Option pricing under a mixed-exponential jump diffusion model / Ning Cai in Management science, Vol. 57 N° 11 (Novembre 2011)  

Public ISBD [article]  inManagement science > Vol. 57 N° 11 (Novembre 2011) . - pp. 2067-2081 Titre : Option pricing under a mixed-exponential jump diffusion model Type de document : texte imprimé Auteurs : Ning Cai, Auteur ; S. G. Kou, Auteur Année de publication : 2012 Article en page(s) : pp. 2067-2081 Note générale : Management Langues : Anglais (eng) Mots-clés : Jump diffusion Mixed-exponential distributions Lookback options Barrier Merton's normal jump model First passage times Index. décimale : 658 Organisation des entreprises. Techniques du commerce Résumé : This paper aims to extend the analytical tractability of the Black–Scholes model to alternative models with arbitrary jump size distributions. More precisely, we propose a jump diffusion model for asset prices whose jump sizes have a mixed-exponential distribution, which is a weighted average of exponential distributions but with possibly negative weights. The new model extends existing models, such as hyperexponential and double-exponential jump diffusion models, because the mixed-exponential distribution can approximate any distribution as closely as possible, including the normal distribution and various heavy-tailed distributions. The mixed-exponential jump diffusion model can lead to analytical solutions for Laplace transforms of prices and sensitivity parameters for path-dependent options such as lookback and barrier options. The Laplace transforms can be inverted via the Euler inversion algorithm. Numerical experiments indicate that the formulae are easy to implement and accurate. The analytical solutions are made possible mainly because we solve a high-order integro-differential equation explicitly. A calibration example for SPY options shows that the model can provide a reasonable fit even for options with very short maturity, such as one day. DEWEY : 658 ISSN : 0025-1909 En ligne : http://mansci.journal.informs.org/content/57/11/2067.abstract [article] Option pricing under a mixed-exponential jump diffusion model [texte imprimé] / Ning Cai, Auteur ; S. G. Kou, Auteur . - 2012 . - pp. 2067-2081. Management Langues : Anglais (eng) in Management science > Vol. 57 N° 11 (Novembre 2011) . - pp. 2067-2081 Mots-clés : Jump diffusion Mixed-exponential distributions Lookback options Barrier Merton's normal jump model First passage times Index. décimale : 658 Organisation des entreprises. Techniques du commerce Résumé : This paper aims to extend the analytical tractability of the Black–Scholes model to alternative models with arbitrary jump size distributions. More precisely, we propose a jump diffusion model for asset prices whose jump sizes have a mixed-exponential distribution, which is a weighted average of exponential distributions but with possibly negative weights. The new model extends existing models, such as hyperexponential and double-exponential jump diffusion models, because the mixed-exponential distribution can approximate any distribution as closely as possible, including the normal distribution and various heavy-tailed distributions. The mixed-exponential jump diffusion model can lead to analytical solutions for Laplace transforms of prices and sensitivity parameters for path-dependent options such as lookback and barrier options. The Laplace transforms can be inverted via the Euler inversion algorithm. Numerical experiments indicate that the formulae are easy to implement and accurate. The analytical solutions are made possible mainly because we solve a high-order integro-differential equation explicitly. A calibration example for SPY options shows that the model can provide a reasonable fit even for options with very short maturity, such as one day. DEWEY : 658 ISSN : 0025-1909 En ligne : http://mansci.journal.informs.org/content/57/11/2067.abstract

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