Orthogonal gamma-based expansions for volatility option prices under jump-diffusion dynamics

Buccioli, Alice (2014) Orthogonal gamma-based expansions for volatility option prices under jump-diffusion dynamics. [Laurea magistrale], Università di Bologna, Corso di Studio in Matematica [LM-DM270]
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Abstract

In my work I derive closed-form pricing formulas for volatility based options by suitably approximating the volatility process risk-neutral density function. I exploit and adapt the idea, which stands behind popular techniques already employed in the context of equity options such as Edgeworth and Gram-Charlier expansions, of approximating the underlying process as a sum of some particular polynomials weighted by a kernel, which is typically a Gaussian distribution. I propose instead a Gamma kernel to adapt the methodology to the context of volatility options. VIX vanilla options closed-form pricing formulas are derived and their accuracy is tested for the Heston model (1993) as well as for the jump-diffusion SVJJ model proposed by Duffie et al. (2000).

Abstract
Tipologia del documento
Tesi di laurea (Laurea magistrale)
Autore della tesi
Buccioli, Alice
Relatore della tesi
Scuola
Corso di studio
Indirizzo
Curriculum A: Generale e applicativo
Ordinamento Cds
DM270
Parole chiave
option pricing VIX Laguerre expansion jump-diffusion
Data di discussione della Tesi
24 Ottobre 2014
URI

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