Estimate the parameters for the Svennson model of spot interest rates (least square method). Finally draw the actual spot rate curve and the interporalted curve
[uopt [,rf]]=svennson(t,r,u0 [,tf]);
The Svennson model assumes that the spot interest rate follows the function (of time)
f(t)=u1+u4*u6/t+(u2+u3)*u5/t*(1-e^(-t/u5))-(u6/t-1)*u4*e^(-t/u6)-u3*e^(-t/u5)
The function estimates the parameters u1, u2, u3, u4, u5, ad u6 with the least square method. It is also possible to foresee some rates for given dates.
First we define the dates and the interest rates (taken from the Euribor curve)
-->t=[ 0.0192308 0.0384615 0.0576923 0.0833333 0.1666667 0.25 0.3333333 0.4166667 0.5 0.5833333 0.6666667 0.75 0.8333333 0.9166667 1];
-->r=[0.00944 0.00949 0.0097 0.01009 0.01213 0.01405 0.01486 0.01534 0.016 0.01636 0.01662 0.01687 0.01716 0.01742 0.01766 ];
Now we can use the function and also foreseen the interest rates for 2 years, 3 years, and 4 years
-->[uopt,rf]=svennson(t,r,ones(6,1)*0.1,[2 3 4]')
-->[uopt,rf]=svennson(t,r,ones(6,1)*0.1,[2 3 4]')
Gradient
- 0.0010055
- 0.0002346
- 0.0001655
- 0.0005862
0.0001849
- 0.0000623
Objective function
0.0000001
rf =
0.0187098
0.0191140
0.0193162
uopt =
0.0199227
- 0.0602590
- 0.0341067
0.0251565
0.0698513
0.1655826
The figure shows the actual interest rates, the estimated ones and the foreseen ones.
Francesco Menoncin - Brescia University - 2010