# how to simulate yield curve using the short rates by Vasicek

#### Mego

Hi, I have a question about Vasicek's model. I've already estimated the parameters in Vasicek's model: pull-back, long term mean, and sigma, using MLE method. But I'm not sure how to go from there: how exactly should I reconstruct the yield curve based on the simulated rates and bond pricing formula?

The bond pricing formula is P[t,T] = Exp[A(t,T) - r B(t,T)]. And we know the relationship b/t the price and yield: Y = -Log[P]/(T-t).
What I'm doing is using the yield formula to fit in the current yield curve to get the parameters, and then sub in my simulated short rates. So each simulation will produce different yield curve, as expected because the simulated rates will be different. However, my problem is that there is not so much variability of my simulated yield curves.

Can anybody help? I'm afraid that I should not have used Y = -Log[P]/(T-t) to fit in the current yield curve. People have been saying using zeros price to fit the yield curve, but the P[t,T] is price, not yield.I can't fit P[t,T] directly to the market yield curve - have to somehow convert it to yields.​

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