Herb Johnson

Option Pricing when the Variance Is Changing

The Monte Carlo method is used to solve for the price of a call when the variance is changing stochastically.

Options on the Maximum or the Minimum of Several Assets

Using an intuitive approach that also provides new intuition concerning the Black and Scholes equation, this paper extends the results of Johnson and Stulz to the pricing of options on the minimum or the maximum of several risky assets.

Changes in the Standard and Poor's 500 List

L. Harris and E. Gurel (1986) and A. Shleifer (1986) examined changes in the Standard and Poors list. Both studies presented evidence inconsistent with efficient markets. Looking at newer data and at bond and option prices, the authors find that case against market efficiency is not compelling. Copyright 1991 by University of Chicago Press.

The Intraday Behavior of Bid-Ask Spreads for NYSE Stocks and CBOE Options

We study the intraday behavior of bid-ask spreads for actively traded CBOE options and for their NYSE-traded underlying stocks. We confirm previous findings that stocks have a U-shaped spread pattern; however, the options display a very different intraday pattern—one that declines sharply after the open, and then levels off. Our results suggest that both the degree of competition in market making and the extent of informed trading are important for understanding the intraday behavior of spreads.

The American Put Option and Its Critical Stock Price

We derive an expression for the critical stock price for the American put. We start by expressing the put price as an integral involving first-passage probabilities. This approach yields intuition for Mertons result for the perpetual put. We then consider the finite-lived case. Using (1) the fact that the put value ceases to depend on time when the critical stock price is reached and (2) the result that an American put equals a European put plus an early-exercise premium, we derive the critical stock price. We approximate the critical-stock-price function to compute accurate put prices. Copyright The American Finance Association 2000.

An Empirical Examination of the Pricing of American Put Options

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.

A Put Option Paradox

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.