Help - Calibrate Hull & White model

[louislobas]

Hello,

I'm an actuary student currently doing an internship in a bank. My task is to create a credit risk model and in order to simulate interest rates I need to use the Hull & White and Vasicek models.

However I'm struggling to calibrate my rates.

I started by doing in interpolation by cubic splines to my rates to get an expression of the instantaneous forward rate (f(0,t)) and thus the short rate (r(0)).

For the Vacisek model, i calibrated the parameters on the bond prices which gave me satisfying results.

As for the H&W model, it follow automatically the current bond prices so I have to calibrate it on either caps or swaptions but i really know which derivates to take (in term ok stiker and maturity).

Could someone be friendly enough to guide me and help me to understand?

Thanxfully
Me

[JMO]

Originally Posted by louislobas

Hello,

I'm an actuary student currently doing an internship in a bank. My task is to create a credit risk model and in order to simulate interest rates I need to use the Hull & White and Vasicek models.

However I'm struggling to calibrate my rates.

I started by doing in interpolation by cubic splines to my rates to get an expression of the instantaneous forward rate (f(0,t)) and thus the short rate (r(0)).

For the Vacisek model, i calibrated the parameters on the bond prices which gave me satisfying results.

As for the H&W model, it follow automatically the current bond prices so I have to calibrate it on either caps or swaptions but i really know which derivates to take (in term ok stiker and maturity).

Could someone be friendly enough to guide me and help me to understand?

Thanxfully
Me

Have you asked your manager? Do that first.

Also, this probably should be in the Finance/Investments area. As the person who created the thread, you can move it there. Use Thread Tools, Move or Copy.

[louislobas]

Originally Posted by JMO

Have you asked your manager? Do that first.

Also, this probably should be in the Finance/Investments area. As the person who created the thread, you can move it there. Use Thread Tools, Move or Copy.

I did, but he didn't know. I also asked my professors but since the university is being restored, they're all on vacations.

[Hydraskull]

I can provide some limited guidance. Which instrument to use for calibration will depend on the intended use of your model.

What are you trying to price? You are using the model to price something, and you want your estimated price to be as close to what the market would estimate the price at, if your instrument was traded openly on the market.

So, for calibration, you want to use the instruments that most closely resemble the instrument you are pricing. Then your model is basically a tool for interpolating between market quotes. Or extrapolating.

[louislobas]

Thanks

I want to things:
The first one is to calibrate the model on my discount rate in order to estimate its value in future dates.

The second is to calibrate the model on any other rate (from its market price) to get the parameters and run simulations of the value of that rate but i don't want to price it directly.
I read that to do so I need the swaption or the caps prices but I don't really understand th process.

[Hydraskull]

Originally Posted by louislobas

Thanks

I want to things:
The first one is to calibrate the model on my discount rate in order to estimate its value in future dates.

The second is to calibrate the model on any other rate (from its market price) to get the parameters and run simulations of the value of that rate but i don't want to price it directly.
I read that to do so I need the swaption or the caps prices but I don't really understand th process.

If this is a credit risk model, the choice of swaptions vs caps for calibration of the risk-free rate process should be a minor detail. Either one should be fine.

The bigger question is how are you modeling credit spreads and defaults?

[louislobas]

I use the CIR model, calibrated from the CDS spreads to retrieve hazard rates.