Box Spread: This is another strategy which seeks to exploit the arbitrage opportunities which are available in the market. In case that the options are correctly priced, this strategy would earn only the risk free rate. However, due to existence of imperfections in the market, this strategy can be used to profit on the mispricing in the market. One type of this strategy is the buying of a call option that has a lower exercise price and buying a put with the higher exercise price while selling the call with the higher exercise price and selling the put with the lower exercise price. The value of this box spread at expiration is given by:
Value = max (0, ST – X1) – max (0, ST – X2) + max (0, X2 – ST) – max (0, X1 – ST)
In this case, two of the four options would definitely expire in the money while two would expire out of money. The holder of the box spread basically ends up with the purchase of the underlying with the exercise of one option (either the long call at X1 or the short put at X1) while at the same time, the investor also sells the underlying asset through either the long put at X2 or through the short call at X2. The net effect is that the investor buys the asset at X1 and sells it X2. If the markets are efficient, only the risk free rate would be earned else the anomalies in the pricing of the security would be gained.