G2++: Calibration to market data

secret2 · September 28th, 2011, 11:50 pm

I am trying to implement the G2++ short rate model as detailed in Brigo. I am wondering, suppose I want to calibrate the model to market cap (or floor, or swaption, not really the point here) data, is it better to1. calibrate to the cap/floor/swaption formula; or2. Treat the cap/floor/swaption as a portfolio of options on bonds as in Jamshidian?Or does it matter in principle?Thanks!

mathmarc · September 29th, 2011, 4:11 pm

QuoteOriginally posted by: secret2I am trying to implement the G2++ short rate model as detailed in Brigo. 2. Treat the cap/floor/swaption as a portfolio of options on bonds as in Jamshidian?If by "Jamshidian" you mean the Jamshidian decomposition described in the paper "An Exact Bond Option Formula", it is valid only for a one factor model (under some monotonicity condition). The G2++ is a two factor model. The option 2. is not possible.

secret2 · September 29th, 2011, 5:08 pm

Huh, I see. I don't have a chance to re-read the paper yet, I always thought the decomposition of cap or swaption is model-independent. Where soes it break down for multi-factor models?

chartreuse · October 3rd, 2011, 7:31 pm

I am interested in knowing what market prices to calibrate the 2FHW tree to. Also, are trinomial trees better than using a MC simulation method?

Joshua2004 · October 6th, 2011, 1:51 pm

you do not need to implement tree or PDE, I implemented 5 yr ago with FFT method, the calculation is very fast. Because you only need to roll back onto the exercise date of your contract.

chartreuse · October 14th, 2011, 7:43 pm

I am confused. I'm a beginner so please bear with me.I posted a new question which is tangentially related to the original question: http://www.wilmott.com/messageview.cfm? ... d=87047Can anyone comment on whether using a tree (binomial or trinomial) or MC simulation would be advisable for MBS?Thanks!

bearish · October 14th, 2011, 7:53 pm

You will probably need to use MC since prepayments are notoriously path dependent. You have not picked an easy problem to work on as a beginner...

secret2 · October 14th, 2011, 9:12 pm

@Joshua2004:FFT is cool, but for things with complicated payoff and cash flow (MBS and alike) is it practical?Also, for choosing x(0) and y(0) for simulation, are they determined once the model is calibrated? For one-factor we have r(0) "from the market" but for multi-factor models in general how do we decide?