Futures Options and the Volatility of Futures Prices
证明在无风险利率不变时，欧式期货期权可视为基于一种称为期货债券的资产的欧式期权，从而套用标准期权定价方法；还推导了美式期货期权的额外套利限制，并实证检验了多个期货期权市场的效率及波动率与到期期限的关系。
Assuming nonstochastic interest rates, European futures options are shown to be European options written on a particular asset referred to as a futures bond. Consequently, standard option pricing results may be invoked and standard option pricing techniques may be employed in the case of European futures options. Additional arbitrage restrictions on American futures options are derived. The efficiency of a number of futures option markets is examined. Assuming that at-the-money American futures options are priced accurately by Black's European futures option pricing model, the relationship between market participants' ex ante assessment of futures price volatility and the term to maturity of the underlying futures contract is also investigated empirically.