# Equity and Currency Forward Valuations

Ok, so I’ve combed through AF and found explanations to this question, but I still don’t get it.

For both equity index and currency forward valuations, you’re supposed to discount the St by their dividend rate and foreign currency rf, respectively. It has been explained in AF that it’s because those are the nominal rates that wouldn’t represent settlement at t, specifically.

But t is the value today, as of valuation date, so why would I need to discount that even further into the past?

I’m trying to make out your question, but if I’m understanding you correctly this would be my answer: any forward commitment is something you’re contractually agreed to transact at at some future date. If you re-price that forward commitment today with whatever the relevant variables are, it’s still an amount to be transacted on at a future date. So the difference between what you originally agreed to, and what you could agree to today if you wanted to liquidate your position needs to be discounted from T to t.

Hope that helped!

Thanks B8M23, but I’m confused (and maybe this is the materials’ fault) because the generic value of a forward contract is described as such (long):

St - [F(0,T) / (1+r)^(T-t)]

However, since the St is today’s value (e.g., currency exchange rate for a currency forward), it didn’t seem to qualify as a forward/obligated rate to me, needing discounting? That generic formula works for forward contracts on bonds so I’m confused on the inconsistency.

You can always rewrite

St - [F(0,T) / (1+r)^(T-t)]

into

[S\_T - F(0,T)] / (1+r)^(T-t), since S_T = St x (1+r)^(T-t)

So, your obligation at maturity T is [S\_T - F(0,T)], which is what you’re looking for

IF and only IF I understand your question, I may have an answer…

The dividend yield and the interest rate on a currency are the Carry Benefits. You only have a contract, not the asset itself, so you aren’t really getting the carry benefits.

You’re locked in to buy it, but you aint gettin no dividend. You aint investing that damn currency at the risk free rate! So by discounting the St in the formula, The value of the long position goes down. Why? Cause you aint gettin them carry benefits!

Sorry, im usually a little more professional. But the constant studying this weekend has made me loopy. I could be wrong, but this explanation makes sense to me You can always rewrite

St - [F(0,T) / (1+r)^(T-t)]

into

[S\_T - F(0,T)] / (1+r)^(T-t), since S_T = St x (1+r)^(T-t)

So, your obligation at maturity T is [S\_T - F(0,T)], which is what you’re looking for

[/quote]

That helps me understand the bond forward contract better. If you don’t mind taking a look, I put the exact example below for better depth into my confusion:

For an equity index forward contract at time=t, value calc below

Vt=([St/(e^(div yield*(T-t)/365))])-[F(0,T)/e^(risk free rate*(T-t)/365)))]

For a currency exchange, it’s similar but you divide the St exchange rate by (1+appropriate rf rate)^(T-t).

My understanding was just St = market value of the underlying asset. So why divide those St(s) by anything?

Thanks btw