The standard put-call parity result does not include equalities based on buy-and-hold strategies for options on the minimum or maximum of two risky assets and for quantity-adjusting options. This article generalizes put-call parity to these contracts. International put-call parity relations and the pricing of a new forward contract, an absolute-value spread forward, is derived from the put-call parity generalization to options on the minimum or maximum of two risky assets. Finally, an inequality comparing the price of quantity-adjusting options to portfolios of standard options is presented, showing that the QAO contract, in the absence of arbitrage opportunities, is cheaper than the portfolio of standard currency and equity contracts which might be used to hedge the domestic value of a foreign portfolio.
Responding to allegations of model errors: SEC enforcement trends