I'm reading Brigo D., Mercurio F. Interest Rate Models - Theory and Practice (Springer, 2006)(ISBN 3540221492) and also a source article on LMM cascade calibration to swaptions by Brigo and Morini.

I completely confused with notation. From what I understand it follows that they reference to volatility of swaptions that mature at time T=0. Either I miss something basic or there are no such swaptions.

Here are more details.

In the article in section 3 they introduce notation for black's swaption volatility $V_{a,b}$ - this is vol of swaptions with maturity at $T_a$ and underlying swap length $T_b - T_a$. But in next section they write: enter image description here

where formula 8 is how to calculate swaption vol from cap vols: enter image description here

My main question is - do $V_{0,1}$, $V_{0,2}$ have any meaning under these definitions (volatility of swaps that mature at T=0 with length 1 and 2 years)?

Also in their book on page 323 in section 7.4 they provide table that completely confuses me. enter image description here

How do indices of $V$'s correlate with these maturities and lenthts? From my understanding table should look like this:

$V_{1,2} V_{1,3} V_{1,4}$

$V_{2,3} V_{2,4}$



Thanks to my research leader, I found what I missed. $V_{0,1}$ is vol of swaption that matures at $T_0$ which is not 0 (as I thought), rather it is maturity of the first libor. So $V_{0,1}$ is the closest available point on market. And now this is all clear with table on page 323 in section 7.4. $V_{0,2}$ is realy vol of swaption that matures at $T_0$=1y and has length = 2y.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.