Forwards and Futures
As the name would suggest, a derivative is a financial instrument whose value is derived from the level of an underlying asset. In this chapter we introduce our first derivative: a forward contract, in which a buyer and seller of a given asset agree to trade based on current prices but with settlement of the trade—that is, the actual exchange of the asset for payment—delayed until a time in the future (anywhere from a few days to several years away). While a forward contract may be written on virtually any type of asset, we will focus primarily on forwards with equity underliers, either single stocks, baskets of stocks, or indices.
To price a forward fairly, we need to determine how the act of delaying the settlement changes the economics of the transaction for both parties. Using the current price as a reference, our goal is to calculate the “fair price” to pay for the asset such that the economics of the forward-settled transaction are identical to those of the equivalent spot market trade. (The spot market, refers to the trading of the underlier for standard settlement [i.e., T+3] and can, in the case of equity underliers, be replaced by “cash market.” I use the more general term “spot” in this chapter because of its common use with futures, which can have many non-equity underliers.)
Before deriving the exact formula for the fair price of a forward, we need to develop some intuition about what it tells us and where it comes from. ...