scholarly journals Optimal Impulse Control for Cash Management with Double Exponential Jump Diffusion Processes

2018 ◽  
Vol 6 (0) ◽  
pp. 45-63
Author(s):  
Kimitoshi Sato ◽  
Atsuo Suzuki
Keyword(s):  
Impulse Control ◽  
Diffusion Processes ◽  
Jump Diffusion ◽  
Cash Management ◽  
Jump Diffusion Processes ◽  
Double Exponential ◽  
Optimal Impulse

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.

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.

scholarly journals Two-sided boundary problem for Kou's process

2013 ◽  
Vol 21 ◽  
pp. 92
Author(s):  
Ie.V. Karnaukh
Keyword(s):  
Boundary Problem ◽  
Diffusion Processes ◽  
Jump Diffusion ◽  
Jump Diffusion Processes ◽  
Double Exponential ◽  
Boundary Functionals

In this paper the distributions of two-sided boundary functionals for double exponential jump diffusion processes are treated.

AVERAGE OPTIONS FOR JUMP DIFFUSION MODELS

2010 ◽  
Vol 27 (02) ◽  
pp. 143-166
Author(s):  
HIROSHI KUNITA ◽  
TAKUYA YAMADA
Keyword(s):  
Diffusion Processes ◽  
Jump Diffusion ◽  
Double Exponential Distribution ◽  
Price Process ◽  
Merton Model ◽  
Jump Diffusion Processes ◽  
Put Option ◽  
Geometric Average ◽  
Double Exponential ◽  
Time Average

In this paper, we study the problem of pricing average strike options in the case where the price processes are jump diffusion processes. As to the striking value we take the geometric average of the price process. Two cases are studied in details: One is the case where the jumping law of the price process is subject to a Gaussian distribution called Merton model, and the other is the case where the jumping law is subject to a double exponential distribution called Kou model. In both cases the price of the average strike option is represented as a time average of a suitable European put option.

THE VALUATION OF RUSSIAN OPTIONS FOR DOUBLE EXPONENTIAL JUMP DIFFUSION PROCESSES

2010 ◽  
Vol 27 (02) ◽  
pp. 227-242 ◽  
Author(s):  
ATSUO SUZUKI ◽  
KATSUSHIGE SAWAKI
Keyword(s):  
Value Function ◽  
Diffusion Processes ◽  
Closed Form Solution ◽  
Jump Diffusion ◽  
Form Solution ◽  
Jump Diffusion Processes ◽  
Double Exponential ◽  
Analytical Properties ◽  
Russian Option ◽  
The Value Function

In this paper, we derive closed form solution for Russian option with jumps. First, we discuss the pricing of Russian options when the stock pays dividends continuously. Secondly, we derive the value function of Russian options by solving the ordinary differential equation with some conditions (the value function is continuous and differentiable at the optimal boundary for the buyer). And we investigate properties of optimal boundaries of the buyer. Finally, some numerical results are presented to demonstrate analytical properties of the value function.

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