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Annualized Forward Premium as Spot–Forward Carry

Article Quant Q&A · Author: Damien
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Summary

The document clarifies that a forward premium is not an option premium paid for a right to exercise. It describes the annualized forward premium as the continuously compounded rate implied by the ratio of the forward price to the current spot price over the contract’s time to maturity. The quantity can be positive or negative; a negative value is commonly described as a forward discount.

The explanation treats the forward premium or discount as a measure of the difference between forward and spot prices. That difference may reflect interest rates, cross-market interest-rate differentials, and the cost of carry, including dividends. The text gives a definition and a brief interpretation but does not develop a pricing derivation or discuss how the measure behaves across particular asset classes. It is therefore best read as terminology clarification: the word “premium” here concerns the forward–spot relationship, not an upfront option price.

Key ideas

  • An annualized forward premium expresses the forward-to-spot price ratio over the contract term.
  • A forward premium can be negative, in which case it is called a forward discount.
  • The term refers to the difference between forward and spot pricing, not an option’s purchase price.
  • Interest rates, rate differentials, and carrying costs such as dividends can contribute to the forward–spot difference.

Tags

FuturesCarryDerivatives pricing
Full text
# What exactly is the annualized forward premium?


# 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.

## Answer by Tal Fishman (score 2)

https://quant.stackexchange.com/a/1616

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).

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.