A jump-diffusion log-return process with log-normal jump amplitudes is presented. The probability density and other properties of the theoretical model are rigorously derived. This theoretical density is fit to empirical log-returns of Standard & Poor’s 500 stock index data. The model repairs some failures found from the log-normal distribution of geometric Brownian motion to model features of ...

The measurement of diffusion parameters like activation energies and translational jump rates of small cations plays a key role in materials science. Especially the in-depth investigation of Li diffusion in ionic conductors is of great interest, because suitable ionic conductors are needed for, e. g., the development of new secondary ion battery systems. As the standard tracer method is not app...

This paper presents some models of exchange rate with jumps, namely jump diffusion models. Jump are quite common in computational and theoretical finance. It is known that rates sometimes exhibit jumps during time periods. Therefore, it important to take into account the presence these modeling general. However, even simplest model introduces analytical difficulty terms finding a solution model...

In this paper we analyze asset returns models with diffusion part and jumps in returns with stochastic volatility either from diffusion or pure jump part. We consider different specifications for the pure jump part including compound Poisson, Variance Gamma and Levy α-stable jumps. Monte Carlo Markov chain algorithm is constructed to estimate models with latent Variance Gamma and Levy α−stable ...

In this paper consistency problems for multi-factor jump-diffusion models, where the jump parts follow multivariate point processes are examined. First the gap between jump-diffusion models and generalized HeathJarrow-Morton (HJM) models is bridged. By applying the drift condition for a generalized arbitrage-free HJM model, the consistency condition for jumpdiffusion models is derived. Then we ...

Reduced European call and put option formulas by risk-neutral valuation are given. It is shown that the European call and put options for log-uniformjump-diffusion models are worth more than that for the Black-Scholes (diffusion) model with the common parameters. Due to the complexity of the jump-diffusion models, obtaining a closed option pricing formula like that of Black-Scholes is not tract...