An Approximate Formula for Pricing American Options

Abstract

American exercise has always presented a problem for option pricing models. For put options and calls on underlying assets with a continuous proportional cash payout, American exercise turns valuation into a free boundary problem with no closed-form solution. The approximation formula derived by Baroni-Adesi and Whaley has been a very useful tool, but the approximation works best only for short maturities and every long maturities. The formula is less accurate for intermediate maturities of a couple of years, which are now common for over-the-counter option contracts and exchange-traded LEAPS. Other approximation methods based on numerical techniques can be made arbitrarily accurate, but are computationally much more burdensome. Ju and Zhong present a very useful new closed-form model, obtained by introducing correction terms to the Baroni-Adesi and Whaley formula. The model is much more accurate than most alternatives and is also computationally more efficient. As important as improved accuracy, for many users, is the fact that as a closed-form solution, programming Ju and Zhong's model is much simpler than setting up a numerical algorithm.