Option Pricing in Garch Models
Dip. Metodi Quantitativi per le Scienze Economiche ed Aziendali
Università di Milano-Bicocca.
Abstract: The literature on option pricing in Garch models is
characterized by the risk premium specification, in fact this
parameter plays an important role in the choice of an equivalent
From a theoretical point of view, following the Duan ’s seminal
work, this approach can be justified by equilibrium arguments
based on the maximization of the expected utility function of a
Two cases are well known in literature :
1. The risk premium is linear in volatility (Duan 1995).
2. The risk premium is linear in variance (Heston-Nandi
Many empirical works show that the difference between the
conditional mean of returns and the risk-free rate under real
measure is more complex than above models (see for example
Engle, Litien and Robins (1987) and recently Bollerslev,
Gibbons and Zhou (2005)). Therefore, using only no-arbitrage
arguments, Christoffersen, Elkami and Jacobs (2005) propose a
more general change of measure that encompasses the
Moreover in a recent work Siu, Tong and Yang generalise this
result choosing an equivalent martingale measure by means of a
conditional Esscher Transform.
In our work we implement this approach and compare the
goodness of calibration of option prices with the models of
Duan and Heston-Nandi.
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Conditional Heteroskedasticity, Journal of Econometrics,
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Model for Option Pricing?, Management Science, 50,
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10. Siu, T. K., H. Tong and H. Yang (2005), On Pricing
Derivatives under Garch Models: A Dymnamic Gerber-
Shiu ’s Approach, Manuscript.