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Analytic techniques for option pricing under a hyperexponential L\'{e}vy model

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  • Daniel Hackmann

Abstract

We develop series expansions in powers of $q^{-1}$ and $q^{-1/2}$ of solutions of the equation $\psi(z) = q$, where $\psi(z)$ is the Laplace exponent of a hyperexponential L\'{e}vy process. As a direct consequence we derive analytic expressions for the prices of European call and put options and their Greeks (Theta, Delta, and Gamma) and a full asymptotic expansion of the short-time Black-Scholes at-the-money implied volatility. Further we demonstrate how the speed of numerical algorithms for pricing exotic options, which are based on the Laplace transform, may be increased.

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  • Daniel Hackmann, 2017. "Analytic techniques for option pricing under a hyperexponential L\'{e}vy model," Papers 1705.05934, arXiv.org.
    • Handle: RePEc:arx:papers:1705.05934
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