A nonparametric approach to American option pricing

Carmichael, Trent Andrew. (2005). A nonparametric approach to American option pricing Honours Thesis, School of Business, The University of Queensland.

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Author Carmichael, Trent Andrew.
Thesis Title A nonparametric approach to American option pricing
School, Centre or Institute School of Business
Institution The University of Queensland
Publication date 2005
Thesis type Honours Thesis
Total pages 137
Language eng
Subjects 1503 Business and Management
Formatted abstract
The accurate pricing of American (put) options has challenged the finance fraternity for in excess of 40 years. Existing valuation techniques are largely parametric in nature and are thus reliant on certain parametric restrictions involving the return dynamics of the underlying asset. As nonparametric approaches do not require such assumptions, they represent a valuable alternative to parametric option pricing techniques, especially given the weight of empirical inconsistencies documented to exist for parametric restrictions assumed by the likes of Black and Scholes (1973). However, a truly nonparametric American option pricing technique is notably absent from the literature. This thesis introduces the Relative Entropic Weighted Least-Squares valuation approach - a new nonparametric method reliant only on historical stock price data to estimate the prices of American options under the risk-neutral framework. The REWLS valuation approach uses the principle of relative entropy (previously implemented by Stutzer (1996) in the context of European option pricing) to estimate the risk-neutral probabilities attached to series of predicted stock-price paths formed using the return-dynamics of the historical stock price data. Using these probabilities as equivalent martingale weights, American options can be valued by computing the optimal exercise boundary with a weighted least-squares valuation approach inspired by the least squares Monte Carlo technique of Longstaff and Schwartz (2001). This thesis documents the ability of the REWLS valuation approach to price American options under a variety of conditions in two simulated enviroI1ffients: a constant-volatility Black-Scholes (1973) world and a stochastic-volatility Heston (1993) world. As the simulated environment moves further from the confines of an (unrealistic) constant-volatility world, the REWLS valuation approach is shown to possess a performance edge over several competing parametric methods. This is an encouraging result which demonstrates the REWLS valuation approach has merit.
Additional Notes Variant title: Nonparametric American option pricing.

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