Local Volatility Function Models under a Benchmark Approach

David Heath and Eckhard Platen ()

No 124, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

Abstract: This paper studies a class of one-factor local volatility function models for stock indices under a benckmark approach. It assumes that the dynamics for a large diversified index approximates that of the growth optimal portfolio. The pricing and hedging of derivatives under the benchmark approach does not require the existence of an equivalent risk neutral martingale measure. Fair prices for index derivatives when expressed in units of the index are martingales under the real world probability measure. The real world transitin densities for the index and the underlying local volatility function can be determined from a continuum of European call option prices. As specific examples a modification of the constant elasticity of variance model and a version of the minimal market model are discussed together with a smoothed local volatility function that fits a snapshot of S&P500 index options data.

Keywords: local volatility function; index derivatives; growth optimal portfolio; benchmark approach; fair pricing; modified CEV model; minimal market model (search for similar items in EconPapers)
JEL-codes: G10 G13 (search for similar items in EconPapers)
Pages: 20 pages
Date: 2004-04-01
New Economics Papers: this item is included in nep-ets, nep-fin and nep-fmk
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Published as: Heath, D. and Platen, E., 2006, "Local Volatility Function Models under a Benchmark Approach", Quantitative Finance, 6(3), 197-206.

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