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This article presents a simple yet powerful new approach for approximating the value of America11 options by simulation. The kcy to this approach is the use of least squares to estimate the conditional expected payoff to the optionholder from continuation. This makes this approach readily applicable in path-dependent and multifactor situations where traditional finite difference techniques cannot be used. We illustrate this technique with several realistic exatnples including valuing an option when the underlying asset follows a jump-diffusion process and valuing an America11 swaption in a 20-factor string model of the term structure. One of the most important problems in option pricing theory is the valuation and optimal exercise of derivatives with American-style exercise features. These types of derivatives are found in all major financial markets including the equity, commodity, foreign exchange, insurance, energy, sovereign,

We examine whether the predictability of future returns from past returns is due to the market's underreaction to information, in particular to past earnings news. Past return and past earnings surprise each predict large drifts in future returns after controlling for the other. Market risk, size, and book-to-market effects do not explain the drifts. There is little evidence of subsequent reversals in the returns of stocks with high price and earnings momentum. Security analysts ' earnings forecasts also respond sluggishly to past news, especially in the case of stocks with the worst past performance. The results suggest a market that responds only gradually to new information. AN EXTENSIVE BODY OF RECENT finance literature documents that the crosssection of stock returns is predictable based on past returns. For example, DeBondt and Thaler (1985, 1987)report that long-term past losers outperform long-term past winners over the subsequent three to five years. Jegadeesh (1990) and Lehmann (1990) find short-term return reversals. Jegadeesh and

Various theories have been proposed to explain momentum in stock returns. We test the gradual-information-diffusion model of Hong and Stein (1999) and establish three key results. First, once one moves past the very smallest stocks, the profitability of momentum strategies declines sharply with firm size. Second, holding size fixed, momentum strategies work better among stocks with low analyst coverage. Finally, the effect of analyst coverage is greater for stocks that are past losers than for past winners. These findings are consistent with the hypothesis that firm-specific information, especially negative information, diffuses only gradually across the investing public. SEVERAL RECENT PAPERS HAVE DOCUMENTED that, at medium-term horizons ranging from three to 12 months, stock returns exhibit momentum-that is, past winners continue to perform well, and past losers continue to perform poorly. For example, Jegadeesh and Titman (1993), using a U.S. sample of NYSE/ AMEX stocks over the period from 1965 to 1989, find that a strategy that buys past six-month winners (stocks in the top performance decile) and shorts past six-month losers (stocks in the bottom performance decile) earns approximately one percent per month over the subsequent six months. Not only is this an economically interesting magnitude, but the result also appears to be robust: Rouwenhorst (1998) obtains very similar numbers in a

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