A stochastic diffusion model of option prices and general jump process
The authors provide a direct modification of the famous Black-Scholes formula for the rational price of a standard European call option on a non-dividend-paying stock. They derive their particular pricing expression assuming that the price process \(\{S_t\}\) of the underlying asset follows a geometric Brownian motion subject to downward jumps occurring at a constant rate \(c\) and with identical magnitude distributions. That is, they suppose that the evolution in the price of the stock is described by the stochastic differential equation NEWLINE\[NEWLINEdS_t=\mu S_t dt + \sigma S_t dB_t - S_tdZ_t,NEWLINE\]NEWLINE where \(\{B_t\}\) is a Brownian motion and \(Z_t=\sum_{i=1}^{N(t)}U_i\), with \(\{N(t)\}\) being a Poisson process with mean \(c\) and \(U_1,U_2,\dots\) independent and identically distributed random variables. NEWLINENEWLINENEWLINEReviewer's remark: The article is full of typographical errors. Some of them, particularly those in which letters ``a'' and ``\(\alpha\)'' are exchanged inside several formulae, could lead to undesired misunderstandings.
scientific article; zbMATH DE number 1672750