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

Marcin Kacperczyk

No 202, Econometric Society 2004 North American Winter Meetings from Econometric Society

Abstract: 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.

Keywords: option pricing; Bayesian nonparametric approach; variance regression (search for similar items in EconPapers)
JEL-codes: G12 G13 (search for similar items in EconPapers)
Date: 2004-08-11
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Persistent link: https://EconPapers.repec.org/RePEc:ecm:nawm04:202

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