# Forward/futures contracts that satisfy $F=S\exp(rT)$

I am interested in estimating riskless rates from forward/futures data. The standard forward pricing formula is given by

$$F=S\exp(rT).$$

From this we can solve the interest rate used in pricing as a function of the spot and forward prices:

$$r=\frac{1}{T}\log(F/S).$$

Now the issue is that the formula assumes no dividends and in the case of commodities, no convenience yields and storage costs. These modify the formula in well-known ways, but complicate the issue as they need to be estimated separately.

My question is: for which contracts is this formula approximately correct, i.e. the underlying pays (approximately) no dividends and the convenience yield and storage costs are small?

Precious metals are often thought to have relatively small net storage costs. Some stocks have never paid dividends but this is rare for mature firms. Do you have other ideas?

• Rates will be the most liquid and easily obtainable market values - so I think the most reliable way to get an implied rate is via FX forwards (covered interest rate parity) using actual daycount, not continuous rates. Spot, forward and one rate; imply the other (less liquid usually but if needed, also works the other way around). Doesn't really answer your question but if the intention is to imply rates, I think it's the most reliable solution. Aug 10, 2021 at 22:42
• @AKdemy Thanks. However, from CIP I can only infer rate differences between countries not absolute rates.
– fes
Aug 11, 2021 at 5:20
• What is an absolute rate? If you think of the second rate as a dividend, it's no different from futures conceptually. Just a lot cleaner and no need to make "guesses" about dividends (or convenience yields) because it is easy to get a reliable market rate for interest rates. Aug 11, 2021 at 6:02
• @AKdemy How do you infer the euro interest rate $r_{EUR}$ from CIP without making assumptions about the US rate?
– fes
Aug 11, 2021 at 6:12
• That is my whole point though. You don't need many assumptions. Rates are easy to obtain as long as you have access to market data and reliable curves. Will be more reliable than some.illiquid future where nothing but a single interest rate may matter. Aug 11, 2021 at 6:15