A Double Exponential Jump Diffusion Process To Modelling Risky Bond Prices

2003 ◽  
Author(s):  
Benoit Metayer
Keyword(s):  
Diffusion Process ◽  
Jump Diffusion ◽  
Bond Prices ◽  
Double Exponential ◽  
Jump Diffusion Process

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.

First passage times of a jump diffusion process

2003 ◽  
Vol 35 (02) ◽  
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.

ANALYTICAL PRICING OF DOUBLE-BARRIER OPTIONS UNDER A DOUBLE-EXPONENTIAL JUMP DIFFUSION PROCESS: APPLICATIONS OF LAPLACE TRANSFORM

2004 ◽  
Vol 07 (02) ◽  
pp. 151-175 ◽  
Author(s):  
ARTUR SEPP
Keyword(s):  
Laplace Transform ◽  
Diffusion Process ◽  
Asset Price ◽  
Option Price ◽  
Jump Diffusion ◽  
Time Dependent ◽  
Barrier Option ◽  
Double Exponential ◽  
Jump Diffusion Process ◽  
Risk Parameters

We derive explicit formulas for pricing double (single) barrier and touch options with time-dependent rebates assuming that the asset price follows a double-exponential jump diffusion process. We also consider incorporating time-dependent volatility. Assuming risk-neutrality, the value of a barrier option satisfies the generalized Black–Scholes equation with the appropriate boundary conditions. We take the Laplace transform of this equation in time and solve it explicitly. Option price and risk parameters are computed via the numerical inversion of the corresponding solution. Numerical examples reveal that the pricing formulas are easy to implement and they result in accurate prices and risk parameters. Proposed formulas allow fast computing of smile-consistent prices of barrier and touch options.

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