FX Cash Rates from Overnight and Tomorrow-Next Swap Points

# What is the instantaneous FX rate and used for a FX Forward?


# What is the instantaneous FX rate and used for a FX Forward?












Could someone please explain me what the instantaneous FX rate corresponds to and why it is used in the valuation of an FX Forward trade?

It is defined as: FX_Instantaneous= FX_Spot-(ON+TN)

where ON and TN corresponds to the Overnight and Tomorrow Next Swap Points. Somehow it is related that it is a cash trade but somehow I cannot perform a bridge here? Normally I selltle these physical but cash? How can I perform a evaluation of a FX Forward with this information and not use instead just the FX Spot rate alone.

## Answer by Phil H (score 6, accepted)

https://quant.stackexchange.com/a/42356

If EURUSD Spot is currently trading at 1.21, then trading today for the usual settlement of EURUSD on today+2 would be at 1.21. If you wanted to trade for immediate exchange of EURUSD, what would be the right rate? 1.21? Not really; if EURUSD was expected to go up or down between today and the spot date, I could arbitrarily profit from taking one side or the other.

So just as the market trades the interest rate differences after spot using FX Swap points, it also trades them before spot too. There are two common trades before spot:

ON: Overnight, trades between today and tomorrow. So instead of having USD overnight tonight, you have EUR (or vice versa).

TN: tom(orrow)-next, trades between tomorrow and the next day (i.e. spot for t+2 currencies).

In order to construct an outright FX price for today, you need to buy ON, buy TN and buy Spot, or sell all three. This way the ON back exchange would cancel the TN front exchange, the TN back exchange would cancel the Spot exchange, and you'd be left with a net exchange today at a known price.

I'm not aware of intraday FX forward trades, so presumably 'immediate' is treated as 'today', but given global trades and differences in posting deadlines I wouldn't be surprised if there was a way to trade between the shortest cash posting deadline and the EoD collateralised worlds for an even more immediate requirement.

## Answer by user35980 (score 1)

https://quant.stackexchange.com/a/81031

This is already a really well-answered question. But when learning about this stuff I found it helpful to work backwards i.e. avoid starting with ON and TN points, but rather considering the three kinds of FX rates: CASH, TOM and SPOT. CASH = FX settlement today (the "instantaneous" rate), TOM = FX settlement tomorrow, SPOT= FX settlement in X days (where X is usually 2 which we'll use for simplicity).

Hence CASH is T+0, TOM is T+1 and SPOT is T+2 (the most liquidly traded FX rate given by the market that we all know and love). We also define ON to be the period T+0 to T+1 and TN to be the period T+1 to T+2.

Now, in addition to the SPOT, we know that:

- $r^f_{ON}=$ foreign interest rate from T+0 to T+1

- $r^d_{ON}=$ domestic interest rate from T+0 to T+1

- $\tau^f_{ON}=$ foreign daycount factor from T+0 to T+1

- $\tau^d_{ON}=$ domestic daycount factor from T+0 to T+1

- $r^f_{TN}=$ foreign interest rate from T+1 to T+2

- $r^d_{TN}=$ domestic interest rate from T+1 to T+2

- $\tau^f_{TN}=$ foreign daycount factor from T+1 to T+2.

- $\tau^d_{TN}=$ domestic daycount factor from T+1 to T+2.

With all that in place, from the standard definition of an FX forward we deduce that: $$SPOT=TOM\frac{1+\tau^d_{TN}r^d_{TN}}{1+\tau^f_{TN}r^f_{TN}}$$ and $$TOM=CASH\frac{1+\tau^d_{ON}r^d_{ON}}{1+\tau^f_{ON}r^f_{ON}}.$$ The key thing to note here is that unlike in "normal FX forwards" formulae where SPOT is the starting point and forward points are added to the SPOT, for ON and TN the SPOT is in the future (so it $is$ the $forward$ in that sense). It's also worth mentioning that in the above method TOM needs to be calculated first, then CASH. Again, this is because we are working backwards from SPOT.

Finally, having now calculated our CASH and TOM FX rates, we are able to deduce the so-called ON and TN points simply as:

- $ON_{points}=$ TOM-CASH

- $TN_{points}=$ SPOT-TOM

and this is where the relation CASH=SPOT-($ON_{points}+TN_{points}$) mentioned in the question comes from.

The above explanation is simply to give an intuitive understanding of ON and TN. In practice the market provides the ON and TN points and these will usually differ from points calculated in the aforementioned manner due to presence of cross currency basis (unless of course one uses the cross-currency rate curve in the calculation). But it's helpful to know the mechanics of what's actually going on nonetheless.