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1 November 1984 Financial Analysts Journal Volume 40, Issue 6

Modifying the Black-Scholes Option Pricing Model for Alternative Underlying Instruments

  1. James F. Meisner
  2. John W. Labuszewski

The Black-Scholes option pricing model may be used to evaluate options on various types of underlying instruments, but significant modifications are necessary. In addition to financing costs, for example, the formula for commodity options must incorporate storage costs over the option’s life, whereas the formula for securities must consider expected dividends or interest income. Conventional options on futures contracts, on the other hand, entail no holding costs. And the formula for “futures-style” options on futures must recognize that neither holding costs nor short-term rates are a factor in pricing.

These adjustments have implications for the “put-call parity” relationship, which provides information about the relative time values associated with puts and calls. For securities, put time value will exceed call time value if expected dividends or interest income exceed financing costs. In the case of conventional commodity options, call time value always exceeds put time value. The time value of a conventional put (call) on a futures contract will exceed call (put) time value if the call (put) options is in-the-money. Put and call time values are always equal for futures-style options on futures.

The authors provide a computer program, written in BASIC, for calculating “fair market” put and call option premiums for options on securities, commodities and futures.

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