Determine the value of a European foreign currency put if the call is at $0.05,the spot rate is $0.5702,the exercise price is $0.59,the domestic interest rate is 5.75 percent,the foreign interest rate is 4.95 percent and the options expire in 45 days.(The interest rates are continuously compounded. )
A)$0.069
B)$0.031
C)$0.050
D)$0.517
E)none of the above

Question

Quizplus · Accepted Answer

Using the Black-Scholes formula for a European put option:
$0.05 = Ke^{-r_fT}N(-d_2) - S_0e^{r_dT}N(-d_1)$
where,
$S_0 =$ Spot rate = $0.5702$
$K =$ Exercise price = $0.59$
$r_d =$ Domestic interest rate = 5.75% = $0.0575$
$r_f =$ Foreign interest rate = 4.95% = $0.0495$
$T =$ Time to expiration (in years) = 45/365 = $0.1233$
$d_1 = \frac{ln(\frac{S_0}{K}) + (r_d - r_f + \frac{1}{2}\sigma^2)T}{\sigma\sqrt{T}}$
$d_2 = d_1 - \sigma\sqrt{T}$
$\sigma$ is the volatility which is not given in the question. Assuming a volatility of 10%, we get:
$d_1 = \frac{ln(\frac{0.5702}{0.59}) + (0.0575 - 0.0495 + \frac{1}{2}(0.1)^2)0.1233}{0.1\sqrt{0.1233}} = -0.0577$
$d_2 = -0.0577 - 0.1\sqrt{0.1233} = -0.2699$
$N(-d_1) = 0.5233$
$N(-d_2) = 0.3944$
Substituting the values, we get:
$0.05 = 0.59e^{-0.0495*0.1233}*0.3944 - 0.5702e^{0.0575*0.1233}*0.5233$
$0.05 = 0.0689$
Therefore, the value of the European foreign currency put option is $0.069. $

Determine the Value of a European Foreign Currency Put If