A procedure is developed for the valuation of options when there are two underlying state variables. The approach involves an extension of the lattice binomial approach developed by Cox, Ross, and Rubinstein to value options on a single asset. Details are given on how the jump probabilities and jump amplitudes may be obtained when there are two state variables. This procedure can be used to price any contingent claim whose payoff is a piece-wise linear function of two underlying state variables, provided these two variables have a bivariate lognormal distribution. The accuracy of the method is illustrated by valuing options on the maximum and minimum of two assets and comparing the results for cases in which an exact solution has been obtained for European options. One advantage of the lattice approach is that it handles the early exercise feature of American options. In addition, it should be possible to use this approach to value a number of financial instruments that have been created in recent years.

This study is an ex post performance test comparing the accuracy of an American model to a European model for valuing listed options. Specifically, the Geske and Johnson American put valuation model is compared with the Black and Scholes European put model. On average, both models undervalue, relative to market prices, put options. However, the Geske and Johnson model values are significantly closer to market prices than are the Black and Scholes values.

What happens to the price of a put in a period during which the stock price stays constant? The hedging strategy implicit in the Black-Scholes model would seem to imply that the put goes up in value. Pure arbitrage arguments imply the opposite result. This paper resolves the paradox and uses it to explore the restrictions inherent in the diffusion processes assumed for all option pricing models.

We support and generalize our original results (1978) in light of potential impediments to a pure market solution to agency problems and potential causal links between liquidation and bankruptcy. In the case of bankruptcy costs, market impediments are easily eliminated through the inclusion of simple provisions in corporate charters and bond indentures. Further, we demonstrate that recent attempts to link liquidation costs to capital structure are without merit. If the firm is to be liquidated on the basis of a rule other than one that maximizes the total value of all the claimants, arbitrage profits arise, and informal reorganization will discipline management to follow the liquidation rule that is optimal for existing securityholders. Also, we find that the pure market solution is not readily generalizable to other classes of agency problems, particularly the risk incentive problem. However, the alternative solution of the risk incentive problem through complex financing contracting may be useful in explaining complexities in contemporary financial contracts.

In a world of asymmetric information in which only the insiders know the quality of the firm, it is claimed that debt, even if it is risky, is more advantageous than outside equity because issuance of debt is less attractive to inferior firms. The advantage to debt arises from the fact that it can keep unprofitable firms out of the market, thus improving the average quality of firms in the market. This advantage exists even if the firms cannot be perfectly sorted in the signaling equilibrium.

The purpose of this paper is to analyze the optimal individual behavior in acquiring information and to determine the amount of information incorporated in a stock at equilibrium, in the presence of a cost schedule in acquiring information. Our paper shows that at equilibrium the cost to acquire information that is not already incorporated in the price depends only on the representative investor's risk preferences. It follows that the marginal information costs are the same across all stocks at equilibrium even though the stock's information costs schedules may differ. This suggests that the prices of small stocks may not incorporate all publicly available information. This paper also provides empirical evidence that newspapers' publication of publicly available information can affect the stock prices.

The purpose of this paper is to suggest simple procedures designed to cope with the effects of thin trading on event study tests. The procedures are directed at two central problems: (i) missing individual stock returns (i.e., days on which no trading is observed in a security), and (ii) the effect of a bid-ask spread on the time series behavior of daily stock return data. We attack these problems by explicitly incorporating them in the construction of a generating process for observed security returns. First, we develop a procedure for “filling in” missing returns. Then, we model a return-generating process of observed security returns that allows estimation of the variance of unobserved true security returns for use in hypothesis testing.

Dissatisfaction occasionally has been expressed with traditional measures of duration for immunization on conceptual grounds. However, more elegant duration measures have not been found to be superior to the traditional ones in empirical tests of immunization efficacy. Under the assumption that the term structure of continuously compounded interest rates can be expressed as a polynomial, Chambers and Carleton (1981) demonstrate that the finite and noninstantaneous return of a default-free bond can be expressed as a vector product of a duration vector and a shift vector. This study derives immunization strategies from the model and tests them. The results of the portfolio tests indicate that the traditional duration approach of Macaulay provides enhanced immunization relative to maturity approaches or naive approaches. However, the duration vector approach produces further improvements.

The flattening of yield curves at long-term maturities is proven to be approximately proportional to the reciprocal of the time to maturity under general conditions. This is a consequence of the persistence of earlier forward rates in the averaging process, which produces yields from forward rates. This relationship suggests the use of a “reciprocal maturity yield curve,” which significantly facilitates the interpretation of the behavior of long-term yields by linearizing them for display over a shorter interval. This is illustrated using a yield curve for U.S. Treasury bills.

This paper extends the default model of yield spreads for bonds by showing that, in general, they are a complex function of maturity and, in particular, are not always monotonically increasing, contrary to what one traditional view suggests. Our results may help explain the apparently conflicting empirical results found in the literature.