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Canonical distribution, implied binomial tree, and the pricing of American options

✍ Scribed by Qiang Liu; Shuxin Guo

Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
123 KB
Volume
33
Category
Article
ISSN
0270-7314

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✦ Synopsis

In this study, a new approach to pricing American options is proposed and termed the canonical implied binomial (CIB) tree method. CIB takes advantage of both canonical valuation (Stutzer, 1996) and the implied binomial tree method (Rubinstein, 1994). Using simulated returns from geometric Brownian motions (GBM), CIB produced very similar prices for calls and European puts as those of Black–Scholes (BS). Applied to a set of over 15,000 American‐style S&P 100 Index puts, CIB outperformed BS with historic volatility in pricing out‐of‐the‐money options; in addition, it outperformed the canonical least‐squares Monte Carlo (Liu, 2010) in the dynamic hedging of in‐the‐money options. Furthermore, CIB suggests that regular GBM‐based Monte Carlo can be extended to American options pricing by also utilizing the implied binomial tree. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark

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