# Study Session 12: Fixed Income: Valuation Concepts

## 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?

## Backward induction

I’ve seen inconsistency in CFAI official questions whereby if there is a three year bond, say the coupon is 5 so the value at year 3 is 105 for all nodes, for the second year some take 105/spot rate year 2 and that is the answer. Then some take 105/spot rate + coupon of 5.

Why am I seeing differences here? Is it to do with embedded versus non-embedded bond?

Thanks in advance

## Effective Durations!! Please help

Does anyone know why the book link the effective duration to the maturity of the bond? like a zero coupon bond ED = maturity of the bond? isnt ED measures the sensitivity of the bond price to the yield? came accross a lot of questions asking about strategy if you want to increase or decrease the duration of the portfolio? Can someone please kindly explain? thanks in advance!!!

## Bonds with embedded call options issued at a premium?

Hi,

The curriculum says that bonds with embedded call options are generally issued at a large premium, and at issuance, the calls are generally in the money.

Why would this be? It defies logic.

Why would investors pay a premium for something that goes against them (embedded call options)?

Regards,

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