Question

Suppose a stock valued at $30 today and that European call and put options are offered on this asset today, expire at the same time, and that both carry a strike price of $33. If the premium on the call and put are $12 and $9 respectively and the interest rate stays at 6%, how soon should the options to avoid arbitrage?

Answer 1

CASE 1: Assuming annual compounding
S+P=C+X/(1+r)^t
=>t=log(X/(S+P-C))/log(1+r)=log(33/(30+9-12))/log(1+6%)=3.443872589 years

CASE 2: Assuming continuous compounding
S+P=C+X*e^(-rt)
=>t=-1/r*ln((S+P-C)/X)
=>t=-1/6%*ln((30+9-12)/33)=3.344511591 years