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A Bayesian semiparametric approach to pricing the S&P 500 index options


  • Marcin Kacperczyk; Paul Damien; Stephen Walker


Several studies incorporating estimated volatilities into option pricing formulas have appeared in the literature. However, the models described in these studies tend to perform quite poorly in out-of-sample tests. In particular, significant departures from the observed prices can be seen for the deep out-of-the-money short-term call options where mispricing seems to be somewhat excessive. This paper develops a new family of semiparametric Bayesian models. A particular member from this family that includes a nonparametric component is used to model option prices with the aim of improving the out-of-sample predictions. The principal advantage of injecting a nonparametric component into the model is that wide ranges of kurtosis in the observed asset prices are allowed, leading to lower pricing errors in out-of-sample predictions; that is, significant departures from normality in the underlying distribution of the asset prices when modeled lead to reliable forecasts. A detailed comparative empirical analysis with recent approaches to this problem is made for European out-of-the-money call options for which maturity does not exceed 40 days; it is for this subset of options that the pricing errors from other approaches are significant. The results indicate that the semiparametric Bayesian approach does better in terms of out-of-sample valuation errors compared with other approaches to the problem. Also, consistent with evidence reported in recent literature, for the group of short-term options exhibiting similar moneyness, pricing errors tend to decrease with the time to maturity.

Suggested Citation

  • Marcin Kacperczyk; Paul Damien; Stephen Walker, 2004. "A Bayesian semiparametric approach to pricing the S&P 500 index options," Econometric Society 2004 North American Winter Meetings 202, Econometric Society.
  • Handle: RePEc:ecm:nawm04:202

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    References listed on IDEAS

    1. Cason, Timothy N. & Friedman, Daniel, 1996. "Price formation in double auction markets," Journal of Economic Dynamics and Control, Elsevier, vol. 20(8), pages 1307-1337, August.
    2. Gjerstad, Steven & Dickhaut, John, 1998. "Price Formation in Double Auctions," Games and Economic Behavior, Elsevier, vol. 22(1), pages 1-29, January.
    3. Gode, Dhananjay K & Sunder, Shyam, 1993. "Allocative Efficiency of Markets with Zero-Intelligence Traders: Market as a Partial Substitute for Individual Rationality," Journal of Political Economy, University of Chicago Press, vol. 101(1), pages 119-137, February.
    4. Easley, David & Ledyard, John., "undated". "Theories of Price Formation and Exchange in Double Oral Auctions," Working Papers 611, California Institute of Technology, Division of the Humanities and Social Sciences.
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    More about this item


    option pricing; Bayesian nonparametric approach; variance regression;

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates


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