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Ok, so consider an example of a callable bond with market price P. The Z-Spread calculation takes the cashflows for this bond as if it is a non-callable, vanilla bond to arrive at a Z-Spread value which brings the model price equal to P. Obviously, because the bond is callable, there is a...

Nothing you have said is incorrect. OAS is usually derived via a Monte Carlo approach as the flat spread which can be added to underlying curve in order to bring the Monte Carlo expected price equal to the observed market price. For bonds with no optionality the OAS will be very close to the...
3. ### probability of default annualized vs no of days for loan

Typically used for pricing credit sensitive instruments such as corporate bonds, CDS etc. Usually you would derive a hazard rate curve from observable market data like bond quotes and use it in conjunction with other rates curves to price the instrument or determine sensitivities.

10. ### Basic stats Question

Looks fine to me. $\sigma^2(X)=E(X^2)-E(X)^2$ $\therefore \sigma(X)=\sqrt{E(X^2)-E(X)^2}$ If your spreadsheet is set up correctly you should just be able to change the probabilities to get back to the example 50/50 numbers. You could also memorise the common quantities for a bernoulli...
11. ### Curve shape based on Vasicek model

Vasicek model is for short rates or instantaneous spot rate. It makes no assumptions about the shape of a curve as it is modelling the spot rate dynamics only.
12. ### Forward Rate Formula

Rather than trying to memorise these specific formulae, I find it much easier to remember the basic, underlying concept is the same for both in discount factor/growth factor space: $GF(0,T_2)=GF(0,T_1)*GF(T_1,T_2)$ Then, depending on the question or data provided you just need to calculate...

Of course.
14. ### Completely depends on what you're trying to achieve. You can calculate Daily VaR with as few as...

Completely depends on what you're trying to achieve. You can calculate Daily VaR with as few as 30 days worth but obviously this will not be particularly stable over time. If you want a more long term, stable value I would suggest a years worth or 252 business days.
15. ### YouTube T4-43: Fixed Income: Key rate shift technique

The yield-modified duration world is the simplest, text book situation. Calculating KRDs in this flat curve YTM world is not really done or useful. If you REALLY wanted to do this then you could make a flat curve with the YTM at each tenor point and shift each one in turn before repricing. The...
16. ### YouTube T4-43: Fixed Income: Key rate shift technique

You are correct that the sum of Key Rate Durations should be approximately equal to the Effective Duration. As with all of the these valuation type exercises, consistency is key. In all of the models I've ever seen the KRD and Effective Duration estimation procedure is essentially the same with...
17. ### YouTube T4-43: Fixed Income: Key rate shift technique

The YTM is generally just used as a measure of quoted price or value. Some bonds quote in the market using YTM, some with actual price. You are correct that the derivation or usage of YTM implies a flat curve at the YTM. YTM and Modified Duration form a sort of self-consistent simplistic...
18. ### YouTube T4-43: Fixed Income: Key rate shift technique

I think we should first separate the two issues at play here: 1 - Deriving the zero curve 2 - Determining PV01/KRD values for a non-curve instrument Firstly, zero rate curves are derived from observable market prices/yields and these are almost always coupon bearing instruments. The resulting...
19. ### Portfolio Duration with defaulted bonds

This is not correct. It will lower the overall weighted average duration of the portfolio but this is correct as the defaulted bonds are no longer rates sensitive but still have market value. This is exactly what I've said. This is not correct. Including them with zero actually gives the...
20. ### Portfolio Duration with defaulted bonds

I would set the duration to zero but keep them included in the calculation. Remember, (modified) duration is the sensitivity to Yield but defaulted or distressed securities tend to start trading based on Price (estimate of recoverable value) rather than Yield so rates become essentially...