Aurora Borealis
1 November 1986 Financial Analysts Journal Volume 42, Issue 6

Pricing American Options: Managing Risk with Early Exercise

  1. Edward A. Brill
  2. Richard B. Harriff

The prices and hedge ratios of American spot and futures options are likely to differ significantly from estimates provided by the traditional Black-Scholes and Black option pricing models. Because these models do not take into account the early exercise capability of American options, they cannot explain the differences between the prices of American spot and futures options, nor the convergence of futures and spot prices at expiration.

The probability of early exercise will depend on the relation between the riskless interest rate over the period of the contract and the dividend rate (or equivalent) of the underlying spot commodity or instrument. For example, when the cost of carry is positive, and futures contracts trade at a forward premium, a call on futures is more likely to be exercised early than a call on spot, and a put on spot is more likely to be exercised early than a put on futures. The Black-Scholes model would significantly underprice American futures calls and spot puts.

Because of the effects of early exercise, American hedge ratios can differ substantially from their European counterparts; the divergence increases, moreover, as volatility decreases and as time to expiration approaches. The importance of adjusting traditional option models for early exercise become apparent when one considers that more accurate hedge ratios will decrease portfolio volatility without any commensurate decrease in return.

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