Investment Theory and Risk Management, + Website

Swaps

Let me motivate this important class of derivatives with an example. Suppose a mining company receives spot price for bauxite (an aluminum ore) but would like to hedge out the risk of prices falling. Since the mining company is naturally long bauxite, it could engage in a continuing sequence of short forward contracts with an aluminum producer who takes the long forward position. Alternatively, if there was an active futures market for bauxite, the company could hedge their price exposure by writing short futures contracts for delivery every period (which they would close out before the delivery date). In either case, the company would need to manage their exposure to price risk continuously and assume the administrative costs of doing so. More importantly, if output from the mine is variable, then the amount of exposure to hedge would be unknown ahead of time, further complicating the hedging strategy. In truth, what the mining company wants to receive is a fixed price of bauxite. They could achieve this by entering into an agreement with a counterparty to swap their variable spot price for a fixed price. Thus, they receive spot, which they trade for fixed. Their cash flows would therefore become (S₁ – x), (S₂ – x),..., (S_T – x), which they can scale by any desired notional amount N. This commodity swap would have value therefore, equal to:

Since future spot prices are unknown, ...