Interest rate and arbitrage free valuation-middle forward rate

[h21]

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

 

[S2000magician]

Recall that the rates you have in period 1 are related by rup = rdown(e^2σ).
The (hypothetical) middle rate is rdown(e^σ); it’s the geometric average of rup and rdown. 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/

 

[h21]

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

 

[h21]

S2000magician wrote:
Recall that the rates you have in period 1 are related by rup = rdown(e^2σ).
The (hypothetical) middle rate is rdown(e^σ); it’s the geometric average of rup and rdown. 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/

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?

 

[S2000magician]

h21 wrote: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

Page 170 where?

 

[h21]

sorry the notes

 

[krokodilizm]

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.