# What exactly is the annualized forward premium?

A forward contract has a premium of $0$ because it is an obligation to buy or sell something in the future (hence there is more risk). Call and put options, on the other hand, have premiums of $C$ and $P$ respectively where $C,P>0$ because one has the option to exercise it in the future (hence there is less risk). We price call and put options by using put-call parity: $$PV(F_{0,T}) = C-P+PV(K)$$

The annualized forward premium is defined as $$A = \frac{1}{T} \ \ln \left(\frac{F_{0,T}}{S_0} \right)$$

Question. What is the purpose of defining $A$? What utility does is serve? It is not a premium in the sense of call and put options. Yet it still has the same name.

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## migrated from math.stackexchange.comAug 7 '11 at 16:36

This question came from our site for people studying math at any level and professionals in related fields.

The word "premium" in forward premium is more akin to risk premium than it is to option premium. In fact, the forward premium may be negative, whence it is called a forward discount. The premium/discount is merely the difference between the spot and forward prices, which may be due to interest rates and/or interest rate differentials and cost of carry (dividends).

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