Expansion of The Characteristic Function of Yt = a(Xt + b)2 + c Where Only Xt's Characteristic Known
- Thread starter steve42
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No such thing exists. It's part of certain stochastic volatility process that I've derived a new means of solution for because the paper that it was published in used the Adam's bashforth discretization method in the time domain which is computationally prohibitive since you have to evaluate it for every strike price and every variation of the perimeters so it would be very costly during optimization so therefore the solution is to Fourier transform into the frequency domain and then perform in orthogonal polynomial expansion and then you end up with a method where you can approximate the solution with like 99.9% accuracy using only for instance the first 20 or 30 need the infinite degree accuracy so it's far more computationally efficient because these basis functions can be precomputed ahead of time, memoized basically or cached. The error of the solution is no greater than the magnitude of the last term omitted from the expansion therefore if you know the duration for which you want to calculate this expectation then you can calculate exactly how many terms you need to reach the desired level of accuracy to reach the one penny level of resolution or subpenny if such a thing is being used
The solution method is not entirely new but no one has written about using the orthogonal polynomial expansion for the fractional Ricatti process in finance.
I'm trying to decide whether I should just sit and using myself or license it to some trading houses or something
The technique is described here
https://www.sciencedirect.com/science/article/pii/S0307904X15003893
Close but no cigar The idea is to replace the probability density of the original process with its expression as an inverse Fourier transform and then apply through Fubinis theorem to exchange the order of integration and summation and then you can actually calculate a closed form solution for that inner integral using the method of residues which is that exponential term you see in the integrand that I left out of the derivation. You don't have to stop here though you can apply for Fubinis theorem again to derive the expression as an integral of that inner integral against each of the hermite polynomials because they are orthogonal with respect to the Brownian motion over the interval of 0 to infinity.. it could be possible to expand in other bases besides her The hermite basis but that is probably the best one due to its elementary properties and orthogonality with respect to the standard gaussian process
How about a performance report?
What the f*** you talking about I'm not here to qualify myself to you. How about you drop down on both knees? The past 3 years I got right at 55% returns no losses whatsoever this year I had a major surgery and I didn't trade much so I only made 20% returns this year and that's after tax. I haven't parted with any money that I didn't intend to or was impelled to via threat of penalties like paying taxes and stuff like that
You must do a lot of deep scuba diving, because you didn't take a breath through that whole bit, hehe. Commas, man!
I will soon im taking my ass to hawaii, but yeah I use voice-to-text quite a bit now because fuxing with the keyboard slows me down, i use this for code and stuff, not communicating extemporaneously. maybe I'll have enough money to hire an editor soon, but i cant be bothered with fuxing commas man! insert them where you see fit
Not you, geez. The technique in particular. Blow me otherwise soon in Hawaii lol.