Question

6. (10 points) Assume the Black-Scholes framework. For an at-the-money, T-year European call option on a non-dividend-paying

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

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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

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