This paper concerns the optimal stopping time problem in a nite horizon of a controlled jump diiusion process. We prove that the value function is continuous and is a viscosity solution of the inte-grodiierential variational inequality arising from the associated dynamic programming. We also establish comparison principles, which yield uniqueness results. Moreover, the viscosity solution approa...

We consider European options pricing with double jumps and stochastic volatility. We derived closed-form solutions for European call options in a double exponential jump-diffusion model with stochastic volatility SVDEJD . We developed fast and accurate numerical solutions by using fast Fourier transform FFT technique. We compared the density of our model with those of other models, including th...

From the spot prices we have to identify the following six parameters: α , μ, σ, Km , γ, Φ. If necessary, a seventh parameter, λ, should be identified from the futures prices. The six parameters mentioned above can be identified using the maximum likelihood method (Ball and Torous, 1983; Lien and Strom, 1999; Clewlow and Strickland, 2000) or the moments method (Lien and Strom, 1999; Deng, 1999)...

This paper introduces and studies the econometric properties of a general new class of models, which I refer to as jump-driven stochastic volatility models, in which the volatility is a moving average of past jumps. I focus attention on two particular semiparametric classes of jump-driven stochastic volatility models. In the first the price has a continuous component with time-varying volatilit...

The wide availability of high-frequency data for many financial instruments stimulates an upsurge interest in statistical research on the estimation of volatility. Jump-diffusion processes observed with market microstructure noise are frequently used to model high-frequency financial data. Yet, existing methods are developed for either noisy data from a continuous diffusion price model or data ...

the stochastic reaction diffusion systems may suffer sudden shocks‎, ‎in order to explain this phenomena‎, ‎we use markovian jumps to model stochastic reaction diffusion systems‎. ‎in this paper‎, ‎we are interested in almost sure exponential stability of stochastic reaction diffusion systems with markovian jumps‎. ‎under some reasonable conditions‎, ‎we show that the trivial solution of stocha...

The aim of this paper is to present ways of pricing financial derivatives in the Kou Model, [9], [10], using Quasi-Monte Carlo Methods. Quasi-Monte Carlo Methods have been applied successfully to the Black-Scholes model, e.g. [3], and also to some Lévy processes, e.g. [8], [11], [13], [2] and [16]. The Kou model can be considered to be an interesting model in its own right, however it is also a...

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 ...