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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                      ?                                                ?

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,