◽  
Jump Diffusion Process ◽  
Passage Times

This paper studies the first passage times to flat boundaries for a double exponential jump diffusion process, which consists of a continuous part driven by a Brownian motion and a jump part with jump sizes having a double exponential distribution. Explicit solutions of the Laplace transforms, of both the distribution of the first passage times and the joint distribution of the process and its running maxima, are obtained. Because of the overshoot problems associated with general jump diffusion processes, the double exponential jump diffusion process offers a rare case in which analytical solutions for the first passage times are feasible. In addition, it leads to several interesting probabilistic results. Numerical examples are also given. The finance applications include pricing barrier and lookback options.

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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