The Valuation of Options on Futures Contracts
推导了美式期货期权价值的理性约束，发现提前行权虽可能最优但影响很小，布莱克欧式公式可作近似；在随机利率下，忽略利率位置会导致定价误差-5%到7%。
ABSTRACT Rational restrictions are derived for the values of American options on futures contracts. For these options, the optimal policy, in general, involves premature exercise. A model is developed for valuing options on futures contracts in a constant interest rate setting. Despite the fact that premature exercise may be optimal, the value of this American feature appears to be small and a European formula due to Black serves as a useful approximation. Finally, a model is developed to value these options in a world with stochastic interest rates. It is shown that the pricing errors caused by ignoring the location of the interest rate (relative to its long‐run mean) range from −5% to 7%, when the current rate is ±200 basis points from its long‐run value. The role of interest rate expectations is, therefore, crucial to the valuation. Optimal exercise policies are found from numerical methods for both models.