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11

The usual technique of computing the mean and standard deviation of returns happens to coincide with the maximum likelihood estimate when the data are regularly spaced. However, when the data are not regularly spaced, you can still do a maximum likelihood estimate. It's just more computationally intensive than before. That is to say, assume you have ...


6

This answer only deals with obtaining higher frequency data from low frequency data. The second method is taken from the draft of a master thesis of a friend of mine, i.e. most of this is taken from an unpublished source. Jones (1998) propose an algorithm to this using something similar to Gibbs sampler to get the most likely parameter values for a ...


4

I think you need to say something about what you want to do with the "filled in" series. If you're interested in statistical properties, the usual technique is maximum likelihood estimation using the EM algorithm. That gives you something like a completion of the missing values, but only in the context of the statistic being extracted -- that is, you're "not ...


3

You must apply the E-M algorithm to an invariant (time-homogenous i.i.d. variable) such as log-returns -- not prices. The key to the E-M is is the simplifying assumption that the invariant (namely the distribution of returns) as well as the distribution of missings are i.i.d. Prices do not obey this property. The trick of assuming an i.i.d. invariant and ...


1

I believe that your problem can be formulated as: Find PD matrix that is as close as possible to a given PD matrix (result of some previous calibration, or the matrix computed using average hazard rate, or any other "target", or the penalty on non-smoothness) subject to the following constraints: The values that are given must be matched exactly ...


1

The typical approach is to try to fit a ratings migration matrix to available rating transition data. If default rates are all you have then that's going to be difficult. Instead, I might try to fit a separate reduced form credit model on survival probability $P_\ell$ for each rating $\ell$ by fitting the function $$ P_\ell(T) = \exp\left( -\int_0^T h(t) ...


1

Assume we have $r(t)$ continuously compounded spot rate for maturity $t$. The price of the 2-year bond with semi-annual coupon $C$ is known to be $P$. We already have $r(0.5)$ and $r(1)$. We need $r(2)$ and $r(1.5) = f(r(1), r(2))$. Then $$ P = C [e^{-0.5 \times r(0.5)} + e^{-r(1)}+e^{-1.5 \times r(1.5)}] + (1+C)e^{-2 \times r(2)} $$ Using linear ...


1

There is no such thing as a "proper" interpolation of CDS spreads. The only criterium your interpolation must obey is the absence of arbitrage. Note that, assuming that $spread(3M) < spread(6M)$, $spread(4M)$ can take any value between $spread(3M)$ and $spread(6M)$ without creating an arbitrage opportunity (actually it can be even slightly less than ...


1

5 minutes is a very short time period! If you have access to real time data of Implied Volatility and transaction Volume of the underlying of your option than you can take a look to the following article: Volatility Forecasts, Trading Volume, and the ARCH versus Option-Implied Volatility Trade-off In this article, the authors use the information from ...


1

There are quite a few strategies you could take. Use models that are more resistant to noises. As others have already mentioned, parametric models such as Nelson-Siegel or Svensson may do the trick. I have also used Merrill Lynch Exponential Spline Model successfully (http://www.bankofcanada.ca/wp-content/uploads/2010/02/wp04-48.pdf). Change your objective ...


1

http://uk.reuters.com/article/2012/11/27/efsf-bond-idUKL5E8MR6I220121127 Nov 27: The order book on the European Financial Stability Facility one-year syndicated issue is over EUR 5bn according to a bookrunner on the deal. The eurozone rescue fund opened books this morning via JP Morgan, Morgan Stanley and Natixis at guidance of 0.23% to 0.25% with pricing ...


1

The basic rule to keep causality during resampling/interpolation of financial data is not to use information from future. You need to use stepwise interpolation by "dragging" the last known information along new samples until the next monthly update. You must know when exactly these monthly values where sampled/calculated. This guarantees causality, but ...



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