Unlike European-type derivative securities, there are no simple analytic valuation formulas for American options, even when the underlying asset price has constant volatility. The early exercise feature considerably complicates the valuation of American contracts. The strategy taken in this...

This paper provides a survey of recent numerical methods for pricing derivative securities. Methods for standard American options on a single underlying asset, barrier and lookback options and options on multiple assets are reviewed. Criteria for comparison of different approaches are discussed....

In this paper we provide lower and upper bounds on the prices of American call and put options written on a dividend paying asset. Based on the bounds, we provide two option price approximations. Our second approximation, which uses both lower and upper bound information, has an average accuracy...

In this paper we provide valuation formulas for several types of American options on two or more assets. Our contribution is twofold. First we characterize the optimal exercises regions and provide valuation formulas for a number of American option contracts on multiple underlying assets with...

In this paper, we consider American option contracts when the underlying asset has stochastic dividends and stochastic volatility. We provide a full discussion of the theoretical foundations of American option valuation and exercise boundaries. We show how they depend on the various sources of...

We provide a comprehensive treatment of option pricing with particular emphasis on the valuation of American options on dividend-paying essets. We begin by reviewing valuation principles for European contingent claims in a financial market in which the underlying asset price follows an Itô...

This paper addresses the problem of valuing American call options with caps on dividend paying assets. Since early exercise is allowed, the valuation problem requires the determination of optimal exercise policies. Options with two types of caps are analyzed: constant caps and caps with a...