Hedging for the Long Run

Eckhard Platen () and Hardy Hulley

No 214, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

Abstract: In the years following the publication of Black and Scholes [7], numerous alternative models have been proposed for pricing and hedging equity derivatives. Prominent examples include stochastic volatility models, jump diffusion models, and models based on Levy processes. These all have their own shortcomings, and evidence suggests that none is up to the task of satisfactorily pricing and hedging extremely long-dated claims. Since they all fall within the ambit of risk-neutral pricing, it is thus natural to speculate that their deficiencies are (at least in part) attributable to the modelling constraints imposed by the risk-neutral approach itself. To investigate this idea, we present a simple two-parameter model for a diversifed equity accumulation index. Although our model does not admit an equivalent risk-neutral probability measure, it nevertheless fulfils a minimal no-arbitrage condition for an economically viable financial market. Furthermore, we demonstrate that contingent claims can be priced and hedged, without the need for an equivalent change of probability measure. Convenient formulae for the prices and hedge ratios of a number of standard European claims are derived, and a series of hedge experiments for extremely long-dated claims on the S&P 500 total return index are conducted. Our model serves also as a convenient medium for illustrating and clarifying several points on asset price bubbles and the economics of arbitrage.

Keywords: long-dated claims; risk-neutral pricing; real-world pricing; arbitrage; minimal market model; squared Bessel processes; hedge simulations; asset price bubbles (search for similar items in EconPapers)
JEL-codes: G10 G12 G13 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-fmk and nep-rmg
Date: 2008-02-01
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