a) Price a 3-year at the money call for a stock with a forward of 150 and a vol of 30%.

b) Price a 3-year at the money cap for a 1-year rate with a vol of 100 bps.

c) Suppose I wanted to know the PV of the option premium from the question above. Suppose 3 year rates are 4%. What adjustment would I need to make?

please answer part c) based on part a) and b)

At the money options=0.4xFwdxVolxsqrt(t) For normal options, vol is quoted in form of Fwd x Vol so we just use that quote for Fwd x Vol Price a 3-year at the money call for a stock with a forward of 150 and a vol of 30%. =0.4x30%x150xsqrt(3)=31.18 Price a 3-year at the money cap for a 1-year rate with a vol of 100 bps. = 0.4 x 0.01 x sqrt(3) = 0.693% Swaption = 0.4 x Normalized Vol x sqrt(t)

I did part a) and b) here, feel free to use it as a refernce if you think they are right. Build on your answer for part c) please.