P1 T3 Ch10 (notes) Forward and futures

[daisypm]

Hi everyone,

On p.5, from the heading "Forward price given by the Cost of Carry Model", I think the formula is related to forward. When I read the notes, it says "the cost-of-carry model sets the futures price as a function of the spot price", which I think it maybe related to future.

I am not sure whether these formula belong to forward or future or both (as I see on p.10, if there is risk-free rate, then forward equals to future price).
And how can I know when it is mentioning future or forward?

Thanks.

Daisy

 

[David Harper CFA FRM]

Hi @daisypm When pricing forward or futures, in general we do not really distinguish: the cost of carry prices (COC) the theoretical forward or theoretical futures price. In this way, the COC formula--i.e., F(O) = S(0)*exp[(r + u - q - y)*T]--typically refers to either. This follows Hull and is based on a simplifying assumption (which assume a constant interest rate):

"5.8 ARE FORWARD PRICES AND FUTURES PRICES EQUAL? Technical Note 24 at www-2.rotman.utoronto.ca/hull/TechnicalNotes provides an arbitrage argument to show that, when the short-term risk-free interest rate is constant, the forward price for a contract with a certain delivery date is in theory the same as the futures price for a contract with that delivery date. The argument can be extended to cover situations where the interest rate is a known function of time. When interest rates vary unpredictably (as they do in the real world), forward and futures prices are in theory no longer the same."

... beyond this, there is a difference that is explained by the convexity bias (aka, convexity adjustment) that accounts for the difference due to daily settlement. But it's not introduced in the basic COC. I hope that's helpful,