A valuation model that allows for jumps in underlying assets’ prices superimposed on to a diffusion process such as geometric Brownian motion. In Black-Scholes option pricing model, trading is assumed to take place continuously in time, while the underlying asset price follows a continuous sample path. However, occasional jumps in asset price are commonplace in asset price dynamics. Such jumps may reflect the release of new important information on a given firm or industry or even local economy. Modeling of the asset price process by combining normal price fluctuation and abnormal jumps was introduced by Merton (1976). The normal fluctuation is modeled by the geometric Brownian process, while the jumps are modeled by Poisson distributed events, where jump events are assumed to be independent and identically distributed.
August 11, 2021
