Question

6. (10 points) Assume the Black-Scholes framework. For an at-the-money, T-year European call option on a non-dividend-paying stock you are given that its delta equals 0.5832. What is the delta of an otherwise identical option with exercise date at time 27? Justify your answer

Answer is 0.62 i just need to know how to get the answer

Answer 1

From Black Scholes

d1=(ln(S/K)+(u-vol^2/2)*t)/vol*sqrt(t)

For ATM options, S/K=1 and hence ln(S/K)=0

d1=(u-vol^2/2)*sqrt(t)/vol

Delta of call option is N(d1)

N(d1)=0.5832

=>d1=norminverse(0.5832)

For 2T expiry options

d1'=sqrt(2)*d1

Hence, delta will be N(d1')=N(norminverse(0.5832)*sqrt(2))

In excel, use the below formula

=NORMDIST(sqrt(2)*NORMINV(0.5832,0,1),0,1,TRUE)

=0.616808