Hi, does anyone know why when we model interest rates there is a risk-neutral version and a real-world version? When modeling future short-rates why does it have to be risk neutral?
It was shown how the risk neutral measure was derived by holding cash and stock in the replicating portfolio. This probability measure was also for a distribution of asset values at the end of contract. I cant see why there is all of a sudden a risk neutral distribution 4 interest rates. I can understand if there is a risk neutral distribution for bond values at the end of the contract...
its there in the chapter "term structure of interest rates" under the section "risk-neutral approach to pricing". even i am not too sure of the purpose of the P and Q measures in modeling r -the course notes are bit vague i think, if am not too dumb that is. may it would work out if i re-re-read it. i understood the P and Q concept relatively clearly in the binomial option pricing context. perhaps more enlightened fellow students or the acted tutors may want to help?
We need short rates under a risk-neutral probability measure Q so that we can carry out risk-neutral valuation of derivatives in a similar way to Chapters 13 & 14. (Recall that we needed an SDE for the share price under Q in order to perform risk-neutral valuation in Chapter 14.) The only difference in Chapter 15 is that short rates (and interest rates more generally) are allowed to vary in Chapter 15, whereas in Chapters 13 and 14 the risk-free rate is assumed to be constant. This leads to the general risk-neutral pricing formula with variable short rates that appears on Page 11 of chapter 15. So, Chapter 15 is really just generalising Chapters 13 and 14, so that we can value deriviatives whose payoffs/values depend on interest rates, allowing for the possibility that interest rates vary.
