Topic 2 Forwards and Futures. Futures and Forwards. The purpose of this lecture is to develop an understanding of the futures and forwards markets. We will first examine the mechanics of the futures markets. Contract specification Margin account behavior
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Most of the time positions are closed out by taking opposite positions in the contract right before the close of the contract. Occasionally, however, a party will take delivery, so it is important that we understand how the delivery mechanism works.
basis= spot price of asset to be hedged - futures price of contract used
S2 + (F1 - F2) = 2.0 + (2.20 - 1.90) = $2.30
For financial futures, basis risk tends to be small. This has to do with arbitrage being relatively easy to implement, and so prices are kept “in check”. The basis risk that does exist is largely due to the unknown future risk-free interest rate and its effect on the price.
If the asset to be hedged is not the one on which the futures contract is based, there is additional basis risk. Define S*2 as the price of the asset underlying the futures at time 2, and S2 be the price of the asset actually being hedged.
Frequently a potential hedger will have two choices of which contract they will use.
An important issue is how many contracts to use to create the hedge. The hedge ratio is the ratio of the size of the position taken in futures contracts divided by the size of the exposure:
HR = (size of futures position)/(size of exposure)
δV/δh = 2hσ2h + 2ρσsσh = 0
2hσ2h = -2ρσsσh or hσh = -ρσs
σF= 0.0313 (st. deviation of change in HHO futures price)
σS= 0.0263 (st. deviation of change in spot jet fuel price)
ρ = 0.928 (correlation coefficient between the two)
The optimal hedge ratio, therefore is:
Note that Hull shows this as 0.78, because he assumes you realize that since you are hedging against increases in prices, you would be taking a short position in the futures contract.