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Closed‐form option pricing formulas with extreme events
Author(s) -
Câmara António,
Heston Steven L.
Publication year - 2008
Publication title -
journal of futures markets
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.88
H-Index - 55
eISSN - 1096-9934
pISSN - 0270-7314
DOI - 10.1002/fut.20298
Subject(s) - jump , jump diffusion , simple (philosophy) , mathematical economics , limiting , mathematics , diffusion , economics , econometrics , statistical physics , physics , engineering , mechanical engineering , philosophy , epistemology , quantum mechanics , thermodynamics
This paper explores the effect of extreme events or big jumps downwards and upwards on the jump‐diffusion option pricing model of Merton (1976). It starts by obtaining a special case of the jump‐diffusion model where there is a positive probability of a big jump downwards. Then, it obtains a new limiting case where there is an asymptotically big jump upwards. The paper extends these models to allow both types of jumps. In some cases these formulas nest Samuelson's (1965) formulas. This simple analysis leads to several closed‐form solutions for calls and puts, which are able to generate smiles, and skews with similar shapes to those observed in the marketplace. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:213–230, 2008