PERFECT HEDGING OF INDEX DERIVATIVES UNDER A MINIMAL MARKET MODEL

David Heath and Eckhard Platen ()
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David Heath: University of Technology Sydney, School of Finance & Economics and Department of Mathematical Sciences, PO Box 123, Broadway, NSW, 2007, Australia

International Journal of Theoretical and Applied Finance (IJTAF), 2002, vol. 05, issue 07, 757-774

Abstract: The paper presents a financial market model that generates stochastic volatility using a minimal set of factors. These factors, formed by transformations of square root processes, model the dynamics of different denominations of a benchmark portfolio. Benchmarked prices are assumed to be local martingales. Numerical results for the pricing and hedging of basic derivatives on indices are described for the minimal market model. This includes cases where the standard risk neutral pricing methodology fails because of the presence of a strict local martingale measure. However, payoffs can be perfectly hedged using self-financing strategies and a form of arbitrage exists. This is illustrated by hedge simulations. The different term structure of implied volatilities is documented for calls and puts on an index.

Keywords: Derivative pricing; arbitrage; minimal market model (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1142/S0219024902001729

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