Saturday, April 18, 2015

Instantaneous forward rate within the HJM framework


within the HJM framework, the dynamics of the instantaneous forward rate are defined by:


ft(T)=f0(T)+t0αs(T)ds+t0σs(T)dWs


or in differential form: dft(T)=αt(T)dt+σt(T)dWt


In the litterature (like Tankov, you can find the url below), it is written that: d(Ttft(u)du)=ft(t)dt+Ttdft(u)du

I could not find a proof and Tankov mentions it like it is trivial.


page 96 in :https://masterfinance.math.univ-paris-diderot.fr/attachments/article/47/processus_en_finance_6_7.pdf


Thank you for your help.





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