# Valuing currency forward in derivative session and in Econ session

Is valuing currency foward calculated differently in economics session compared to derivatives?

In Econ:

V=(FPt - FP)*contract size/(1+r)

in derivative:

V=[St/(1+Rfc)]-[Ft/(1+Rdc)]

I tried to apply the formula from derivative section to Econ section, but got different numbers. Can anyone advise?

i’m unclear on this too…

You have to multiply the derivative formula by the contract size to get it to equal the Economics formula.

unfortunately for the purpose of the test you gotta do it this way.

also, how are you applying the deriv section formula to the equity if you don’t have spot price, etc. do you have an example?

Actually, they’re equivalent, as long as . . .

. . . you’re using either nominal rates for both (e.g., LIBOR), or effective rates for both (e.g., the risk-free rate).

The problem is that the Econ formula is written with nominal rates, while the Derivatives formula is written with effective rates.

I’ll rewrite the Econ formula using effective rates and show you how it works; you’ll forgive the complexity of the notation. (I’ll call the price currency domestic (dc) and the target currency foreign (fc); all exchange rates will be (dc/fc). Also, I’ll remove the contract size, so we’re talking about one unit of fc.)

Vt = (FPt – FP) / {(1 + Rd)^[(T – t)/365]}

By IRP, FPt = St × {[(1 + Rd)/(1 + Rf)]^[(T – t)/365]}. Thus,

Vt = (FPt – FP) / {(1 + Rd)^[(T – t)/365]}

= (St × {[(1 + Rd)/(1 + Rf)]^[(T – t)/365]} – Fp) / {(1 + Rd)^[(T – t)/365]}

= St × {[(1 + Rd)/(1 + Rf)]^[(T – t)/365]} / {(1 + Rd)^[(T – t)/365]} – Fp / {(1 + Rd)^[(T – t)/365]}

= (St / {(1 + Rf)]^[(T – t)/365]} – Fp / {(1 + Rd)^[(T – t)/365]}

Look familiar?