instantaneous rates

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pwyborn
Posts: 25
Joined: Sat Oct 29, 2011 12:42 pm

instantaneous rates

Postby pwyborn » Mon Dec 31, 2012 6:15 pm

Hi Carol,

For III.3.90, i would like to ask why we take expectation?

Thank you!

Pete
l

coalexander
Posts: 815
Joined: Sun Sep 28, 2008 10:30 pm

Re: instantaneous rates

Postby coalexander » Tue Jan 01, 2013 6:23 pm

Hi Pete, Without taking an expectation the r.h.s. is a distribution, whist the l.h.s. is a single number. Cheers, and happy new year, Carol

pwyborn
Posts: 25
Joined: Sat Oct 29, 2011 12:42 pm

Re: instantaneous rates

Postby pwyborn » Tue Jan 01, 2013 9:54 pm

Thanks Carol. And happy new year to you too!

Is it just a fact that we can determine a spot interest rate of any maturity from the current instantaneous short rate and all the successive instantaneous short rates leading up to the time of maturity of the spot interest rate we are trying to determine?

Section III.3.8.4 is all about short rate models in the context of spot rates. But the next section III.3.8.5 switched gears to forward rate model. So I am a bit confused - when we do interest rate modelling for pricing and hedging interest rate options purposes, which interest rate are we modelling - spot or forward??

When we model a set of forward rates, from III.3.8.5 denotation of the forward rate, it seems that all these forward rates we are trying to model share the same tenor i.e. from t(i) to t(i+1), but different terms as i is from 1 to n. But, arent we supposed to do it the other way round i.e. model the forward rates with the same term, but different tenors? This way, we are modelling the future term structure of spot interest rates prevailing at a future time t, for example.

Each forward rate has its own natural measure, with numeraire being the value of a zero coupon bond. So, is it the case that when we change this numeraire to discretely reinvested money market account, two things happen - first, all forward rates share the same measure called the spot LIBOR measure; second, this measure has a drift term punched in??

What is the second equation in III.3.92? What is the index of the accrual period as in III.3.93?

Sorry for these numerous questions. I found these couple of sections quite technical, but nonethless enjoyable.

Sincerely hope you can help or shed some light!

Pete
l

pwyborn
Posts: 25
Joined: Sat Oct 29, 2011 12:42 pm

Re: instantaneous rates

Postby pwyborn » Thu Jan 17, 2013 5:32 pm

Hi Prof. Carol,

Would you take a look at my post please? I know you are very busy leading the sussex business school there. But if you ever have a moment to give me a reply, I'd be so grateful!

Look forward to hearing from you!

Pete
l


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