Testing Alternative Measure Changes in Nonparametric Pricing and Hedging of European Options

Authors

  • Jamie Alcock,

    Corresponding author
    1. Department of Land Economy, The University of Cambridge, Cambridge, United Kingdom
    2. School of Mathematics and Physics, The University of Queensland, St Lucia, Queensland, Australia
    • Correspondence author, Department of Land Economy, The University of Cambridge, 19 Silver Street, Cambridge CB3 9EP, United Kingdom. Tel: +44-1223-337152, Fax: +44-1223-337130, e-mail: jta27@cam.ac.uk; School of Mathematics and Physics, The University of Queensland, St Lucia 4072, Queensland, Australia. Tel: +61-7-33653271, Fax: +61-7-33651477, e-mail: j.alcock@uq.edu.au

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  • Godfrey Smith

    1. School of Mathematics and Physics, The University of Queensland, St Lucia, Queensland, Australia
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  • We thank Trent Carmichael, Diana Auerswald, and Joe Grotowski for their valuable comments and suggestions as well as participants of the 25th Australasian Finance and Banking Conference 2012 and seminar participants at the University of Queensland.

Abstract

Haley and Walker [Haley, M.R., & Walker, T. (2010). Journal of Futures Markets, 30, 983–1006] present the Euclidean and Empirical Likelihood nonparametric option pricing models as alternative tilts to Stutzer's [Stutzer, M. (1996). Journal of Finance, 51, 1633–1652] Canonical pricing method. We empirically test the comparative strengths of each of these methods using a large sample of traded options on the S&P100 Index. Furthermore, we explore an additional tilt based on Pearson's chi-square, and derive and empirically test nonparametric delta hedges for each of these approaches. Differences in the pricing performance of the various tilts are a function of differences between the sample distribution and the real distribution of the underlying. When the sample distribution displays fatter (thinner) tails and/or higher (lower) volatility than the true distribution, the Euclidean (Pearson's chi-square) model outperforms. Significantly, when these nonparametric methods utilize information contained in a small number of observed option prices they often outperform the implied volatility Black and Scholes [Black, F., & Scholes, M. (1973). Journal of Political Economy, 81, 637–654] model. These pricing performance differences do not translate into static and dynamic hedging performance differences. However, each of the nonparametric models induce an implied volatility smile and term structure that generally agree in form with the smile and term structure embedded in market prices. © 2013 Wiley Periodicals, Inc. Jrl Fut Mark 34:320–345, 2014

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