Calibrating CIR to euro cap premium (methods issue)

Discussion relating to general questions on Market Risk Analysis
Forum rules
DISCLAIMER: We do not warrant or represent that this forum or its content is free of viruses, worms or other code that might be contaminating or destructive. We cannot guarantee that documents or files downloaded from the Site will be free from viruses and we do not accept any responsibility for any damage or loss caused by any virus. Accordingly, for your own protection, you must use virus-checking software when using the forum. You must not post or provide to us via the forum, any document or file which you believe may contain a virus. You must virus check any document or file which you intend to post or provide to us via the forum. You must ensure that any document or file you intend to post to the forum does not contravene any applicable laws or contravene any person's legal rights. We do not accept any responsibility for any damage or loss you may suffer.
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

a (mean reversion speed)
b (mean reversion level)

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.

Return to “General”

Who is online

Users browsing this forum: No registered users and 1 guest