Jump-diffusion models with constant parameters for financial log-return processes

Abstract

We present five alternative approaches to modelling assets using jump-diffusion processes. Three of them are known in the literature and they give analytical solutions for option pricing problems. We present two further models, which are better motivated by the market and we compare all five models with each other and with the Black–Scholes model. Good criteria of goodness of fit of the model to the data are statistical tests, whose values are also helpful in comparing the models. In this paper, we use Kolmogorov, Anderson–Darling and Cramer–von Mises statistics.