Used an abbreviated version to of the kelly criterion along with Markowitz portfolio optimization and applied it to sports betting. All I can say is that past results do not indicate future returns
The part that all these nice theories miss is that you actually do not know the distribution p(win) (in the case of Kelly) or the expected return and covariance (in the case of Markowitz).
Well 'knowing' the 'true probability' is a philosophical can of worms anyway.
The good news is that you don't need to know it exactly, you just need to make a better guess than the bookies (w.r.t. the Kullback Leibler divergence or cross-entropy, whichever takes your fancy).
The fact that Black-Scholes has only one unknowable parameter makes it quite usable, more so than more complicated option pricing models. You can work backwards from the market price to solve for the implied volatility, treating it as a generalized 'price' for the option after factoring out things that are easily adjusted for. You can also abuse the implied volatility (adjusting it up or down) to account for factors outside of the idealized model.
You can’t pinpoint probabilities of many things that make the world run everyday, you can’t even pinpoint probabilities of things that happen in your personal life. It’s useful to at least know some mechanics behind these arcane things rather than completely disregarding them because you don’t fully know their distributions.
That's something of a moot argument, though, since BSM computes prices in terms of the future volatility. Since we have the actual price, the volatility is actually what we solve for with BSM.
Even if we had neither price nor volatility, we can still talk about the surface of possible (price, volatility) pairs which are compatible with the model.
Yeah, basically. Also need the strike, spot, an estimate of the risk free rate (probably not today).
The implied vol is a useful way to make sense of the actual market prices of options. We also might have some predictions about the market's implied vol changing going forward and we can reverse those errors back into expected price changes (and maybe trade on them).
