Pricing Options on an Asset with Bernoulli Jump-Diffusion Returns

Robert R Trippi, Edward A Brill and Richard Harriff

The Financial Review, 1992, vol. 27, issue 1, 59-79

Abstract: The price movements of certain assets can be modeled by stochastic processes that combine continuous diffusion with discrete jumps. This paper compares values of options on assets with no jumps, jumps of fixed size, and jumps drawn from a log-normal distribution. It is shown that not only the magnitude but also the direction of the mis-pricing of the F. Black-M. Scholes (1973) model relative to jump models can vary with the distribution family of the jump component. This paper also discusses a methodology for the numerical valuation, via a backward induction algorithm, of American options on a jump-diffusion asset whose early exercise may be profitable. These cannot, in general, be accurately priced using analytic models. The procedure has the further advantage of being easily adaptable to nonanalytic, empirical distributions of period returns and to nonstationarity in the underlying diffusion process. Copyright 1992 by MIT Press.

Date: 1992
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