# Transforming 3M volatilities into 6M volatilities in EUR forecast curves

I have implemented a stripping algorithm to extract forward volatilities from cap/floor flat volatilities for different currencies. I am however struggling a bit when implementing a method to convert the first 2 year 3M flat vols into 6M flat vols for the EUR currency.

The information I have available is the forecast curves (1M, 3M, 6M) and discount curve.

I have found some papers detailing a solution that involves the calculation of the correlation coefficient between different 3M forward rates, but that is unfortunately information that is not available to me. I have also found a paper from Bloomberg ("Bloomberg Volatility Cube" by Zhang and Wu) with some standard formulas to do the conversion, but they do not take into account the basis spread, which to me it seems key in doing the conversion.

Any help or guidance from professional practitioners would be very helpful.

Thanks in advance!

• I've looked into this. I'm pretty sure there is no accepted method for this -- I couldn't find one. The spread is essentially an expectation of counterparty credit risk, similar to the spread between an IBOR 3M and an IBOR 6M (the basis spread you are mentioning). You kinda see something similar in the swaption volatility surface. A (5x10) swaption overlaps with a (5x5) and a (10x5) swaption, but there is no way to determine the spread in volatility between these instruments using other instruments. Market quotes is all that matters.
– Olaf
Commented Apr 1, 2016 at 14:16

## 1 Answer

You won't get a arbitrage-free estimate of 6M curve volatility based on 3m curve. That point is actually a relief -- meaning that if you make reasonable assumptions, it should be fine. The basis is all that matters here along with the correlation between the basis and the 3m curve. It becomes an empirical problem. Having said those, if you have to have something that's theoretically sound, you may come up with multi-factor interest rate model that fit into both 3m and 6m curves. Many shops think this is more appealing (good sell to risk managers), but in reality it just turns one assumption into another assumption.