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Zbl 1216.91039
Kou, S.G.
A jump-diffusion model for option pricing. (English)
[J] Manage. Sci. 48, No. 8, 1086-1101 (2002). ISSN 0025-1909; ISSN 1526-5501/e

Summary: Brownian motion and normal distribution have been widely used in the Black-Scholes option-pricing framework to model the return of assets. However, two puzzles emerge from many empirical investigations: the leptokurtic feature that the return distribution of assets may have a higher peak and two (asymmetric) heavier tails than those of the normal distribution, and an empirical phenomenon called ``volatility smile" in option markets. To incorporate both of them and to strike a balance between reality and tractability, this paper proposes, for the purpose of option pricing, a double exponential jump-diffusion model. In particular, the model is simple enough to produce analytical solutions for a variety of option-pricing problems, including call and put options, interest rate derivatives, and path-dependent options. Equilibrium analysis and a psychological interpretation of the model are also presented.

MSC 2000:: *91G80
91G10
60J75 Jump processes

Keywords: contingent claims; high peak; heavy tails; interest rate models; rational expectations; overreaction and underreaction

Cited in: Zbl 1233.91286 Zbl 1230.60088 Zbl 1216.91040 Zbl 1233.91330

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