|
Abstract
|
GARCH is a parametric family of time series models that has been very successful in reproducing various features (leptokurtosis, volatility clustering,...) that are empirically observed in the distributions and in the dynamics of the returns associated to stock prices, currency exchange rates, or prices of certain commodities. The pricing of derivative products whose underlying asset is modeled using GARCH is not straightforward since the associated market is incomplete and hence perfect replication using a self-financing portfolio is, in general, not available. In this talk, I will start with a brief review of the different approaches to this problem that have been proposed in the literature and will show how the quadratic hedging scheme introduced, among others, by F.A. Nvllmer, Schweizer, and Sondermann is applicable in this context under conditions that I will carefully spell out and, more importantly, sheds a new light on some of the standard result on this topic
|