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


1d
revised Comparison of multicurve calibration methods
added issue
1d
comment Comparison of multicurve calibration methods
I don't even get the comment: it is bootstrapping that fits datapoints perfectly giving awkward curves... and no-arbitrage conditions are rarely satisfied by either approach.
1d
asked Comparison of multicurve calibration methods
Jul
2
awarded  Curious
Apr
30
comment Usage of Brownian Bridge?
Yes, sorry for being brief while at work... Another nice related paper is Quasi-Monte Carlo Methods in Financial Engineering: An Equivalence Principle and Dimension Reduction
Apr
29
answered Usage of Brownian Bridge?
Apr
7
comment Graduating Quantitative Finance (please don't move it to meta immidiately)
Could you please do some spell checking of the linked question? :) Anyway I personally think it would demotivate us, I'd give it a few more months of spicy beta...
Apr
1
answered What are the merits of pseudo random numbers over quasi random numbers in monte-carlo simulation?
Mar
28
comment Effects of random-generator-choice on derivative's price
There's a lot of discussion about PRNGs in finace forums or some books, but given modern generators quality the issue is now kinda solved. Roughly said one samples from AES (or any other good hash function) by feeding in successive numbers, their encrypted values are then pseudorandom; check the so called "counter mode" of AES.
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
added 136 characters in body
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.