Calibrating CIR to euro cap premium (methods issue)

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Mikaw
Posts: 1
Joined: Thu Apr 18, 2013 10:02 am

Calibrating CIR to euro cap premium (methods issue)

Postby Mikaw » Thu Apr 18, 2013 10:27 am

Hello everybody,

First, I appologize if I do some mistakes in English (it's not my mother tongue ;) )

Second, I subscribed because I was very suprised that an author takes the time to create a forum to answer to questions. (Sir, I will definetely have a look a your books). I don't know if my question is related to one of your book but I posted my question here because it's hard to find an aswer (forum, teachers didn't help.)

For my master's thesis I'm trying to calibrate a simple one-factor CIR to euro-cap premium. I have concerns about the methodology I'm using.
(purpose of the calibration (Monte Carlo simulation to price a structured swap))

Here is how I procede (I'll try to be as precies as I can):

The euro-cap premium (input, market data):
I take maturities: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 20, 25
I take ATM strike: 0,24 0,27 , etc.
I take ATM premium: 6, 13, 24, etc

I calculate the price for each of these caps with the CIR model (I use finite difference)

I calculate the squared sum of error: sum of (market value - model value)^2

parameters:
r(0)
a (mean reversion speed)
b (mean reversion level)
volatility

Questions:
1) when I calclulate the price of a cap with the model, I use for r(0) the euribor 3m for the cap 1y and cap 2y (because cap 1y and 2y is vs euribor 3m: that is indicated on murex), I use (r0) = euribor 6m for the other cap. Is it correct?
2) When I minimize the sum of the errors, I use the excel solver (GRG non linear):
i put the constraint : 2*a*b > volatility^2
i also set non negative constraints
question: the target is to minimise the sum by changing values : which one ? a, b and the volatility ? Or do I have to calculate the b (mean reversion level) with an average on historical data ?
3) cap 1y and cap 2y is vs euribor 3m so It means that I should do two minimization: one to get parameters for CIR (euribor 3m) and one to get parameters for (CIR 6m) ? This is the big question.
----------------------
once it's done,

I will calculate the implied volatility (Newton-Raphson) from the cap premium obtained with my model, and I will compare them with the black volatility.
I'll be able to criticize the CIR model.


In advance, thank you.

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