# 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?

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