A General Derivation of the Jump Process Option Pricing Formula

The following paper presents a general derivation of the jump process option pricing formula. In particular, a general jump process formula is derived via an analysis of the limiting behavior of the binomial option pricing formula. In deriving the formula, a very simple central limit theorem known as Poisson's Limit Theorem is applied. The simplicity of the analysis allows the establishment of precisely the connections between the specification of the underlying binomial stock return process and the specific form of the corresponding continuous-time jump process formula. Several examples are provided to illustrate these connections.