First Passage times of a Jump Diffusion Process
نویسنده
چکیده
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 runningmaxima, 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.
منابع مشابه
Efficient Estimation of First Passage Time Density Function for Jump-Diffusion Processes
The first passage time problem has attracted considerable research interest in the field of stochastic processes. It concerns the estimation of the probability density of the time for a random process to cross a specified boundary level. Even though there are many theoretical advances in solving this problem, for many classes of random processes no analytical solution exists. The jumpdiffusion ...
متن کاملFirst Passage Times of a Jump Di usion Process
This paper studies the rst passage times to at boundaries for a double exponential jump di usion 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 rst passage times and the joint distribution of the process and its running...
متن کاملDouble-barrier first-passage times of jump-diffusion processes
Required in a wide range of applications in, e.g., finance, engineering, and physics, first-passage time problems have attracted considerable interest over the past decades. Since analytical solutions often do not exist, one strand of research focuses on fast and accurate numerical techniques. In this paper, we present an efficient and unbiased Monte-Carlo simulation to obtain double-barrier fi...
متن کاملPricing of Commodity Futures Contract by Using of Spot Price Jump-Diffusion Process
Futures contract is one of the most important derivatives that is used in financial markets in all over the world to buy or sell an asset or commodity in the future. Pricing of this tool depends on expected price of asset or commodity at the maturity date. According to this, theoretical futures pricing models try to find this expected price in order to use in the futures contract. So in this ar...
متن کاملA Structural Credit-Risk Model based on a Jump Diffusion
In this paper, we generalize the pure diffusion approach for structural credit risk modeling by including jumps in the firm-value process. In pure diffusion models, the probability for a solvent company to default within a small interval of time is negligible, whereas a real company may face sudden financial distress. Our generalization allows those unpredicted extremal events, raising the prob...
متن کامل