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.

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

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.

Kalok Chan, Y. Peter Chung, Herb Johnson, The Intraday Behavior of Bid-Ask Spreads for NYSE Stocks and CBOE Options, The Journal of Financial and Quantitative Analysis, Vol. 30, No. 3 (Sep., 1995), pp. 329-346