Great question. I am very eager to complete the arduous task I am currently finishing up. As soon as that is done it will not take me long to implement the solution to the quadratic rough Heston process which is the first model to jointly calibrate to the index and its corresponding volatility index jointly with continuous sample paths. I settle upon the spectral Jacoby tau method whereby you compute the solution to the fractional ricatti equation by expanding the solution in terms of the (shifted) Jacobi polynomials. Interestingly I could not find any papers that specifically tied this solution technique to this particular equation. We simply do not know what institutions and other participants in this sector of the market use as far as their volatility models but that matters not to me given that this model calibrates perfectly and parsimoniously and I can solve it with a very elegant and efficient method that is great both theoretically and for practical computational concerns it took a while to drive this because all the academic papers use completely unrealistic methods that would never work you can definitely tell some of these folks never traded at all but that does not detract from the applicability of models I'm referring to because academia is a rather diverse place apparently. I'm just an outsider that really digs SCI-HUB.
My first approach at implementing this model used numerical techniques and even if they were not unstable due to fixed point arithmetic they would take centuries to price options you'd have to buy a freaking cluster or rent half of Amazon to compute the option prices that way. That's when I embarked upon the ARB4J project which is actually quite awesome by now and has capabilities that you cannot even purchase any commercial product (as far as I am aware was publicly available as of the last time I checked a few months ago). Feel free to check it out. If you want to use it for trading whoever it is will definitely be required to purchase a license from me and it reverts to open source in 4 years. Details are in the license file of the project.
I will have a companion library that will implement these techniques that would be of interest to anyone that wants to price options or futures I suppose it could also be applied and depending on the case I would also implement models on a custom basis. I guess the fancy way of saying this would be, bespoke. The companion library will not be even business source licensed the buyer will just know it's awesome by virtue of the fact of its capabilities and also the author having provided a proof of the Riemann hypothesis using the same framework would also provide much exposure I suppose. Well I wouldn't sell any packages that I didn't use myself for real trading. I'm not quite to the point where I tell BlackRock that if they don't get this then Morgan Stanley's going to have it and they will be at a competitive disadvantageThe wall of secrecy in Wall Street might be a hindrance in the regard that they might due to ego claim that they have and implementation of The thing I've produced but who knows there are many firms out there just got to be at least a few buyers.VIX is a huge market. Voice recognizer sucks. Open AIs voice recognition is stellar they should sell a subscription service to that as an Android plugin so you can just use it in place of this Samsung or Google crap
What type of numerical techniques? Similar to root finder? I've used gradient descent techniques with great successes