Analytic techniques for option pricing under a hyperexponential Lévy model

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We develop series expansions in powers of q⁻¹ and q⁻¹/² of solutions of the equation ψ(z) = q, where ψ(z) is the Laplace exponent of a hyperexponential Lévy 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.