Spot and Forward Premiums for European FX Options

Summary

The document distinguishes a European FX option’s forward premium from its spot premium by expressing the Garman–Kohlhagen option value using the forward exchange rate. In this formulation, the option payoff terms are discounted at the domestic-currency interest rate. The forward premium is described as the value before applying that discount factor; discounting it to the premium payment date gives the spot premium.

The explanation emphasizes that the discount period runs to delivery and depends on the dates used, including the interval between delivery and premium payment. It cites a 365-day year convention and notes that many currencies use a standard T+2 premium date. The answer assumes this specific option-pricing meaning of “forward premium,” rather than a broader FX-market use of the term. It offers a compact relationship, but does not provide a worked numerical example or discuss currency-pair-specific conventions beyond the stated assumptions.

Key ideas

• The forward exchange rate can be used to express the Garman–Kohlhagen option formula.
• The forward premium is obtained before applying the domestic-rate discount factor.
• Discounting the forward premium to the premium payment date gives the spot premium under the described convention.
• The discount period depends on delivery and premium dates, with the answer assuming a 365-day basis.

Tags

# Difference b/w Spot Premium and Forward Premium for FX Options


# Difference b/w Spot Premium and Forward Premium for FX Options












Can someone elaborate the difference between the two, and what is the typical convention used in markets? If there is a mathematical relationship. Any helpful links/guides would be appreciated as well, all in the context of European FX Options.

## Answer by AKdemy (score 4, accepted)

https://quant.stackexchange.com/a/63432

I am assuming you do NOT refer to Investopedia: Forward Premium which does not change the way you value an option.

I assume you mean the following: Wikipedia: Garman-Kohlagen

The call formula (similar for put) can also be expressed in terms of Fwd instead of S (covered interest rate parity) which yields:

$$exp^{-r_d*t}[FN(d_1) - KN(d_2()]$$ where $r_d$ is domestic interest rate (in case of EURUSD, the USD rate). I prefer to use ccy1 and ccy2 (CCY1CCY2) to avoid any potential confusion.

If you exclude discounting $(exp^{-r_{ccy2}*t})$ you get forward premium: discount this to your premium date(usually standard T+2 for many currencies), you get spot premium.

Note that `t` in the discount factor is time to delivery, which is days/365 (assuming 365 daycount). Days is computed as actual days between delivery date and premium (or spot date).

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.