CHAPTER 18
On Model Selection and
its Impact on the
Hedging of Financial
Derivatives
Giuseppe Di Graziano and Stefano Galluccio
18.1 INTRODUCTION
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.
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