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Monte Carlo, risk, QMC, statistical efficiency, high dimensional approximation...


Mar
26
answered Effects of random-generator-choice on derivative's price
Mar
13
comment Normally Distributed Returns Become Leptokurtic Due to Compounding
This effect will vanish if you use log returns. Be aware of the difference between the two and when each is appropriate. See also the papers by Meucci on this.
Mar
7
comment An alternative to the Gaussian distribution to describe/fit market stock returns
@Aksakal: yes, SV is certainly better, also as a fit to data, but can be unpractical for certain tasks. Anyway one can circumvent the Student t aggregation "problem" quite easily in practice. PS: for most dof-s Student t log-returns shall also have finite mean, or not?
Mar
6
comment An alternative to the Gaussian distribution to describe/fit market stock returns
@Aksakal we all know Student t is not a perfect distribution, I was just pointing out that alpha stable ones have even more problems. And again, the fact that aggregating t returns thins down the tails is wanted, due to empirical observations, while stable ones do remain in the family but at the high cost of tail persistence. Why sacrifice accuracy of approximation for mathematical "elegance"? Moreover afaik that issue with price expectation is even more pronounced with stable distributions, please correct me.
Mar
6
comment An alternative to the Gaussian distribution to describe/fit market stock returns
@Aksakal and why would that be a disadvantage? On the countrary, empirical distributions are well known to be far from stable, that's why one has to resort at least to hacks like tempered stable distributions.
Mar
5
comment Is it more accurate to analyze returns on a calendar day basis than a trading day basis?
I would not expect as much as a $\sqrt{3}$ factor, since in the weekend no trading activity occurs, that's one of the volatility sources. The factor must however be higher than 1 since news still arrive during weekends.
Mar
5
comment An alternative to the Gaussian distribution to describe/fit market stock returns
Nice references! Why are you not even mentioning Student t? Are there any major drawbacks? Do you know of comparisons with NIG and VG?
Feb
21
comment Fitting Student t-distributions to log-returns
Check: quant.stackexchange.com/a/10319/3015
Feb
21
answered Consensus on Cauchy distribution for stock prices
Feb
19
comment Estimate weekly, yearly quantities from finite samples
@shnauz check the edit in response to your comment. Sorry for delay.
Feb
19
revised Estimate weekly, yearly quantities from finite samples
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Feb
19
comment Parameters for numerically fitting t-distribution to log-returns
The excess kurtosis is defined here and you can solve for the parameter $\nu$ from the estimated kurtosis without estimating its volatility. Beware that excess kurtosis is only defined and finite for $\nu>4$, so for the common range of $\nu\in[3, 4.5]$ encountered in finance the sample kurtosis is at best unrelieble.
Jan
23
revised Lattice Boltzmann method for pricing options
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Jan
23
answered Lattice Boltzmann method for pricing options
Jan
23
comment Lattice Boltzmann method for pricing options
Nice idea, but I fear that this is overkill. Better use methods targeting the heat equation and diffusions directly than taking the convoluted route taking convections into account. How would you map f(x,v) to f(s)? But still, maybe Boltzmann for treating jumps might be interesting... There are a lot of works on kinetic modeling of wealth distributions&c, but this is more economics.
Sep
28
awarded  Yearling
Sep
3
comment Should I use Resampling or Expectation Maximization to compute a robust covariance matrix?
Whops sure, sloppy speed writing on my part, of course I just wanted to say that neither method adresses both aspects and that they are not mutually exclusive, and having different targets they can't be compared. There's a vast literature nowadays (even just for variants of EM), no need to stick to (rough and outdated) resampling. My favourite combined method is: ecares.org/ecaresdocuments/seminars1011/frahm.pdf . However it's not extensible to asynchronous quotes.
Sep
2
comment Should I use Resampling or Expectation Maximization to compute a robust covariance matrix?
What is your primary concern: robustness (w.r.t. outliers) or missing data? Neither resampling or EM do adress the former. There are however ways to deal with both, are you interested?
Aug
29
comment Brownian motion - first passage time
Are you sure the solutions found deal with a GBM starting point at 0? :-)
Aug
29
answered Brownian motion - first passage time