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Distinguished limits of Lévy-Stable processes, and applications to option pricing

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2003-08-19
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In this paper we derive analytic expressions for the value of European Put and Call options when the stock process follows an exponential Lévy-Stable process. It is shown that the generalised Black-Scholes operator for the Lévy-Stable case can be obtained as an asymptotic approximation of a process where the random variable follows a Damped- Lévy process. Finally, it is also shown that option prices under the Lévy-Stable case generate the volatility smile encountered in the financial markets when the Black-Scholes framework is employed
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Lévy-Stable processes, Stable Paretian hypothesis, Damped Lévy-Stable, Option pricing
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