
262 INTERNATIONAL FINANCIAL MANAGEMENT
where
C = Value of the option
S = Spot rate of the underlying currency
The delta of a European call option on a currency, in terms of the Black–Scholes model, is
∆=
−
eN
r
f
T
d
1
For a European put option on a currency, the delta is
∆= −
−
eNd
r
f
T
[(
]
The Black–Scholes model implies a riskless portfolio that is created by taking a position in
the underlying currency for a position in the option.
The same can also be expressed as follows:
h
Su d
u
d
=
−
0
(or)
h
Su d
u
d
=
0
−
This indicates the number of call options needed to create a risk-free hedge portfolio.
Suppose that a hedge ratio is (–) 2.00. The hedger can ...