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Im trying to calculate monthly ZCB bond prices with a fixed maturity T, over a period of months via Monte Carlo methods.

Here is my attempt:

For the first month, the price is $P_{t_0}(0,T) = E[exp(-\int_{t_0}^T r_s ds)]$, for the second month, the price is $P_{t1}(0,T) = E[exp(-\int_{t1}^{T+t1} r_s ds)]$, and so on up to the last month.

I construct N interest rate paths $r_t$ via Euler discretization, and approximate the expectations by taking the mean of each row of the matrix with elements

exp[-(T/M+1)*sum(r_s[t_i:t_{i+M}, j])]

where M is the number of months between maturity T and the "start month" of the bond price, j from 1 to N.

The maturity T is 3 years. So I let dt = 1/12 (in the Euler discretization) and T=3.

Where does it all go wrong?

-Hannah

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1  
What process do you use to simulate short rate r ? And what is the problem with your simulation? –  adelm May 5 at 16:51
    
@adelm Vasicek. I am aware of the affine term structure, but I want to extend it to a Levy driven model later on. I am trying to calibrate it to market data, but the resulting interest rates are about twice as high as they should be. –  Desperate May 5 at 18:11
1  
I think you have to give more information, preferably code. –  Bob Jansen May 5 at 19:12

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