the box anything under 20 is profit and long anything over, has hedged all risk . A present value of zero for B leads to a parity relation. Two well-known parity relations are: Spot futures parity: The current price of a stock equals the current price of a futures contract discounted by the time remaining until settlement: Put call parity: A long European call c together with a short European put p at the same strike price K is equivalent to borrowing and buying the stock at price S. In other words, we can combine options with cash to construct a synthetic stock: Note that directly exploiting deviations from either of these two parity relations involves purchasing or selling the underlying stock. The box spread Now consider the put/call parity equation at two different strike prices and . The stock price S will disappear if we subtract one equation from the other, thus enabling one to exploit a violation of put/call parity without the need to invest in the underlying stock. The subtraction done one way corresponds to a long-box spread; done the other way it yields a short box-spread. The pay-off for the long box-spread will be the difference between the two strike prices, and the profit will be the amount by which the discounted payoff exceeds the net premium. For parity, the profit should be zero. Otherwise, there is a certain profit to be had by creating either a long box-spread if the profit is positive or a short box-spread if the profit is negative. [Normally, the discounted payoff would differ little from the net premium, and any nominal profit would be consumed by transaction costs.] The long box-spread comprises four options, on the same underlying asset with the same terminal date. They can be paired in two ways as shown in the following table (assume strike-prices < ): Reading the table horizontally and vertically, we obtain two views of a long box-spread. A long box-spread can be viewed as a long synthetic stock at a price plus a short synthetic stock at a higher price . A long box-spread can be viewed as a long bull call spread at one pair of strike prices, and , plus a long bear put spread at the same pair of strike prices. We can obtain a third view of the long box-spread by reading the table diagonally. A long box-spread