Basis Risk in Swap Valuation Under OIS Discounting

# Basis risk, spreads and discounting


# Basis risk, spreads and discounting












There is a lot of information to be read on basis risk, spreads and discounting. After reading some information, I have an idea about what basis risk is about and why this type of risks should be considered, but I don't know very well how one accounts for this risk in practice, say in discounting cash flows in a swap. How is basis risk incorporated here? Is this simply an additional term that is added to the floating rate? Can someone provide me with a clear example?

Secondly, after the financial crisis, one has moved from LIBOR to OIS for discounting purposes. How is the OIS spread (which I assume is the difference between LIBOR and OIS) linked to basis?

Perhaps I am mixing up these things, but I hope someone can explain with a clear example.

Thanks!

## Answer by Attack68 (score 4, accepted)

https://quant.stackexchange.com/a/38349

First lets clear one thing up, 'basis' and 'spreads' are the same thing. Often this is called the 'basis spread'. This represents the difference between curves at different points in time.

For example if from 1st Jan 2019: 6M (from 6M LIBOR cv) is 1.20% and 6M (from 3M LIBOR cv) is 1.10% then the 6M/3M basis on 1st Jan 2019 is 10bps. You have equivalent basis numbers between any curves you choose, 1M/3M or OIS/3M or OIS/6M etc. The specific basis you are interested in referencing discounting is the LIBOR/OIS basis.

Now lets give you a practical example of what happens in a hypothetical scenario:

Say 6M Libor are forecast to be 2% every day for the next five years, i.e. you have a perfectly flat curve. It is not hard to see that the 5Y IRS fixed rate is 2% in that case, and that every cash flow (assuming equal payment frequencies on the fixed and floating legs) would be zero for an IRS struck at 2% (this is irrespective of whatever discount method you choose).

But instead suppose that your fixed rate is struck at 2.10% in 10mm USD. Now if you are the receiver you are ITM by 5,000 USD every 6M cashflow. The total value of the swap is roughly 5K x 10periods x some discounting = say 45K.

Your profit has been derived from the discounting methodology applied, if you have higher discount factors the swap is worth more to you. And that means you need a lower discount (OIS) curve, so if the basis widens this is favourable to you (6M LIBOR remains the same so your floating and fixed cashflows are stable but your valuations of them changes). So you have exposure to basis moves, i.e. you have basis risk.

In this particular case you would have roughly 11 USD pv01 exposure to the 5Y 6M/OIS basis, so if the 6M/OIS basis widened by 1bp you would make 11 USD on mark-to-market. Note this was calculated with the approximation: $$Discounting Basis Risk = \frac{PV}{10,000} * \frac{Tenor}{2}$$

## Answer by MCM (score 1)

https://quant.stackexchange.com/a/38347

Hope that give you an overview and helps you.

In the financial crisis it can be seen on the difference between IBOR spot rates and OIS rates, which we will further refer to as the IBOR-OIS spread. As IBOR market quotes now involve the average credit and liquidity risk of the interbank money market, OIS rates have become the new proxy for the risk-free rate.

The new risk-free curve for discounting is built from OIS rates. We can still decompose the swap into two legs. However, the floating payments estimated by implied forward rates change under OIS discounting.