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Pricing Options on an Asset with Bernoulli Jump‐Diffusion Returns
Author(s) -
Trippi Robert R.,
Brill Edward A.,
Harriff Richard B.
Publication year - 1992
Publication title -
financial review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.621
H-Index - 47
eISSN - 1540-6288
pISSN - 0732-8516
DOI - 10.1111/j.1540-6288.1992.tb01307.x
Subject(s) - jump diffusion , jump , bernoulli's principle , econometrics , log normal distribution , valuation (finance) , asset (computer security) , diffusion , valuation of options , economics , diffusion process , mathematics , computer science , statistics , finance , physics , computer security , quantum mechanics , thermodynamics , economy , service (business)
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 lognormal distribution. It is shown that not only the magnitude but also the direction of the mispricing of the Black‐Scholes 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.