 # interest rates in forward contracts

hy you all,

i have one question.

When determining forward price of a contract, we usually get RFR. In a practice problem I got 3 month, 6 months and 12 months rates, and I was supposed to get the FP. One dividend is due in 3 months, one in 6, and the contract is due in 6 months.

Which rate do I use to discount dividends, which for the contract?

Same question for put-call parity, sinthetic put, 6 months, same problem, which rate do I use to discount the bond?

And why?

D

For a payment in 3 months, use the 3-month rate.

For a payment in 6 months, use the 6-month rate.

I have one more question, continuing on the last one.

If we have 3 month discount rate, and 3 month dividend (i.e. 0.5% rate), why do we use 1.005^1/2 in case of 6 month contract to get the PV.

If we had risk free rate, and 1 year contract, we would use (1+RFR)^12/12, why ist the same logic here?

If you see my problem?

At least they used the 1.005^1/2 in the answers, and i dont get it?

Thanks again,

D

You use 1.005^1/2 because you’re attempting to bring the current spot price to the forward rate at expiry. Non-arbitrage theory says that the spot should only move up or down in accordance to the movement of the RFR during the time frame.

Don’t forget that you are bring the dividends forward in time to match expiry of the contract.