Hi all,
I noticed there’s a slight difference in the binomial model calculation of interest rate options (under derivatives topic) and straight bonds/embedded options (under Fixed income topic).
Eg.
t=2 is maturity
Interest rate option:
To find t=2 bond price, bond price = (Principal + Coupon)/(1 + r )
Callable bond:
To find t=2 bond price, bond price = (Principal + Coupon)
Why is there such difference? On the textbook, it is stated that both uses forward rate.
Thank you.
They are two completely different products.
With interest rate options the payoff is paid in ARREARS meaning at the end of the period. Similar to FRAs. Therefore you need to discount this payoff back 1 period to get the value of the caplet/floorlet.
With all due respect, bonds also pay in arrears; interest rate options paying in arrears is not a source of difference.
If you have a capped floating-rate bond, and an identical interest rate cap, the payoffs on the embedded cap and the interest rate cap will be identical (in amount and timing), and their values will be equal.
I wrote two articles that may be of some help here:
Full disclosure: as of 4/25 I’ve installed the subscription software on my website, so there’s a charge for viewing the articles.
So now you cannot send links on your own web than on other sources. 
All interest bearing instruments are paid in arrears - I can’t think of one that isnt.
However I think the question is why do we discount the payoff we found at node T=2 by the node T=2 rate for interest rate options? And the answer is that it is because it is paid in arrears so you have to discount back one period. At least I think that is the question - or are they talking about options on bonds? Now that I think about it I think they are talking about options on bonds maybe???