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DCH
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Shreve on HJM - missing dt term?

May 18th, 2010, 11:06 am

Hi Folks,Having some difficulty following Shreve, Stochastic Calculus for Finance vol II, p, 429, sec 10.3.4, line 5 He says "we may rewrite (10.3.5) as "... he then gives the SDE form of the integral equation in 10.3.5, then the next line he substitutes 10.3.16 which replaces the drift term alpha(t,T) which gives us the no-arb condition. Fine but we have then ... sigma(t,T) [ Theta(t) + dW(t)]and this term, i.e. "sigma(t,T) x Theta(t)" should have a dt, should it not? If it was there, then it would make a mess of the application of Girsanov (5.2.3), but I don't see the justification for dropping it.Thanks!
 
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AvovA
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Shreve on HJM - missing dt term?

May 18th, 2010, 11:43 am

there should be "dt" there, yes.
 
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DCH
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Shreve on HJM - missing dt term?

May 18th, 2010, 3:15 pm

Thanks. I realised dt fits with Girsanov too as we integrate.
 
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jfuqua
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Shreve on HJM - missing dt term?

May 20th, 2010, 1:36 pm

I can't tell from your comment and his Errata if this is the same typo. His Errata is at http://www.math.cmu.edu/~shreve/
 
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DCH
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Shreve on HJM - missing dt term?

May 26th, 2010, 3:12 pm

Yes - I found the errata after posting (sorry). Yes, it's the same.