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arXiv · 1705.05934

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

Daniel Hackmann
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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. 2017-05-16. Analytic techniques for option pricing under a hyperexponential L\'{e}vy model. https://arxiv.org/abs/1705.05934

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