Expected value for Vasicek

[amar singh]

 

Hi Quantlib,

 

How can I get the expected value of the short rate at a given time in the future,for the Vasicek model?

After calibrating the model using the swaptions as given in the example for BermudanSwaption, the values I obtained are:

a =     0.0162584
b =     0.744713
sigma = 0.0294303

 

Assuming a spot rate of 0.05, I tried using the expectation method of the underlying dynamics of Vasicek, but the values seem to decrease as time is increased from 1 to 30 years. I wonder, if it should approach the long term mean towards 0.744 . I also tried using shortRate method ,but it returns a constant value.

 

Thanking you,

asd

 

Following is the code I tried(Also attached the files):

 

 

 

   Handle<Model> modelVasicek(new Vasicek());

        std::cout << "Calibrating to swaptions" << std::endl;
      
        swaptions.setPricingEngine(
            Handle<PricingEngine>(new JamshidianSwaption(modelVasicek)));

        calibrateModel(modelVasicek, swaptions, 0.25);
        std::cout << "calibrated to "
                  << modelVasicek->params()
                  << std::endl
                  << std::endl;

        ofstream myfile("outvas_file.txt");
        myfile << "a =     " << modelVasicek->params()[0] << endl ;
        myfile << "b =     " << modelVasicek->params()[1] << endl ;
        myfile << "sigma = " << modelVasicek->params()[2] << endl ;

  

        Handle<Vasicek::ShortRateDynamics> dynamics = ( (Vasicek*)(&(*modelVasicek)) )->dynamics();

        Handle<DiffusionProcess> diffProcess = dynamics->process() ;

       
        for (i=0;i<30;i++)
        {
          double expectation = diffProcess->expectation(i,0.05,i);
          myfile << "(T-t) : " << i << " expectation " << expectation <<  " short rate " << dynamics->shortRate(i,0.05) << endl;
        }

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a =     0.0162584
b =     0.744713
sigma = 0.0294303
(T-t) : 0 expectation 0.05 short rate 0.794713
(T-t) : 1 expectation 0.0491937 short rate 0.794713
(T-t) : 2 expectation 0.0484003 short rate 0.794713
(T-t) : 3 expectation 0.0476198 short rate 0.794713
(T-t) : 4 expectation 0.0468518 short rate 0.794713
(T-t) : 5 expectation 0.0460962 short rate 0.794713
(T-t) : 6 expectation 0.0453528 short rate 0.794713
(T-t) : 7 expectation 0.0446214 short rate 0.794713
(T-t) : 8 expectation 0.0439018 short rate 0.794713
(T-t) : 9 expectation 0.0431938 short rate 0.794713
(T-t) : 10 expectation 0.0424973 short rate 0.794713
(T-t) : 11 expectation 0.0418119 short rate 0.794713
(T-t) : 12 expectation 0.0411376 short rate 0.794713
(T-t) : 13 expectation 0.0404742 short rate 0.794713
(T-t) : 14 expectation 0.0398215 short rate 0.794713
(T-t) : 15 expectation 0.0391793 short rate 0.794713
(T-t) : 16 expectation 0.0385474 short rate 0.794713
(T-t) : 17 expectation 0.0379258 short rate 0.794713
(T-t) : 18 expectation 0.0373142 short rate 0.794713
(T-t) : 19 expectation 0.0367124 short rate 0.794713
(T-t) : 20 expectation 0.0361203 short rate 0.794713
(T-t) : 21 expectation 0.0355378 short rate 0.794713
(T-t) : 22 expectation 0.0349647 short rate 0.794713
(T-t) : 23 expectation 0.0344008 short rate 0.794713
(T-t) : 24 expectation 0.0338461 short rate 0.794713
(T-t) : 25 expectation 0.0333002 short rate 0.794713
(T-t) : 26 expectation 0.0327632 short rate 0.794713
(T-t) : 27 expectation 0.0322348 short rate 0.794713
(T-t) : 28 expectation 0.031715 short rate 0.794713
(T-t) : 29 expectation 0.0312035 short rate 0.794713