In your other comment, you said you are looking to price "weird derivatives". How weird are we talking? If its OTC I won't be able to help anyway, if its standard then I can at least try to point you in the right direction. The fact you mention Black Scholes makes me think it might be something closer to "vanilla" than the other way around.
It’s looking like the goal will be to create downward pressure on derivative beta (especially in the case of a rapidly increasing underlying: big pools of Hopper cards basically).
I have a vague intuition that transaction costs will be sort of cumulatively symmetric: participants who get in quickly will pay a lot per unit time, but conversely, people who VWAP in will get zero-rated on the way out.
There’s a legitimate underlying switching cost, there’s a stability premium thereby, making that equitable for all participants is an interesting problem.
Am I correct in understanding that you have the spot price of Hopper card compute as your underlying and then come up with a pricing equation for some derivative instruments for that?
If what you have is FX-like I wouldn't be able to help beyond that anyway, FX modelling is its own thing and I haven't done anything there since the obligatory uni courses(in equity space myself). AFAIK the general way to do things in rates/FX is SABR for vanilla and then PDE/MonteCarlo for exotics, but I was never on an FX desk so don't want to point you in the wrong direction.
As I’m sure you can tell, pricing exotic derivatives isn’t my day job.
But your reminder to think of SABR/implied-vol is useful: I think there’s a convexity argument that can be made around how fat the tails would need to be.
I’m not sure anyone is going to be thrilled at “anywhere between one hundred dollars and one hundred million dollars”, but my job is to figure out the bounds.
