- Forward and Futures Contracts 139
‘m2m’ represents the payments due to marking to market and the last column
shows the interest accrued up to the delivery date.
Scenario 1
n S(n) f(n, 3 /12) m2m interest
0 100 102. 02
1 102 103. 37 − 1. 35 − 0. 02
2 101 101. 67 +1. 69 +0. 01
3 105 105. 00 − 3. 32 0. 00
total: − 2. 98 − 0. 01In this scenario we sell the stock for $105.00, but marking to market brings
losses, reducing the sum to 105. 00 − 2. 98 − 0 .01 = 102.01 dollars. Note that if
the marking to market payments were not invested at the risk-free rate, then
the realized sum would be 105. 00 − 2 .98 = 102.02 dollars, that is, exactly equal
to the futures pricef(0, 3 /12).
Scenario 2
n S(n) f(n, 3 /12) m2m interest
0 100 102. 02
1 98 99. 31 +2. 70 +0. 04
2 97 97. 65 +1. 67 +0. 01
3 92 92. 00 +5. 65 0. 00
total: +10. 02 +0. 05In this case we sell the stock for $92.00 and benefit from marking to market
along with the interest earned, bringing the final sum to 92.00 + 10.02 + 0.05 =
102 .07 dollars. Without the interest the final sum would be 92.00 + 10.02 =
102 .02 dollars, once again exactly the futures pricef(0, 3 /12).
In reality the calculations in Example 6.2 are slightly more complicated
because of the presence of the initial margin, which we have neglected for
simplicity. Some limitations come from the standardisation of futures contracts.
As a result, a difficulty may arise in matching the terms of the contract to our
needs. For example, the exercise dates for futures are typically certain fixed
days in four specified months in a year, for example the third Friday in March,
June, September and December. If we want to close out our investment at the
end of April, we will need to hedge with futures contracts with delivery date
beyond the end of April, for example, in June.