郑振龙 期权期货及其衍生市场 Chapter 2

Delivery
If a contract is not closed out before maturity, it usually settled by delivering the assets underlying the contract. When there are alternatives about what is delivered, where it is delivered, and when it is delivered, the party with the short position chooses. A few contracts (for example, those on stock indices and Eurodollars) are settled in cash
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Short Hedge
Suppose that
F1 : Initial Futures Price F2 : Final Futures Price
S2 : Final Asset Price
You hedge the future sale of an asset by entering into a short futures contract Price Realized=S2 -F2+F1 = F1 + Basis
Optimal Hedge Ratio
Proportion of the exposure that should optimally be hedged is where
h r s s
S F
S : spot price, F : futures price, sS : standard deviation of DS , sF : standard deviation of DF r: coefficient of correlation between DS & DF
Basis Risk
Basis is the difference between spot & futures Basis risk arises because of the uncertainty about the basis when the hedge is closed out
Long Hedge
Example of a Futures Trade
An investor takes 2 long positions in December gold futures contracts on June 3


2

contract size is 100 oz. futures price is US$400 margin requirement is US$2,000/contract (US$4,000 in total) maintenance margin is US$1,500/contract (US$3,000 in total)
期货合约与远期合约比较
标准化程度不同 交易场所不同 违约风险不同 价格确定方式不同 履约方式不同 合约双方关系不同 结算方式不同
期货市场的功能
转移价格风险的功能 价格发现功能

What can be delivered, Where it can be delivered, & When it can be delivered
Settled daily
Margins
A margin is cash or marketable securities deposited by an investor with his or her broker The balance in the margin account is adjusted to reflect daily settlement Margins minimize the possibility of a loss through a default on a contract
Hedge Ratio
Short Hedge
DV DS hDF
s
2 P
s
2 P
2 S
h s
2 2 F
2 F
2 h rs S s
F
F
s
h
2hs
2 rs S s
0
h r
s s
S F
Rolling The Hedge Forward
We can use a series of futures contracts to increase the life of a hedge Each time we switch from 1 futures contract to another we incur a type of basis risk
Suppose that
F1 : Initial Futures Price F2 : Final Futures Price
S2 : Final Asset Price
You hedge the future purchase of an asset by entering into a long futures contract Cost of Asset=S2 -F2+F1 = F1 + Basis

used for the daily settlement process
Volume of trading: the number of trades in 1 day
Convergence of Futures to Spot (Figure 2.1, page 32)
Futures Price
Roughly speaking, this is what the treatment of futures in the U.S.and many other countries attempts to achieve
Long & Short Hedges
A long futures hedge is appropriate when you know you will purchase an asset in the future & want to lock in the price A short futures hedge is appropriate when you know you will sell an asset in the future & want to lock in the price
Day
2,660 + 1,340 = 4,000 . . . . . < 3,000
17-Jun 387.00 . . . . . .
24-Jun 392.30
(1,140) . . .
260
(2,600) . . .
(1,540)
2,740 + 1,260 = 4,000 . . . . . .
5,060 0
Spot Price
Spot Price Futures Price
Time
Time
(a)
(b)
Questions
When a new trade is completed what are the possible effects on the open interest? Can the volume of trading in a day be greater than the open interest?
Some Terminology
Open interest: the total number of contracts outstanding

equal to number of long positions or number of short positions
Settlement price: the price just before the final bell each day
Choice of Contract
Choose a delivery month that is as close as possible to, but later than, the end of the life of the hedge When there is no futures contract on the asset being hedged, choose the contract whose futures price is most highly correlated with the asset price. There are then 2 components to basis: F1+(S2*-F2)+(S2-S2*)
Other Key Points About Futures
They are settled daily Closing out a futures position involves entering into an offsetting trade Most contracts are closed out before maturity
Accounting & Tax
If a contract is used for


Hedging: it is logical to recognize profits (losses) at the same time as on the item being hedged Speculation: it is logical to recognize profits (losses) on a mark to market basis