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Dec
6
comment What is the right group of durations?
Do you mean the set of Ito Processes with constant coefficients? They will be proportional to $e^{R(t+W_t)-R^2t/2}$ of course and I think the "link" gets lost here because of the $R^2$-term. One more point: If you take $R_+^*$, it is only a group with the operation $*$, not with $+$. Semantically, when refering to duration, we measure the difference of time points. Of course, when using $+$, the group property and therefore the exponential as a homomorphism is lost. Thats why I asked about "group of durations"...
Dec
6
comment What is the right group of durations?
Can you define "group of durations"? you don't mean interest rate sinsitivities right? what is the group operation? And in your point 1, you have an mapping of $\mathbb{R}_+^*$ on what space?
Dec
6
comment Large (5K-10K) non positive definite (particularly near singular) covariance matrices and treatments for Cholesky decomposition
Ok, now we are getting close... :-) I couldn't agree more with what @John said. Keep in mind that parametrizing the curves and modelling the parameters will effectively result in a dimension reduction. If you wanted to use your cholesky decomposition to simulate random paths for example, one realization gives you all the changed curves. Using those, you can reprice ALL your thousands of futures contracts (from your curves) and thus get the price changes. There can be other issues though: You will see them when you get there ;-)
Dec
6
comment Single Most Important Fact about a Fund - Interview Question
Agree, this is a strange question. I think he just wanted to hear "performance". However, I hope the question will be closed.
Dec
5
comment Large (5K-10K) non positive definite (particularly near singular) covariance matrices and treatments for Cholesky decomposition
@acmh I said that. Basically, I suggested to use some kind of dimension reduction techniques. Instead of including all of those highly correlated returns you could take, say 1000 of them and use the returns of a corresponding index or sector instead. Probably, the derivations from the index returns would be about equal the estimation error. Roughly spoken, if you want to have more stable results, there is only one way: Try to reduce the estimation error by taking some bias. See also Richards shrinking suggestion. Thats also what you did by fiddling around with the Eigenvalues.
Dec
5
comment Large (5K-10K) non positive definite (particularly near singular) covariance matrices and treatments for Cholesky decomposition
IMHO, trying to estimate about 50 million parameters from only 1000 observations does not seem to be very wise. First of all, if there are linear dependencies, the matrix will be singular. If you fiddle around with the spectrum (by your method or shrinkage), this property will definitely be lost. You should try to reduce the dimension here. There are numerous ways to do this, all of them have their weaknesses. For a start, you could pool those returns with similar properties into asset classes and the problem becomes more feasible...
Nov
19
comment Are there any other standard rates term structure decomposition than PCA?
@user2763361 can you provide a paper/reference or more details?
Nov
18
comment Library for interactive financial charts
Did you look at GoogleVis? It comes as an R package too and should be quite easy to modify although I didn't put a lot of effort into it.developers.google.com/chart/interactive/docs/gallery
Oct
23
comment Examples of Spectral Risk Measures
@statquant Well, the aim is not to try a different spectrum $\phi$ but rather to identify the spectra of other well known risk measures. Brian B: I dont understand your comment about units. The units are irrelevant for a risk measure as far es the spectral property is concerned, right?
Oct
18
comment Is there a Bloomberg field for a bonds (upcoming) coupon dates?
Thats exactly what I was looking for, thank you.
Oct
17
comment Is there a Bloomberg field for a bonds (upcoming) coupon dates?
Yeah I found those but I didnt want to play around with calenders, weekends, public holidays and so forth. Nevertheless, there is the sad possibility that the field I am looking for does not exist. For now, I only upvoted your answer.
Oct
2
comment Can option prices be characterised by an ODE?
You can alway use a semidiscretization for your PDE or some kind of Galerkin method to end up with an ODE system. I suppose this would correspond to a process with either discrete timestep or discrete state space but thats a guess.
Sep
30
comment Asynchronous Data Across Time Zones - RiskMetrics
Be sure to look at this answer: quant.stackexchange.com/questions/7650/data-synchronization
Sep
30
comment What is the correct Stutzer index and Sharpe ratio relation, assuming a normal returns distribution?
I doubt that it makes a lot of sense with only twelve data points but opinions can vary. Some people may argue that its better to calculate something than nothing. If you calculate it, be sure to compare it with the sharpe ratio. One thing I did not mention above is that the equality with the sharpe ratio only holds when we consider the expectations (instead of approximating them by means as in $I_p$ above). So even for this comparison you would want to have more returns...
Sep
12
comment How to show that the risk contribution function is or is not injective?
The $x_i$ should be a $w_i$ right? In this case $\sigma$ is a function that satisfies the Euler condition as in your other question. You could also add some constraints for your risk measure. Spontaneously, I am thinking about some kind of convexity condition and the implicit function theorem.
Jan
16
comment Comparison of Brownian Motion Expected Drawdown and simulated results
@ManInMoon I edited my post
Jan
7
comment Yield of a risky bond
@Freddy I edited my answer according to your suggestion and hope you can agree with me now. Still, in my opinion, yield-to-maturity is not directly risk related but yield spread is. Nevertheless, I think we are all talking about the same things here.
Jan
7
comment Yield of a risky bond
I am sorry but I disagree on the point where you say simple-to-calculate risk premia. For most corporate bonds for example you have to work hard to separate default risk from other risk factors. Further more, you don't arrive at a "probability measure" but rather at a yield spread as I stated in my answer. The probability of default still remains unclear. You still have to model the default probability for a given yield spread.
Jan
7
comment Yield of a risky bond
@Freddy thats precisely what I said in the second statement about the yield spread. There is no point we disagree on. The textbook way to calculate a yield just depends on the price and the coupons though. Of course the default risk has impact on the price, thus on the yield-to-maturity.
Dec
27
comment How to detect regime change when estimating asset correlation from historical time series?
@strimp099 Are there any resources in these search results you find particularly instructive and interesting? Introductions, surveys, papers, books?