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...
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.
Maybe take a hazard rate type approach? A little bit rusty on this so may be wrong! I'm sure someone will correct me :)
If probability of default in a year is 2% then probability of survival must be 98%. Use this to obtain the hazard rate/default intensity:
\( P(S)=e^{-Ht} \)
\( \therefore...
In the vast majority of practical applications of KRDs I've worked on the starting point has always been to shift observable market data rather than the zeros. You may get results which are not particularly intuitive because of the extra step of re-deriving the spot curve but ultimately these...
\[ VAR(A-B)=VAR(A)+VAR(B)-2COV(A,B) \]
In this case, since the returns of Fund A and B are independent the covariance of A and B is zero. Leaving:
\[ VAR(A-B)=VAR(A)+VAR(B)=0.4^2+0.3^2=0.25=0.5^2 \]
Therefore \[\sigma_{A-B}=0.5\] or 50%
This is all about compounding assumptions. By using continuous compounding you are making the assumption that the spot rates are continuously compounded rates, obtaining a valuation of 98.39. If you then calculate a YTM in the same fashion with continuous compounding you will obtain a YTM of...
The difference is the assumed compounding. \( x_n/x_{n-1}-1 \) assumes compounding at the base frequency of your series. i.e. daily, monthly etc. \( \ln(x_n/x_{n-1}) \) assumes continuous compounding. Bearing this in mind, it's a case of how you anticipate the numbers will be used.
In your...
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...
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.
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...
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.
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...
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