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JejeBelfort
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Posts: 9
Joined: December 7th, 2016, 3:02 pm

Caps pricing - How to build the caps volatility curve?

December 19th, 2016, 5:23 pm

Hello everybody,

I would like to price some caps using Black's formula (see eq (1.26) from Brigo & Mercurio bible Interest Rate models: Theory and Practice or eq. 5 of the reference further below.
Basically, pricing a caps boils down to price a strip of caplets (with the use of Black's formula). To do so, one of the required ingredient is the implied volatility.
I understand that this volatility can be bootstrapped from caps volatility quotes.
However, say I only have ATM caps volatility available, but I have to price some caplets that are not likely to be ATM (the underlying LIBOR rate changes frequently).

1) Is it a strong assumption to say that my volatility curve is constant across strikes? If not, then I can price my caplets at each tenor given this term structure of the volatility I can build from ATM market quotes (say at 1Y, 2Y, ..., 5Y, 7Y and 10Y). I can then infer the caps price.

2) Should I have the possibility to get swaptions data, can they be used to build the caps volatility surface? More generally, are there additional traded instruments that can be used to build the implied volatility surface that is used to price caplets?

An available reference on the topic can be found here: http://www.opengamma.com/sites/default/ ... ngamma.pdf.

Thank you in advance for your help,
Cheers,
Jeje
 
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Martinghoul
Posts: 188
Joined: July 18th, 2006, 5:49 am

Re: Caps pricing - How to build the caps volatility curve?

December 20th, 2016, 4:30 pm

You should be able to get premia for specific strike caps and floors.  You can then use those for your process.