The key problem for option pricing in Garch models is that the risk-neutral distribution of the underlying at maturity is unknown. Heston and Nandi solved this problem by computing the characteristic function of the underlying by a recursive procedure. Following the same idea, Christoffersen, Heston and Jacobs proposed a Garch-like model with inverse Gaussian innovations and recently Bellini and Mercuri obtained a similar procedure in a model with Gamma innovations. We present a model with tempered stable innovations that encompasses both the CHJ and the BM models as special cases. The proposed model is calibrated on S&P500 closing option prices and its performance is compared with the CHJ, the BM and the Heston–Nandi models.

Mercuri, L. (2008). Option pricing in a Garch model with tempered stable innovations. FINANCE RESEARCH LETTERS, 5(3), 172-182 [10.1016/j.frl.2008.05.003].

Option pricing in a Garch model with tempered stable innovations

MERCURI, LORENZO
2008

Abstract

The key problem for option pricing in Garch models is that the risk-neutral distribution of the underlying at maturity is unknown. Heston and Nandi solved this problem by computing the characteristic function of the underlying by a recursive procedure. Following the same idea, Christoffersen, Heston and Jacobs proposed a Garch-like model with inverse Gaussian innovations and recently Bellini and Mercuri obtained a similar procedure in a model with Gamma innovations. We present a model with tempered stable innovations that encompasses both the CHJ and the BM models as special cases. The proposed model is calibrated on S&P500 closing option prices and its performance is compared with the CHJ, the BM and the Heston–Nandi models.
Articolo in rivista - Articolo scientifico
Option pricing; Garch; Tempered stable distribution; Semi-analytical valuation; Esscher transform
English
172
182
Mercuri, L. (2008). Option pricing in a Garch model with tempered stable innovations. FINANCE RESEARCH LETTERS, 5(3), 172-182 [10.1016/j.frl.2008.05.003].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/6390
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