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sriramkgg
Topic Author
Posts: 2
Joined: October 8th, 2017, 6:27 am

### Fixing mean reversion parameter in the 1F HW model

I am trying to calibrate the 1 factor Hull White model to ATM swaptions. The strategy which I use is to minimise the sum of squared difference between model and market prices for the swaptions on the diagonal of the swaption matrix. I am using only swaption maturities till 10 years. So the swaptions which I am using for the calibration are 10x1, 9x2, ..., 1x10. And I am running a DE algorithm for jointly calibrating both the mean reversion parameter and volatility parameter (both assumed constant).

Now I understand that a lot of practitioners fix the value of the mean reversion parameter and only calibrate for the volatility parameter. However I have not been able to find any references for how a "best value" for the mean reversion parameter is decided. So it would be great if someone could shed some light on what exactly are the steps to decide on a "best value" for the mean reversion.

The swap curve for GBP (reference 3m GBP LIBOR)  is what I am using

frolloos
Posts: 1566
Joined: September 27th, 2007, 5:29 pm
Location: Netherlands

### Re: Fixing mean reversion parameter in the 1F HW model

If you'd like to 'fix' the mean reversion rate you could fix it based on historical behaviour of the short rate and calibrate the other parameters to the ATM swaptions. But is the short rate really mean reverting, what time horizon are you looking at also matters.

At risk of stating the obvious: the LMM model and its generalizations might be a better choice for modelling / pricing rates derivatives.

VivienB
Posts: 130
Joined: August 6th, 2012, 3:32 pm

### Re: Fixing mean reversion parameter in the 1F HW model

At risk of stating the obvious: the LMM model and its generalizations might be a better choice for modelling / pricing rates derivatives.
Not really obvious. It really depends on what you want to price. Furthermore LMM models have a lot of drawbacks: slow calibration and pricing, the correlation structure is difficult to calibrate, the "standard" version (lognormal) doesn't match very well the smile in the current market situation (a term structured HW will provide a much better fit of the smile for the major currencies, even if calibrated only on ATM), lots of factors, etc.

IMHO, better choices are multiple factor extensions to handle the slope correlation (HW2F) or volatility generalization to handle the smile (quasi Gaussian models / quadratic Gaussian models), eventually combined (multi factor quasi / quadratic Gaussian), what remain fast, easy to calibrate and have small dimension.

frolloos
Posts: 1566
Joined: September 27th, 2007, 5:29 pm
Location: Netherlands

### Re: Fixing mean reversion parameter in the 1F HW model

I'm not too experienced in rates derivatives, so thanks VivienB for adding the nuance / correction!

In your opinion then, for the more vanilla derivatives such as swaptions, short rate models are preferable to market models?

VivienB
Posts: 130
Joined: August 6th, 2012, 3:32 pm

### Re: Fixing mean reversion parameter in the 1F HW model

I'm not too experienced in rates derivatives, so thanks VivienB for adding the nuance / correction!

In your opinion then, for the more vanilla derivatives such as swaptions, short rate models are preferable to market models?
For the vanilla such as swaptions or caps/floors, a market model with closed form solution seems preferable, typically (shifted) SABR.