Yeah, when calculating the integral you usually have to discretize if there isnt a closed-form expression. im not trading options or futures intraday.. just calculate and wait couple weeks for payoff.. rinse, repeat, kinda boring, but whatever.
It's the assumptions about variance that I don't like in all of these models. I don't price options and I don't really care about that. But assuming variance of something like VIX or SPX or any financial time series is stochastic is math speak for assuming it has a stable distribution. I dropped out of higher math (figuratively speaking), so stochastic calc and measure theoretic probability ended up being the thing I walked away from (at least a formal study of it -- have a good enough intuition). I don't regret that decision. You can make money with time series transformations, predator/prey models, liquidity hunt algos, and knowledge of microstructure. Distributions are for deriving probabilities, and in practice unless attempting to price volatility it's not so useful, IMO. The guys over at quant stackexchange said the research around differencing is the new edge. I guess I should be reading the literature on difference stationary methods (fractional differencing, nonlinear differencing, etc). All the vol pricing stuff seems cool, but for me at least it just wasn't related to the markets knowledge I was amassing. Microstructure stuff, and market making, that is. Basis spreads, rate spreads, and index spreads are my favorites and the vol pricing stuff just doesn't seem to offer much in that domain.
The stochastic volatility assumption is not just an assumption .. also has not much to do with stable distributions. time series assumes uniform spacing which is not appropriate for intraday timescales. I tried market making but even with 60 microseconds lag I was getting sniped by faster predatory hfts. I doubt differencing is going to turn up anything new, that is age old stuff. At the hedge fund I used to work at my old boss used to tell people they used neural nets just to throw them off and waste their time. The reason is that probabilistic models can be used to calculate the likelihood. If the residuals are uniformly distributed and small. The model fits and its not a curve fit. That always tells u something useful
"Whut?" That is the stupidest stuff I've heard. Half-or-better of any guidebooks I'm using are the grad school texts (all pretty basic) from when I was in school in the early 80s. Puh-lease. And to be clear, when citing papers, these texts are citing from the 40s, 50s, 60s, and 70s. My X never wanted her "Basic Input-Output Models" book; I kept it; used it, too. But it was "Basic..." 40 years ago. Fergawdsakes. "The new edge..." They should be ashamed. Or maybe they just don't know? Or, more likely, just don't care. (Who keeps the crappy-assed high-priced dreque that passes for textbooks nowadays?) Sorry for the rant.
Lmao. Yeah. ARMA processes are cutting edge . Most likely whoever said that is delusional or uneducated. Wow, autocorrelation, now on the cloud with Javascript react action kubernetes 2.0 on neural ai container!
"Stable data..." Yeah, you can preach about that all you want, but you are calling "Naked!" on the A.I. Emperor's New Clothes. (Woven from Machine Learned looms, y'know! ) You're going to be ignored. (As you might have guessed.) Anyway, a little haiku for you.... Poisson sought Gauss' café Who poured a bell-shaped hot mess "Stop moving your cup!" I crack me up.
You are young. And a little quick on the trigger to fire off such a vile post in reply to some innocuous commiseration. Whatever. Offense not taken. My artful haiku remains artful and wonderful. (IMNSHO. YMMV. OIMMBCTTA.)
Yeah, my apologies I my humor detector must be broken. I did not see your comment as innocuous commiseration but rather as arrogant uneducated dismissal and misinterpretation of a term that has a real technical meaning and not some fuzzy concept.
Ha. To a mathematician any thing in the last 100 years is 'new' so you need to put it into the right context McGinnish. Differencing is pretty fucking useful for trading off internals, mm spreads, or intermarket spreads/momentum. It's a convenient way to to use the relevant datas in an intelligent way. Why the fuck wouldn't you want to transform time series? I'm talking about differencing against an exponential MA or a measure of direction like an OLS curve. Do I really give a fuck about the actual index basis trade or am I just trying to know when the thing is moving and relatively how much? The only ones trading it are colocated HFT groups with competitive execution. For the uninitiated: I'm talking about CME/NYSE index arbitrage against a rate basis differential. Same with the VIX basis spread. I'm not trading the thing, but I have nice little transformations for it that are proving useful for what I do.