# Newton's Method in Hull-White model-Matlab

#### d.koutsomito

Hi all,

I currently want to use Jamshidian's trick for pricing a coupon bond option in Hull-White model, which is to represent
the strike price K as a price of a coupon bond with a yield r_star.
To do so, one has to use a non linear solver to obtain this yield, r_star, of the coupon bearing bond with price K.
I have implemented Newton's method in Matlab but I do not get the correct yield.
The strange thing is that if I use the same algorithm for Vasicek model, I get exactly the correct result, in contrast to the Hull-White model where the result is NaN.

Does anyone know why this problem occurs?

Thanks.

#### Daniel Duffy

##### C++ author, trainer
I did BDT model using NR for yield fitting and the major issue for me was that it did not always converge because of bad seed value.

So I use Bisection to bracket to TOL = 1.0e-1 and then NR.

#### d.koutsomito

I did BDT model using NR for yield fitting and the major issue for me was that it did not always converge because of bad seed value.

So I use Bisection to bracket to TOL = 1.0e-1 and then NR.

Finally, I used bisection method too. Concerning the NR method, I plotted the Coupon Bond prices for different r_star in both HW and Vasicek and I show that when r_star increases then the prices decreases very fast in HW and much less in Vasicek. Therefore, NR method does not converge in HW model as the function for coupon bond prices reaches its assymptotics quickly. By the way, bisection method is much faster than I was expecting initially.

#### Daniel Duffy

##### C++ author, trainer
Finally, I used bisection method too. Concerning the NR method, I plotted the Coupon Bond prices for different r_star in both HW and Vasicek and I show that when r_star increases then the prices decreases very fast in HW and much less in Vasicek. Therefore, NR method does not converge in HW model as the function for coupon bond prices reaches its assymptotics quickly. By the way, bisection method is much faster than I was expecting initially.
Well done

This nasty NR experience (lost time....) is not well documented in general. People tend to use seed = 0.05 as if was the Bible!

#### Daniel Duffy

##### C++ author, trainer
Well, at the time I had sleepless nights because of that NR

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