Knowledge that Transforms

We consider the problem of pricing an American contingent claim whose payoff depends on several sources of uncertainty. Using classical assumptions from the Arbitrage Pricing Theory, the theoretical price can be computed as the maximumover all possible early exercise strategies of the discounted expected cash flows under the modified risk-neutral information process. Several efficient numerical techniques exist for pricing American securities depending on one or few (up to 3) risk sources. They are either lattice-based techniques or finite difference approximations of the Black-Scholes diffusion equation. However, these methods cannot be used for high-dimensional problems, since their memory requirement is exponential in the number of risk sources. In this paper, we present an efficient numerical technique that combines Monte Carlo simulation with a particular partitioning method of the underlying assets space, which we call Stratified State Aggregation (SSA). Using this technique we c...

Using synchronous transactions data for IBM from the New York, Pacific, and Midwest Stock Exchanges, we estimate an error correction model to investigate whether each of the exchanges is contributing to price discovery. Johansen's test yields two cointegrating vectors, which together verify the expected long-run equilibrium of equal prices across the three exchanges. Two error correction terms specified as the differences from IBM prices on the NYSE indicate that adjustments maintaining the long-run cointegration equilibrium take place on all three exchanges. That is, IBM prices on the NYSE adjust toward IBM prices on the Midwest and Pacific Exchanges, just as Midwest and Pacific prices adjust to the NYSE.

Unlike previous studies, this paper finds a consistent and highly significant relationship between beta and cross-sectional portfolio returns. The key distinction between our tests and previous tests is the recognition that the positive relationship between returns and beta predicted by the Sharpe-Lintner-Black model is based on expected rather than realized returns. In periods where excess market returns are negative, an inverse relationship between beta and portfolio returns should exist. When we adjust for the expectations concerning negative market excess returns, we find a consistent and significant relationship between beta and returns for the entire sample, for subsample periods, and for data divided by months in a year. Separately, we find support for a positive payment for beta risk.