Q6.3 Option Delta

[anand99]

6.3. The spot EUR/USD exchange rate is $1.30 (i.e., USD 1.30 per 1 EUR) with a volatility of 30% per annum. The USD riskless rate is 4% per annum and the EUR riskless rate is 3% per annum. What is the delta of a one-year call option on the Euro with a strike price of EUR/USD $1.36?
a) 0.4980
b) 0.5131
c) 0.5529
d) 0.6078



6.3. A. 0.4980



We substitute the foreign riskfree rate for the dividend yield:

d1 = [LN(S/K) + (Rf_USD - Rf_EUR+ sigma^2/2)*T] / [sigma * SQRT(T)], so that:

d1 = [LN(1.30/1.36) + (4% - 3% + 30%^2/2)*1] / [30% * SQRT(1)] = 0.0329, and

N(d1) = 0.5131, and again substitute the foreign riskfree rate for the dividend yield:

delta of call = N(d1) * exp(-qT) = 0.5131 *exp(-3%*1) = 0.4980


Hi David,

I understand up to the part in bold above. I do not understand how there is a dividend of 3% in the above question. Can you please explain?

 

[ABFRM]

1. It is not dividend, it is risk free rate for Euro.
2. delta of call = N(d1) * exp(-qT) = 0.5131 *exp(-3%*1) = 0.4980 in this formula q shud be replaced by Rf_Euro becoz it is call option on Euro. we always put foreign excahnge rate in place of dividend yield. So the formula becomes delta of call = N(d1) * exp(-Rf_Euro*T).

 

[anand99]

Thanks for the response. I get it now.