R-Minimizing Hedging in an Incomplete Market: Malliavin Calculus Approach

37 Pages Posted: 7 May 2009

See all articles by Yajun Xiao

Yajun Xiao

University of Freiburg - Department of Economics

Date Written: May 7, 2009

Abstract

In this paper we derive the locally risk-minimizing hedging for a general contingent claim in an incomplete market via the generalized Clark-Ocone formula. Using this result in a stochastic volatility model, we study its connection with the hedge obtained via PDE approach. We see these hedging strategies, under weak conditions, are the same as the ones generated by the PDE approach. Within the same model we establish the pricing and the locally risk-minimizing hedging formulas for the path-dependent options, particularly pronouncing an impact from the correlation between stock and volatility on pricing and hedging. These formulas provides a basis to derive the approximations, which are much more computationally accessible.

Keywords: R-minimizing hedging, Delta hedging, incomplete markets, stochastic volatility model, Clark-Ocone formula, Malliavin Calculus, path-dependent options

JEL Classification: G13, C61, C63

Suggested Citation

Xiao, Yajun, R-Minimizing Hedging in an Incomplete Market: Malliavin Calculus Approach (May 7, 2009). Available at SSRN: https://ssrn.com/abstract=1400662 or http://dx.doi.org/10.2139/ssrn.1400662

Yajun Xiao (Contact Author)

University of Freiburg - Department of Economics ( email )

Freiburg, D-79085
Germany

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