An Algorithm for Computing Values of Options on the Maximum or Minimum of Several Assets
Johnson (1981) and Stulz (1982) independently derived prices for options on the maximum and the minimum of 2 assets. The results of Johnson and Stulz are extended to the pricing of options on the minimum or the maximum of several risky assets. A simple, intuitive approach is presented, using the Cox and Ross (1976) approach and a trick based on a device used by Margrabe (1978), to write down the solution for the general case of an option on several assets. First, the procedure for the Black and Scholes (1973) equation is illustrated, thereby obtaining some new intuition about this equation. Then, the equations are developed for calls on the maximum and the minimum. The equations reduce to the findings of Stulz and Johnson when there are only 2 assets.
Journal of Financial and Quantitative Analysis
Cambridge University Press
Boyle, P. P. and TSE, Yiu Kuen.
An Algorithm for Computing Values of Options on the Maximum or Minimum of Several Assets. (1987). Journal of Financial and Quantitative Analysis. 25, (3), 277. Research Collection School Of Economics.
Available at: http://ink.library.smu.edu.sg/soe_research/75