# Study Session 12: Fixed Income: Valuation Concepts

## Multiplying interest rate x e^(x) on Binomial Interest Rate trees

Can someone post the steps involved in taking a binomial interest rate tree’s rate (say at the bottom) and finding the rate 2 nodes above it (or below)?  Struggling to find an example right now…

Let’s say the interest rate is 1%.  And the node we’re looking for is 1 above and 2 above at t=2.

1% x e^(2)

1% x e^(4)

How do I enter this into the calculator?

## Derivatives and FI

Hello there,

I have been spending great amount of time on fixed income and derivatives and I find I can’t grasp all the concepts properly. Is it normal that I am having such a hard time with these two topics ?
I am watching Ift videos and practicing from the curriculum and schweizer, but still I feel far from these two topics .
can you guys share how you have studied for these two topics?

thanks

## Spot vs. Forward Curve

Question in regards to realized return in Spot vs. Forward Curve…

When a Portfolio Manager “project’s a spot curve above or below the forward rate curve,” how do you approach questions like that as the sentence continues… for example, say the end of the question is “and the spot curve truly ends up being above (or below) the forward rate curve, what is the realized return relative to the risk-free interest rate?

## Valuation of bonds with embedded options

R34 it says for the binomial int rate tree the upper rate is = lower rate x e(2x σx √t) however in R33 we used int rate tree to value without embedded options and it didnt have the square root of t. Please explain why the difference?

## Swap Fixed Rate

Pretty simple question but I’m simply stuck on calculating a swap curve from spot rates.  I know the answer is simple but I’m at my wits end.

I’m using CFAI L2 material at the moment, volume 5 page 28.  The example is creating a swap curve from spot rates.

Given a spot rate for year 1 (5%) and year 2 (6%) the formula to solve is as follows

(SFR2/1.05) + (SFR2/(1.06)2) + 1/(1.06)2 = 1

I get to through the 1st step and end up with (SFR2/1.05) + (SFR2/(1.06)2) = 0.110004

## Binomial Model

Correct me if I am wrong, but the binomial model is used to value any bond with or without embedded options. And:

1. in the practical world, why do we need to derive an arbitrage-free price for a bond, besides the obvious reason that we can take advantage of arbitrage?

2. In what circumstances should I use the binomial model to derive a bond’s price and when should I not?

## Binomial Model

Correct me if I am wrong, but the binomial model is used to value any bond with or without embedded options. And:

1. in the practical world, why do we need to derive an arbitrage-free price for a bond, besides the obvious reason that we can take advantage of arbitrage?

2. In what circumstances should I use the binomial model to derive a bond’s price and when should I not?

## Binomial Model

Correct me if I am wrong, but the binomial model is used to value any bond with or without embedded options.

1. In the practical world, why do we need to obtain an arbitrage-free price for a bond?

2. In what circumstances should I use the binomial model and when should I not?

Please forgive me if these questions sound so naive.

## A very different spot rate and forward rate question

Hey guys,

long time lurker here. Just came across this question and have confusion about it. Could you help:

Bond Principal    Maturity (yrs)    Coup Rate    Quoted Yield    Bond price  Zero Coupon(Spot) Rates   Last period implied forward rate

100                     0.25                  0.00%           1.6064              99.6000                      ?                                                ?

## Why is Macauley Duration a better measure of duration, especially in the context of ZCBs?

Why is Macauley Duration a better measure of duration, especially in the context of zero coupon bonds?