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Option Pricing Under a Double Exponential
Apr 20, 2001
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| Abstract: Although Brownian motion and normal distribution have been widely used in finance, two puzzles have got much attention recently; namely the leptokurtic feature that empirically the return distribution of assets may have a higher peak and two (asymmetric) heavier tails than those of the normal distribution, and an empirical abnormality called volatility smile in option pricing. To incorporate these, the double exponential jump diffusion model was proposed, in which the price of the underlying asset is modeled by two parts: a continuous part driven by Brownian motion, and a jump part with the jump size having a double exponential distribution. The model is also simple enough to produce analytical solutions for a variety of option pricing problems, including barrier, lookback, and perpetual American options, in terms of the Laplace transform and the $Hh$ function. The numerical implementation will also be discussed. |
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2001 Purdue University Last Update: July 10, 2001 Please send comments and suggestions to the Webmaster. |