Question

A put option on a bond has a strike price of 104 1/8 (104.125). The bond has a MD of 17.97 and a YTM of 3.5%. The bond currently trades at 109.24. What yield would make the put option be at the money? (Use MD to get your answer,)

Answer 1

Put option is at the money when strike price is equal to price of the bond

Hence, price of the bond should be=104.125

% change in price of the bond required=(104.125/109.24-1)=-4.6824%

Case 1: Converting MD to Mod D
Assuming the coupon is paid annually
% change in yield required=-% change in price/MD*(1+ytm)=-(-4.6824%/17.97*(1+3.5%))=0.2697%

Yield=3.5%+0.2697%=3.7697%

Case 2: Not converting MD to Mod D
% change in yield required=-% change in price/MD=-(-4.6824%/17.97)=0.2606%

Yield=3.5%+0.2606%=3.7606%