Interest rate tree - time period??

CFA Level II
#1

Hi guys, please help…

I can’t understand the reason the below two seemingly similar questions using binomial trees are discounted at different points on the binomial tree. Both questions require that we find the price of 2 period instrument…

In the EXAMPLE 1 we need to discount back at rate T =2, in EXAMPLE 2 we need to discount back at T =1… why is it so when we are looking at 2 year values for both of these questions???

EXAMPLE 1 – find interest rate call value

A two-period interest rate tree has the following expected one-period rates:

t = 0 …… t = 1 ………. t = 2

………………………7.12%

………….6.83%

6.00% ………………….6.84%

…………. 6.17% ………………………… 6.22%

The price of a two-period European interest-rate call option on the one-period rate with a strike rate of 6.25% and a principal amount of $100,000 is closest to:

In the above question answer says we NEED TO DISCOUNT BACK BEGINNING AT THE T = 2 RATE

EXAMPLE 2 – find straight bond value…

Find the value of normal bond “not callable” using the below binomal tree.

t = 0 …… t = 1 ………. t = 2

……………………………9.324%

………….8.53%

7.250% …………………7.634%

………… 6.983% ……………………………6.250%

In the above question answer says we NEED TO DISCOUNT BACK BEGINNING AT THE T = 1 RATE

Why the difference between the two examples above? What am I doing wrong? Any thoughts? Would greatly appreciate any feedback…

#2

Here you are talking about 2 different securities.

Example 1 is an interest rate Cap. These are paid in ARREARS meaning at the end of the period - similar to FRA’s. Therefore your payoff is MAX(0, Current Rate-Strike Rate)*Notional Principal. This payoff will actually occur at the end of next period - i.e. t=3. Therefore you need to discount by the current rate (t=2 rate).

Example 2 is a Straight Bond. Therefore you discount the cash flows that happen at t=3 by the t=2 rate and the cash flows at t=2 by the t=1 rate. This is actually the same thing as example 1 in the sense that you are discounting future cash flows at the current rate. You must realize that in example 1 your cash flow is computed using the current periods rate but actual cash flow occurs one period in the future - meaning you need to discount this future cash flow at the current rate.

#3

Thank you so much bfry, great explanation! Thanks again…

#4

No problem. Hope it made sense. Good luck!