Extended Nonparametric American Option Pricing
35 Pages Posted: 29 Feb 2008
Date Written: February 29, 2008
Abstract
A nonparametric method of pricing American options was recently developed that requires only historical underlying price data (Alcock and Carmichael, 2008). We derive an extension to this method to include conditioning information from a small number of observed option prices. This additional information improves the overall accuracy of the method and enables pricing of illiquid options in an incomplete market. We explore the statistical properties of both the original method and our extension using a series of simulation studies. The original method slightly outperforms Black-Scholes estimators and numerical estimators (Crank-Nicholson) that use historical volatility. In contrast, the extended method presented here produces significant reductions in mean pricing errors. These reductions are most dramatic for out-of-the-money options; a result that is consistent with empirical results for related entropic methodologies for pricing European options.
Keywords: Nonparametric Option Pricing, American Options, Canonical Pricing
JEL Classification: G12, G13, C14, C63
Suggested Citation: Suggested Citation
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