Question

Determine the lower bound of the price (minimum price) for a six month call when the share price is 100, the call’s exercise price is 100, and the interest rate for the six month period is 4 per cent.

Answer 1

The question is not very clear as it does not provide compounding frequency and whether the rate of 4% is annualised or not

Hence, giving all the possible case solutions

Case A: ASSUMING RATE OF 4% IS ANNUALISED RATE

Case 1: Continuous Compounding
Lower bound for European Call option is MAX(S0-Ke^(-rt),0)=MAX(100-100*e^(-4%*6/12),0)=1.980132669

Case 2: Annual Compounding
Lower bound for European Call option is MAX(S0-K/(1+r)^t,0)=MAX(100-100/(1+4%)^(6/12),0)=1.941932431

Case B: ASSUMING RATE OF 4% IS NOT ANNUALISED RATE

Case 1: Continuous Compounding
Lower bound for European Call option is MAX(S0-Ke^(-rt),0)=MAX(100-100*e^(-4%),0)=3.921056085

Case 2: Annual Compounding
Lower bound for European Call option is MAX(S0-K/(1+r)^t,0)=MAX(100-100/(1+4%),0)=3.846153846