Interest rate and arbitrage free valuation-middle forward rate

CFA Level II
#1

I cant seem to comprehend the idea- the middle forward rate in a period is approximately equal to the implied one period forward rate of that period

what does middle forward rate even mean? where is this whole middle idea coming from

#2

Recall that the rates you have in period 1 are related by _r_up = r_down(e^2_σ).

The (hypothetical) middle rate is _r_down(e^σ); it’s the geometric average of _r_up and _r_down. It should be close to the 1-period forward rate.

So all they’re saying is that the forward curve runs roughly through the middle of the tree.

I wrote an article on creating binomial interest rate trees that may be of some help here: http://financialexamhelp123.com/creating-a-binomial-interest-rate-tree/

#3

thanks

maybe i am just brain jammed but page 170 binominal tree example question b, why is there a forward rate tree and how does this connect to the bigger picture

#4

so all its saying is, if you get the implied forward rate, treata it as middle spot you can get the up and down spot rate with sigma?

#5

Page 170 where?

#6

sorry the notes

#7

It is always good to quote Reading Number and question number because some of us use the VitalSource application and have no idea what a page is.