Analytic techniques for option pricing under a hyperexponential L 'evy\n model

2017/05/16 by Daniel Hackmann, Hackmann, Daniel
Economics, Econometrics and Finance · Mathematics · #60G51 #91G20 #91G60 #Complex Systems and Time Series Analysis #FOS: Economics and business #Mathematical Dynamics and Fractals #Mathematical Finance (q-fin.MF) #Pricing of Securities (q-fin.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1705.05934

openalex publication_date 2017/05/16 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

We develop series expansions in powers of q^-1 and q^-1/2 of\nsolutions of the equation \ψ(z) = q, where \ψ(z) is the Laplace\nexponent of a hyperexponential L 'evy process. As a direct consequence we\nderive analytic expressions for the prices of European call and put options and\ntheir Greeks (Theta, Delta, and Gamma) and a full asymptotic expansion of the\nshort-time Black-Scholes at-the-money implied volatility. Further we\ndemonstrate how the speed of numerical algorithms for pricing exotic options,\nwhich are based on the Laplace transform, may be increased.\n

Related

• A transform approach to compute prices and greeks of barrier options driven by a class of Levy processes
• Option pricing under jump diffusion model
• Lévy driven models and derivative pricing
• A variation of the Canadisation algorithm for the pricing of American options driven by Lévy processes
• Option Pricing with Orthogonal Polynomial Expansions