Derivatives

CHAPTER 3Forward and Futures Prices

Aims

• To construct a synthetic or replication portfolio whose cash flows mimic the cash flows in an actual forward contract.
• To show how cash-and-carry arbitrage can be used to determine the correct (no-arbitrage) ‘fair’ price for a forward contract on a (non-dividend paying) stock.
• To interpret cash-and-carry arbitrage in terms of the implied repo rate and the actual repo rate.
• To extend our arbitrage approach to determine the fair forward price when the underlying asset pays an income stream (e.g. dividends on a stock) or has storage costs (e.g. oil, wheat) or can be used as an input to the production process (e.g. the convenience yield of owning oil).
• To distinguish between the price of a forward contract at inception and the value of a forward contract that has been in existence for some time.

3.1 PRICING FORWARD CONTRACTS

In this section we analyse how forward and future prices are determined as functions of known variables such as the current market price of the underlying asset and the risk-free interest rate. Forward contracts are easier to analyse than futures contracts, since the latter have the added complication of daily settlement (i.e. marking-to-market) whereas for the forward contract there is one payment at the maturity date. However, it can be shown that the futures price closely follows that of the forward price (for contracts with the same maturity date). Therefore, for the most part the reader can consider the analysis ...