Local volatility function models under a benchmark approach

David Heath and Eckhard Platen ()

Quantitative Finance, 2006, vol. 6, issue 3, 197-206

Abstract: Without requiring the existence of an equivalent risk-neutral probability measure this paper studies a class of one-factor local volatility function models for stock indices under a benchmark approach. It is assumed that the dynamics for a large diversified index approximates that of the growth optimal portfolio. Fair prices for derivatives when expressed in units of the index are martingales under the real-world probability measure. Different to the classical approach that derives risk-neutral probabilities the paper obtains the transition density for the index with respect to the real-world probability measure. Furthermore, the Dupire formula for the underlying local volatility function is recovered without assuming the existence of an equivalent risk-neutral probability measure. A modification of the constant elasticity of variance model and a version of the minimal market model are discussed as specific examples together with a smoothed local volatility function model that fits a snapshot of S&P500 index options data.

Keywords: Local volatility function; Index derivatives; Growth optimal portfolio; Benchmark approach; Fair pricing; Dupire formula; Modified CEV model; Minimal market model (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (6)

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DOI: 10.1080/14697680600699787

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