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knadk
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Joined: July 7th, 2013, 11:56 pm

Heath Jarrow Morton and BGM models (Paul Wilmott on quantitative finance 2nd edition)

July 10th, 2013, 11:01 pm

In the chapter on HJM models, the author derives dr(t) from r(t) under the HJM model using the SDE for the evolution of the forward rate. He uses differentiation under the integral sign to get the result. I did not understand why dX is present in the last term on the right hand side of the expression for dr. How does one use differentiation under the integral sign on an integral with respect to a random term? Also, I do not see why he has flipped the order of the arguments in some of the partial derivative terms. e.g [$]\mu(s,t)[$] to [$]\mu(t,s)[$] and [$]\sigma(s,t)[$] to [$]\sigma(t,s)[$].