Derivation of E(r_s|r_t) for Vasicek model

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Derivation of E(r_s|r_t) for Vasicek model

Postby wuyiquant_tobe » Thu Mar 21, 2013 2:39 pm

Hi All,

I am reading thorugh some material of how Expectation of future short rate can be derived by using the SDE of Vasicek short rate model.

However, I am stuck at the Row 3 & 4 of the formula derivation due to the fact that I can not exactly recreate the row 3 formula on the LHS if i take a partial derivate of the LHS from row 4, especially i can not see where the dt comes from after taking the partial derivative.

Could someone help me with this?

Cheers.
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Re: Derivation of E(r_s|r_t) for Vasicek model

Postby mj » Sun Mar 24, 2013 8:42 pm

this is really just notation. When we write

d(e^{at} r_t) = ... dt + ... dW_t

this is shorthand for

e^{at} r_t = \int ... dt + \int ... dW_t
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