we derive closed formulas for the prices of european options andtheir sensitivities when the underlying asset follows a double-exponentialjump diffusion model, as considered by s. kou in 2002. this author hasderived the option price by making use of double series where each termrequires the computation of a sequence of special functions, such thatthe implementation remains difficult for a large...

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...

The stochastic analysis is presented for the parameter estimation problem for fitting a theoretical jump-diffusion model to the log-returns from closing data of the Standard and Poor’s 500 (S&P500) stock index during the prior decade 1992-2001. The jump-diffusion model combines a the usual geometric Brownian motion for the diffusion and a space-time Poisson process for the jumps such that the j...

Abstract: This paper studies the pricing of forward starting options under regime switching jump diffusion models. We suppose that a market economy has only two states, one is a stable state, the other is a high volatility state. The dynamics of a risky asset is modeled by a geometry Brownian motion when the market state is stable, otherwise, it follows a jump diffusion model. We propose two ty...

A computational solution is found for a optimal consumption and portfolio policy problem in which the underlying stock satisfies a geometric jump–diffusion in which both the diffusion and jump amplitude are log– normally distributed. The optimal objective is to maximize the expected, discounted utility of terminal wealth and the cumulative discounted utility of instantaneous consumption. The ju...

A computational solution is found for a optimal consumption and portfolio policy problem in which the underlying stock satisfies a geometric jump–diffusion in which both the diffusion and jump amplitude are log–normally distributed. The optimal objective is to maximize the expected, discounted utility of terminal wealth and the cumulative discounted utility of instantaneous consumption. The jum...

The jump diffusion process has come to play an important role in many branches of science and industry. In their book [25], Øksendal and Sulem have studied the optimal control, optimal stopping and impulse control for jump diffusion processes. In mathematical finance theory, many researchers have developed option pricing theory, for example, Merton [24] was the first to use the jump process to ...

This paper treats jump-diffusion processes in continuous time, with emphasis on the jump-amplitude distributions, developing more appropriate models using parameter estimation for the market in one phase and then applying the resulting model to a stochastic optimal portfolio application in a second phase. The new developments are the use of uniform jump-amplitude distributions and time-varying ...