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


Mar
26
comment An alternative to the Gaussian distribution to describe/fit market stock returns
Of course S can be larger than all the money out there: we live in a fractional reserve system. :) Anyway that would be an ex ante fixed boundary, so that one is not really solving that integral but a variant; it's not the same as having freedom of truncation.
Mar
26
comment An alternative to the Gaussian distribution to describe/fit market stock returns
@Aksakal: I don't get it: if the integral explodes you can clip arbitrarily and get any desired pseudoresult, or not? What's the meaning and use? Unless of course the boundary is fixed ex ante. Anyway I'm still not convinced, need to work out that integral: t-s approximate a normal arbitrarily. Thanks for the link!
Mar
26
comment An alternative to the Gaussian distribution to describe/fit market stock returns
@Aksakal: right, I should have checked first... what a silly cheat!
Mar
26
comment An alternative to the Gaussian distribution to describe/fit market stock returns
@Aksakal: Student t pricing.
Mar
26
revised Effects of random-generator-choice on derivative's price
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Mar
26
comment Effects of random-generator-choice on derivative's price
For qMC you can check the book from Lemieux, it also deals with various finance examples. Or the shorter introductions also by Lemieux&L'Ecuyer or by Larcher&Leobacher, or the chapter in Glasserman. Anyway it's quite a tricky topic, don't expect to use it as a black-box without surprises.
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