Smiling Hybrids

Lapin · Post by **Lapin** » Mon Dec 10, 2007 3:30 pm

Hi,

I am trying to get my hands on Smiling hybrids from V.Piterbarg.

It was published in Risk Magazine in 2006.

Cheers

jsl1 · Post by **jsl1** » Tue Dec 11, 2007 2:45 pm

According to the abstract, the paper deals with option pricing with stochastic interest rate for fx or equity derivatives.

I do not have your paper but suspect that it is based on the some approximation relying on the Markovian projection technique as described by V. Piterbarg (search in SSRN for more details). It may be pretty robust. An alternative relies on using a forward PDE to calculate the local volatility in presence of stochastic rates. You can find some details in the attached article from RiskMag. This technique was also discussed in [url=/Show%20Post.aspx?PostIDKey=64558]this thread[/url].

[url=/User%20Files/869/fwd%20PDE%20technique%20for%20local%20vol%20calibration.pdf]Attached File: fwd PDE technique for local vol calibration.pdf[/url]

Lapin · Post by **Lapin** » Tue Dec 11, 2007 3:42 pm

Thanks for the paper.

Luckily it is about what I am working on right now. It could not be better timing.

Cheers

PS: Do you know if this technique is qidely used in the IBs?

EDIT: Isn't this paper is naturally linked with Piterbarg Averaging Parameter calibration method? In my view Piterbarg makes his study with a fixed form of local volatility function and does not explain how he gets his "instantaneous" parameters from. Here you could work with a market implied local vol surface...

prince · Post by **prince** » Wed Jan 02, 2008 6:17 pm

I think the technique is pretty new and not widely adopted by banks. Market implied local vol surface makes more sense for equity indices and stocks that have a liquid option market.