Mathematics of the Financial Markets: Financial Instruments and Derivatives Modelling, Valuation and Risk Issues

7

Futures

7.1 INTRODUCTION TO FUTURES

By definition, a future contract is an engagement between two parties – a buyer and a seller – (the seller) to deliver, respectively (the buyer) to receive;

• on a given maturity date,
• a given quantity,
• an underlying financial instrument,
• at a price agreed upfront (on the contracting day).

(The future seller will deliver the underlying, to be received by the future buyer.)

So far, such a definition should also apply to an interbank forward contract. To be qualified as a future contract, the operation must be traded on a futures exchange. This implies two key features.

Contract Standardization

Unlike the interbank market, the futures exchange operations are fully transparent, in prices, volumes and contract specifications. To ensure enough market liquidity for attracting buyers and sellers, the exchange must standardize the contract specifications as much as possible, that is:

• maturities: only 4–12 times a year;
• a nominal (notional) amount for one contract, the “contract size”;
• quoted price intervals, called tick: one distinguishes between the:
  • tick size = minimum price movement, and the
  • tick value = tick size × nominal (notional) amount;

• settlement, at maturity: either physical, that is, in units of the underlying instrument, or in cash. The exchange imposes one of these alternatives, depending on the underlying.

Example. Euro Stoxx 50 futures: standardized contract parameters:

• underlying: Euro Stoxx 50 index;
• maturities: March, June, ...