On Model Selection and its Impact on the Hedging of Financial Derivatives
The mathematical theory of derivatives pricing and risk-management is one of the most active fields of research for both academics and practitioners. The celebrated Black-Scholes-Merton (BS) pioneering work paved the way to the development of a general theory of option pricing through the concept of absence of market arbitrage and dynamic replication (Harrison and Pliska, 1981). As is well-known, the simplistic assumptions behind the BS model make it unsuitable to capture and explain the risk borne by complex (exotic) financial derivatives. The need for a departure from the BS paradigm is in fact evident from the analysis of historical time series (Bates, 1996; Pan, 2002; Chernov, Gallant, Ghysels and Tauchen, 2003; and Eraker, Johannes and Polson, 2003, among others), as well as from the observation of the volatility smile phenomenon (Heston, 1993; Dupire, 1994, among others). For these reasons a number of alternative models have been advocated by many authors. Roughly speaking, all dynamic arbitrage-free models aiming at generalizing BS theory can be divided in three main classes, according to the characteristics of the stochastic process driving the dynamics of the underlying assets.
KeywordsOption Price Stochastic Volatility Implied Volatility Contingent Claim Stochastic Volatility Model
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