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Distinguished Limits of Levy-Stable Processes, and Applications to Option Pricing

Listed author(s):
  • Alvaro Cartea
  • Sam Howison

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

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Paper provided by Oxford Financial Research Centre in its series OFRC Working Papers Series with number 2002mf04.

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Date of creation: 2002
Handle: RePEc:sbs:wpsefe:2002mf04
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