In a way, yes. A lot of money follows these standard formulas for pricing which do not necessarily reflect accurate probabilities of the underlier price movement. After an idiosyncratic price shock (disappointing earnings, geopolitical news etc), people blindly following a trailing 1 month volatility or something will misprice the option as volatility reverts back to the mean. This probably has been arbed away to a large extent by trading algorithms.
The underlying assumption Black-Scholes makes, that stock price movements can be modeled by a log-normal distribution, is known to be false. However not since the 1980s has this lead to the ability to make money of the model itself being imperfect.
The true distribution of the market beliefs in future stock prices can be understood by empirically studying the volatility smile [0]. That is, because investors know Black-Scholes is not a perfect mathematical model of real world stock behavior, every strike price has a different implied volatility. By looking at these different IVs you can get a sense of what the market believes are the true probabilities of "long tail" events.
In theory, the opportunities you have to make money should be cases where you believe the market has mispriced risk. In my amateur experience, I have found that virtually every time you think the market has mispriced some extreme event, when you look at the volatility smile, you realize you are mistaken.
Not really. The equation is just saying "based off these assumptions here is the best price" and you would make money if your assumptions differ from market assumptions in a favorable direction. Arbitrage is the closest to exploiting "bugs" in finance to get risk free returns but in a liquid enough market all these obvious opportunities quickly close (if there's free money on the ground, someone will pick it up, and then there's no more free money ond the ground. Some hedge funds build ultra fast private internet networks just to be able to pick up that free money nanoseconds faster than someone else). It's more that the equation is telling you if you think you have a better estimate for some of these values, what you should be willing to pay.
In a way, yes. A lot of money follows these standard formulas for pricing which do not necessarily reflect accurate probabilities of the underlier price movement. After an idiosyncratic price shock (disappointing earnings, geopolitical news etc), people blindly following a trailing 1 month volatility or something will misprice the option as volatility reverts back to the mean. This probably has been arbed away to a large extent by trading algorithms.
The underlying assumption Black-Scholes makes, that stock price movements can be modeled by a log-normal distribution, is known to be false. However not since the 1980s has this lead to the ability to make money of the model itself being imperfect.
The true distribution of the market beliefs in future stock prices can be understood by empirically studying the volatility smile [0]. That is, because investors know Black-Scholes is not a perfect mathematical model of real world stock behavior, every strike price has a different implied volatility. By looking at these different IVs you can get a sense of what the market believes are the true probabilities of "long tail" events.
In theory, the opportunities you have to make money should be cases where you believe the market has mispriced risk. In my amateur experience, I have found that virtually every time you think the market has mispriced some extreme event, when you look at the volatility smile, you realize you are mistaken.
0. https://en.wikipedia.org/wiki/Volatility_smile
Not really. The equation is just saying "based off these assumptions here is the best price" and you would make money if your assumptions differ from market assumptions in a favorable direction. Arbitrage is the closest to exploiting "bugs" in finance to get risk free returns but in a liquid enough market all these obvious opportunities quickly close (if there's free money on the ground, someone will pick it up, and then there's no more free money ond the ground. Some hedge funds build ultra fast private internet networks just to be able to pick up that free money nanoseconds faster than someone else). It's more that the equation is telling you if you think you have a better estimate for some of these values, what you should be willing to pay.