Hello everyone,
We know that the forward price for an underlying asset which has benefit and cost of holding it can be calculated as:
F0(T) = [S<sub>0</sub> + PV<sub>0</sub>(cost) - PV<sub>0</sub>(benefit)](1 + Rf)T
However, we can also create a synthetic asset by buying a risk-free discount bond that returns F0(T) and taking a long position in a forward contract. Therefore, due to no-arbitrage condition and because there is no cost of entering a forward contract, we can calculate forward price as:
F0(T)/(1+Rf)T = S0 <=> F0(T) = S0(1+Rf)T
So we have 2 different ways of calculating forward price which leads to PV0(cost) = PV0(benefit) or that there is an arbitrage opportunity.
Can anyone please help me explain this? Thank you.