Your LinkedIn post only gives the computation time for your method, it doesn't give the computation time for the Monte Carlo method which gives the same accuracy. And it's not clear from it how you implemented the MC pricer.
This sounds naive: "The overall error on the entire portfolio of 1024 AutoCall is 0.2% (relative error on price), which corresponds to a convergence factor of rate 1 / N with N = 512". What about the constant factor? Convergence rate O(1/N) refers to how error eps(N) scales with N, not that eps = 1/N for some particular value of eps and N.
And first you're saying that your method converges at rate 1/N^2, but then you report rate 1/N for an AutoCall portfolio.
And buried in a footnote is the shocker news that your exciting 1/N^2 convergence rate does not work for bounded variation functions, a class which includes most reasonable payoff functions one can think about (e.g. (S(T) - K)+) ! So for all practical purposes, your method has the same convergence properties as Sobol numbers...
I think the problem you have in selling your method comes from the fact that you're overselling it too much and are not presenting its strengths and limitations clearly enough.
This is a Linkedin post. The MC Pricer is basically an encapsulation of boost libraries. Computation time is not very important there, as we were looking to a reference price.
Computational time is very important for people who need to deliver risk numbers to the boss at 7am every morning. These are the people you're selling your stuff to.
And you didn't answer my question (again
) - did you run the MC pricer separately for every option, or once for the whole portfolio? It doesn't affect only the computational time, but also the accuracy...
The relevant question in your answer is : "what about the constant factor ?". For instance, variance is a relevant constant factor for Monte-Carlo methods. Here, for this approach, the relevant constant is a "Sobolev" type norm.
Well, my criticism was even simpler: it's just not accurate or correct to say "0.2% (relative error on price), which corresponds to a convergence factor of rate 1 / N with N = 512" even if, in fact, 1/512 ~= 0.002. You CANNOT estimate the convergence rate for a single value of N. Either you prove it analytically (in the limit N -> infinity) or you try a series of N's and fit a linear function to error as a function of log N.
As you read in the footnote, autocalls are discontinuous functions, they are less regulars than calls options : they are like barriers options, to be snobbish, they are heavyside-like functions. I am saying that these methods converges at rate 1/N^2 for call options.
You seem to be contradicting your LinkedIn post now (or I don't understand something). In it you wrote that "a bounded variation function, a function class for which we know that the convergence rates of a sampling method can not exceed 1 / N, not 1/N^2." The payoff of a call option, (S - K)+, is a bounded variation function, hence the convergence rate should be limited to 1/N.