| Purdue Computational Finance Program | |
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An overview of hedging and pricing in incomplete markets
February 6, 2002
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Abstract:
A traditional model for financial asset prices is that of a solution of a stochastic differential equation, driven by Brownian motion and Lebesgue measure; that is, a standard diffusion. The classic Black-Scholes model is a special case of this class. In some situations, however, such a model is inappropriate. In particular, empirical work has led researchers to conclude that appropriate models often contain price processes with jumps. This is reflected both in simple observations of price processes, and in statistical analysis of tail distributions (that is, the existence and persistence of `heavy tails', that diffusion models do not have). Furthermore, when modeling implied volatility surfaces, models that allow for jumps fit the data better than do models that do not, especially when times are close to maturity. But adding jumps to a model causes an interesting problem, since often the market becomes incomplete. In this case, we can no longer use the standard hedging and pricing methods, and some alternatives are needed. We introduce alternative hedging and pricing methods in incomplete markets and some new and recent approaches. |
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2002 Purdue University Last Update: January 17, 2002 Please send comments and suggestions to the Webmaster. |