International Finance: Putting Theory Into Practice

4.4. THE MARKET VALUE OF AN OUTSTANDING FORWARD CONTRACT 141

discount the face value at the risk-free rate. For thefc pn, we first compute itsPV
infc(by discounting atr∗), and then translate thisfcvalue intohcvia the spot
price:

Example 4.10
Consider a contract that has 4 years to go, signed in the past at a historic forward
price of 115. What is the market value ifSt= 100, rt,T= 21%, r∗t,T= 10%?

• The asset leg is like holding apnoffc1, now worthPV* = 1/1.10 = 0.90909
  nokand, therefore, 0.9090909×100 = 90.909clp.


• The liability leg is like having written apnofhc115, now worthclp115/1.21
  = 95.041.


• The net value now is, therefore,clp90.909 – 95.041 = –4.132

The generalisation is as follows:

[Market value of

forward purchase

atFt 0 ,T

]

=

PV* of as-

set,fc 1

︷ ︸︸ ︷

1

1 +r∗t,T

×St

︸ ︷︷ ︸

translated value

offcasset

−

Ft 0 ,T

1 +rt,T

︸ ︷︷ ︸

PV of hc

liability

. (4.15)

There is a slightly different version that is occasionally more useful: the value is the
discounted difference between the current and the historic forward rates. To find
this version, multiply and divide the first term on the right of [4.15] by (1 +rt,T),
and useCIP:
[Market value of
forward purchase
atFt 0 ,T

]

=

1

1 +rt,T

1 +rt,T

1 +r∗t,T

St

︸ ︷︷ ︸

=Ft,T,(CIP)

−

Ft 0 ,T

1 +rt,T

=

Ft,T−Ft 0 ,T

1 +rt,T

(4.16)

Example 4.11
Go back to Example 4.10. Knowing that the current forward rate is 110, we imme-
diately find a value of (110 – 115)/1.21 = –4.132clpfor a contract with historic
rate 115.

One way to interpret this variant is to note that, relative to a new contract, we’re
overpaying byclp5: last year we committed to paying 115, while we would have