# Pricing a Vanilla swap between coupons; What rates to use?

Vanilla Swap question. Entered into a 5Y fixed for floating HUF swap. Fixed is annual coupons, Float is semi-annual coupons.

1 month later I want to price it. I set up my future values for Fixed coupons for the next 5Y and notional at the end, and my next [coupon + notional] for Float (the coupon is now in 5 months, and a Floating rate is valued at par right after it pays its coupon).

I have the BUBOR rates. For my discount factors for my PV, do I use straight line interpolation of the rates? Or use the next interest rate? For example, with .39Y to go before the floating rate coupon, do I use the 0.5Y rate, the .25Y rate, or the interpolated (weighted average of rate and time) of both?

Also under continuous compounding (e), since my Fixed leg is ACT/365 and BUBOR is ACT/360, do I have to multiply the BUBOR rate by (365/360) before getting my discount rate to make it equivalent?

## 2 Answers

Linear interpolation of the discount factors is not a good idea.

A better idea, in the absence of a full analysis, is to linearly interpolate the logarithm of the discount factors.

You can use the 6M IBOR rate and other yearly tenor IRSs (versus 6M IBOR) to roughly bootstrap the 6M forecast curve. What linearly interpolating the logarithm of the discount factors does is to generate constant overnight (one-day) rates between your knot points. This results in an approximately linearly interpolated 6M rate between knot points. This is the standard method for most simple curves and even more advanced IRS trading desks utilise this form of interpolation in specific sections of their curve.

The best option would be to bootstrap a curve. But lacking shorter interest rates, this doesn't appear to be possible. Linear interpolation is the next best alternative.

Since the BUBOR rates are all annualized, and so long as you're using the portion of the year for the given leg's day count convention, using the given rate (in this case the bootstrapped rate) should be fine.