Upper Bounds for American Options

McGill Finance Research Centre Working Paper No. 2002

41 Pages Posted: 5 May 2003

See all articles by Mo Chaudhury

Mo Chaudhury

McGill University - Desautels Faculty of Management

Date Written: May 2, 2003


This paper provides a fuller characterization of the analytical upper bounds for American options than has been available to date. We establish properties required of analytical upper bounds without any direct reliance on the exercise boundary. A class of generalized European claims on the same underlying asset is then proposed as upper bounds. This set contains the existing closed form bounds of Margrabe (1978) and Chen and Yeh (2002) as special cases and allows randomization of the maturity payoff. Due to the European nature of the bounds, across-strike arbitrage conditions on option prices seem to carry over to the bounds. Among other things, European option spreads may be viewed as ratio positions on the early exercise option. To tighten the upper bound, we propose a quasi-bound that holds as an upper bound for most situations of interest and seems to offer considerable improvement over the currently available closed form bounds. As an approximation, the discounted value of Chen and Yeh's (2001) bound holds some promise. We also discuss implications for parametric and nonparametric empirical option pricing. Sample option quotes for the European (XEO) and the American (OEX) options on the S&P 100 Index appear well behaved with respect to the upper bound properties but the bid-ask spreads are too wide to permit a synthetic short position in the early exercise option.

Keywords: American options, option valuation, bounds

JEL Classification: G13

Suggested Citation

Chaudhury, Mo, Upper Bounds for American Options (May 2, 2003). McGill Finance Research Centre Working Paper No. 2002, Available at SSRN: https://ssrn.com/abstract=385906 or http://dx.doi.org/10.2139/ssrn.385906

Mo Chaudhury (Contact Author)

McGill University - Desautels Faculty of Management ( email )

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