International Finance: Putting Theory Into Practice

234 CHAPTER 6. THE MARKET FOR CURRENCY FUTURES

Table 6.4:HCnet time value effect att= 2assuming thatF 0 , 2 =f 0. 2

case 1 case 2 case 3

state r net time value att= 2 r net time value att= 2 r net time value att= 2

up 0 5 × 1. 00 −5 = 0.00 0.10 5 × 1. 10 −5 = 0.50 0 5 × 1. 08 −5 = 0.40

down 0 − 5 × 1 .00 + 5 = 0.00 0.10 − 5 × 1 .10 + 5 = -0.50 0 − 5 × 1 .12 + 5 = -0.60

E(.) 0.00 0.00 -0.10

• The buyer of the forward contract simply pays 100 at time 2. This is shown under
  the columns “Cash flows from forward,” in Table 6.3.


• The buyer of the futures contract pays 5 or receives 5, depending on the price
  change at time 1. The balance is then paid at timeT= 2, partly as the last m-
  to-m payment and partly as thehcleg of a spot purchase. Thus, the buyer will
  receive/pay the cash flows shown under the columns “Cash flows from futures”—
  either –5 and –95, or +5 and –105.


• The columns labeled “Difference in cash flows” show the cash flows for the futures
  contract relative to the cash flow of the forward contract.

We see that the futures is like a forward except that the buyer also gets a zero-
interest loan of 5 in the upstate, and must make a zero-interest deposit of 5 in
the downstate. Whether this zero-rate money-market operation makes a difference
depends on interest rates. In table 6.4 we look at three cases: a zero interest rate in
both the up and the down state, a 10-percent interest rate in both the up and the
down state, and lastly an 8% rate in the up-state and a 12% one in the down-state.

• In the zero-rate case you of course do not mind receiving a zero-rate loan in the
  up-state, but you do not think this is valuable either: everybody can get that for
  free, by assumption. Nor do you mind the forced deposit at zero percent in the
  down-state: you can borrow the amount for free from a bank anyway. In short,
  the m-to-m flows do not add or destroy any value when interest rates are zero. It
  follows that the conjectureF=fis acceptable.


• In the case with a 10% interest rate you positively love receiving a zero-rate loan:
  you can invest that money and earn 0.50 on it at time 2. In contrast, now you
  do mind the forced deposit at zero percent: you lose 0.50 interest on it. But if
  the up- and down-scenarios are equally probable, a risk-neutral investor still does
  not really mind,ex ante: the expected time-value effect remains zero. It follows
  that the conjectureF=f is still acceptable when the risk-free rate is a positive
  constant.