Evolución de la mortalidad atribuible a alcohol

Futures compared with FRAs

Pricing and hedging FRAs with futures

Trading with interest rate futures

Exercises

OVERVIEW

In general, a futures contract in any market is a contract in which the com-modity being bought and sold is considered as being delivered (even though this may not physically occur) at some future date rather than immediately – hence the name. The significant differences between a “futures contract” and a “forward” arise in two ways. First, a futures contract is traded on a partic-ular exchange (although two or more exchanges might trade identically specified contracts). A forward however, which is also a deal for delivery on a future date, is dealt “over the counter” (OTC) – a deal made between any two parties, not on an exchange. Second, futures contracts are generally stan-dardized, while forwards are not. The specifications of each futures contract are laid down precisely by the relevant exchange and vary from commodity to commodity and from exchange to exchange. Some contracts, for example, specifically do not allow for the commodity to be delivered; although their prices are calculated as if future delivery takes place, the contracts must be reversed before the notional delivery date, thereby capturing a profit or a loss. Interest rate futures, for example, cannot be delivered, whereas most bond futures can.

The theory underlying the pricing of a futures contract depends on the underlying “commodity” on which the contract is based. For a futures con-tract based on 3-month interest rates, for example, the pricing is based on forward-forward pricing theory, explained earlier. Similarly, currency futures pricing theory is the same as currency forward outright pricing theory and bond futures pricing theory is based on bond pricing.

The principle – and the different characteristics of interest rate and cur-rency futures – are most easily understood by examples.

Example 4.1

A 3-month EuroDEM interest rate futures contract traded on LIFFE:

Exchange LlFFE (London International Financial Futures and Options Exchange), where a variety of futures and options contracts on interest rates, bonds, equities and commodities is traded.

Commodity The basis of the contract is a deposit of DEM 1 million (EuroDEM) lasting for 90 days based on an ACT/360 year.

Delivery It is not permitted for this contract to be delivered; if a trader buys such a contract, he cannot insist that, on the future delivery date, his counterparty makes arrangements for him to have a deposit for 90 days from then onwards at the inter-est rate agreed. Rather, the trader must reverse his futures contract before delivery, thereby taking a profit or loss.

Delivery date The contract must be based on a notional delivery date. In this case, the delivery date must be the first business day before the third Wednesday of the delivery month (March, June, September, December and the next two months following dealing).

Trading It is possible to trade the contract until 11:00 am on the last business day before the delivery day. Trading hours are from 07:30 to 16:10 each business day in London for “open outcry” (physical trading, face to face on the exchange), and from 16:25 to 17:59 for “APT” (automated pit trading – computerized trading out-side the exchange).

Price The price is determined by the free market and is quoted as an index rather than an interest rate. The index is expressed as 100 minus the implied interest rate.

Thus a price of 93.52 implies an interest rate of 6.48% (100 – 93.52 = 6.48).

Price movement Prices are quoted to two decimal places and can move by as little as 0.01. This minimum movement is called a “tick” and is equivalent to a profit or loss of DEM 25. This is calculated as:

Settlement price At the close of trading, LIFFE declares an Exchange Delivery Settlement Price (EDSP) which is the closing price at which any contracts still out-standing will be automatically reversed. The EDSP is 100 minus the British Bankers’ Association 3-month LIBOR.

Example 4.2

Yen/dollar futures contract traded on the IMM:

Exchange IMM (International Monetary Market; a division of CME, Chicago Mercantile Exchange, where futures and options on currencies, interest rates equi-ties and commodiequi-ties are traded).

Commodity The basis of the contract is JPY 12.5 million.

Delivery It is possible for the JPY 12.5 million to be delivered, if the contract is not reversed before maturity, against an equivalent value in USD.

Delivery date The third Wednesday in January, March, April, June, July, September, October and December, as well as the month in which the current spot date falls.

Trading It is possible to trade the contract until 09:16 two business days before the delivery date. Trading hours are from 07:20 to 14:00 each business day in Chicago for open outcry, and from 14:30 to 07:05 Monday to Thursday, 17:30 to 07:05 Sundays on GLOBEX (computerized trading outside the exchange – only the next four March / June / September / December months traded on GLOBEX).

Price The price is expressed as the dollar value of JPY 1.

Price movement Prices are quoted to six decimal places, with a minimum move-ment (one tick) of $0.000001. A one tick movemove-ment is equivalent to a profit or loss of USD 12.50.

Settlement price At the close of trading, the EDSP is the closing spot JPY/USD rate as determined by the IMM.

The typical contract specification for short-term interest rate futures is for a

“3-month” interest rate, although, for example, 1-month contracts also exist Amount of contract × price movement ×daysyear

= DEM 1 million × 0.01% × = DEM 2590 360

in some currencies on some exchanges. The precise specification can vary from exchange to exchange but is in practice for one-quarter of a year. Thus the sterling 3-month interest rate futures contract traded on LIFFE, for exam-ple, technically calculates 91q-®days’ settlement.

Suppose, for example, that the sterling futures price moves from 92.40 to 92.90 (an implied interest rate change of 0.5 percent). The settlement amount would be:

Contract amount ×0.0050 ×

q-®

As sterling interest rates are conventionally calculated on an ACT/365 basis, this is equivalent to:

EXCHANGE STRUCTURE AND MARGINS