Knowledge that Transforms

[This article is a reexamination of the clearing and settlement process in financial markets (particularly the futures market) and its performance during the 1987 stock market crash. It provides both some institutional background and some conceptual perspective on the problems faced by the system during the week of October 19. Much of the discussion is based on the useful analogies that can be drawn between the clearinghouse and other financial intermediaries, such as banks and insurance companies. A major conclusion is that the Federal Reserve played a vital role in protecting the integrity of the clearing and settlements system during the crash.]

[The downside risk in a leveraged stock position can be eliminated by using stop-loss orders. The upside potential of such a position can be captured using contingent buy orders. The terminal payoff to this stop-loss start-gain strategy is identical to that of a call option, but the strategy costs less initially. This article resolves this paradox by showing that the strategy is not self-financing for continuous stock-price processes of unbounded variation. The resolution of the paradox leads to a new decomposition of an option's price into its intrinsic and time value. When the stock price follows geometric Brownian motion, this decomposition is proven to be mathematically equivalent to the Black-Scholes (1973) formula.]

[This article generalizes the Cox, Ross, and Rubinstein (1979) binomial option-pricing model, and establishes a convergence from discrete-time multivariate multinomial models to continuous-time multidimensional diffusion models for contingent claims prices. The key to the approach is to approximate the N-dimensional diffusion price process by a sequence of N-variate, (N + 1)-nomial processes. It is shown that contingent claims prices and dynamic replicating portfolio strategies derived from the discrete time models converge to their corresponding continuous-time limits.]

[If returns on some stocks systematically lead or lag those of others, a portfolio strategy that sells "winners" and buys "losers" can produce positive expected returns, even if no stock's returns are negatively autocorrelated as virtually all models of overreaction imply. Using a particular contrarian strategy we show that, despite negative autocorrelation in individual stock returns, weekly portfolio returns are strongly positively autocorrelated and are the result of important cross-autocorrelations. We find that the returns of large stocks lead those of smaller stocks, and we present evidence against overreaction as the only source of contrarian profits.]

[This article analyzes the behavior of stock return volatility using daily data from 1885 through 1988. The October 1987 stock market crash was unusual in many ways. October 19 was the largest percentage change in market value in over 29,000 days. Stock volatility jumped dramatically during and after the crash. Nevertheless, it returned to lower, more normal levels more quickly than past experience predicted. I use data on implied volatilities from call option prices and estimates of volatility from futures contracts on stock indexes to confirm this result.]