Forward Swap Rates, Curve Interpolation, and Discounting Choices

# Interpolating the swap curve


# Interpolating the swap curve












Does anyone know how I can calculate the swap rate in between main tenors for specific dates? For example: what is the implied swap rate in 1 year, 60 days time.

Is there an easy way to do this in Bloomberg? I need to be able to calculate the implied swap rate for 100 different investments over a 7-year range.

## Answer by oronimbus (score 2)

https://quant.stackexchange.com/a/46864

You can calculate the forward starting rates by hand in Excel using the relationship of spot and forward rates. Ignoring any daycount intricacies, we can say that:

$$(1 + r_{2y})^2 = (1 + r_{1y}) * (1 + r_{1y1y})$$ $$r_{1y1y} = \frac{(1 + r_{2y})^2}{1 + r_{1y}} - 1$$

There are plenty of posts on this board that give you more detailed examples and information.

Alternatively you can use Bloomberg's Excel tools that do the interpolation for you. You can find an overview on XLTP XCTK , there are formulas such as:

> =BCurveFwd(BCurveStrip("s23"),"par.mid","term=1y","tenor=1y")

Term and tenor can both be dates here.

## Answer by Phil H (score 2)

https://quant.stackexchange.com/a/46865

Which swap curve are you trying to interpolate? And what swap are you trying to price? The 60d to 1y60d swap (1y long, starting at 60d), or now to 1y60d (not a usual length)?

Really by interpolating the swap rates, easy though it seems, you are implicitly building a curve of forward rates. You are also ignoring the structure of the market where the fixing rate (e.g. a Libor) is not the rate used for discounting (typically an OIS).

The process of constructing a curve of forward rates from market prices is called bootstrapping or curve calibration, and the 'interpolation' you describe would be pricing from that curve.

There are entire systems to provide this calculation for you, or libraries you can use to calculate the rates using a viable market model. The question is really whether you want an exact, defendable answer or an approximate one.

## Answer by Edward Watson (score 0)

https://quant.stackexchange.com/a/47193

yes it sounds like you are looking for forward rates in the form of say 1yr forward 2yr swap. If you simply want a spot starting 3.5yr swap you can use a spline function (bloomberg has a nice one) on the rates that you've shown. If you want forward rates for a libor swap discounted at ois (vanilla) you really can't use oronimbus formula like you might for zero treasury yields. It might work for really short forwards but it will be miles off for like 10y10y. You should use a model (bbg swap pricer works great) or ICVS or similar for that. This is because the transition to ois discounting has made everything more complicated so like you can't just use the old bootstrapping method that you would use for treasuries.