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How does this square with "past market returns are do not (entirely) determine future market returns"? Surely the same applies to the historical stddev?
Volatility is a bit more predictable than price. And there are more complex formulae that also model volatility rather than treat it as a constant.
Earlier quoted context omitted.
Eh, put-call parity is the hedging argument [1]. Black-Scholes-(Merton) was a breakthrough because it lets one understand why the hedge works, and thereby hedge and price more precisely. [1] https://en.m.wikipedia.org/wiki/Put–call_parity
What I never fully understood is there’s a free parameter in the equation (Implied Volatility)- which has no solid definition besides “the number that makes the rest of the equation work”. At that point… how much value are you really getting from the rest of the equation?
Black-scholes is a hedging argument, the eqn isn't the essence of it
Eh, put-call parity is the hedging argument [1]. Black-Scholes-(Merton) was a breakthrough because it lets one understand why the hedge works, and thereby hedge and price more precisely. [1] https://en.m.wikipedia.org/wiki/Put–call_parity
Earlier quoted context omitted.
Eh, put-call parity is the hedging argument [1]. Black-Scholes-(Merton) was a breakthrough because it lets one understand why the hedge works, and thereby hedge and price more precisely. [1] https://en.m.wikipedia.org/wiki/Put–call_parity
Taleb and Derman have argued that put call parity implies BS but other disagree quite strongly.
Earlier quoted context omitted.
Taleb and Derman have argued that put call parity implies BS but other disagree quite strongly.
Under reasonable assumptions, put call parity is true so it's not an important statement to say that it implies BS.
How does this square with "past market returns are do not (entirely) determine future market returns"? Surely the same applies to the historical stddev?
1) where there are pretty complete markets for implied volatility, looking at the past matters less to little, because there is a market for the "future volatility" you can hedge and interact with
2) when there isn't a good volatility market and hedging future volatility exposure is difficult, looking towards the past for some guidance increases in importance
Both things can get complicated at times and in both cases it isn't strictly speaking the stddev you care about, but the quadratic variation (which can be the same under some assumptions).
Earlier quoted context omitted.
What I never fully understood is there’s a free parameter in the equation (Implied Volatility)- which has no solid definition besides “the number that makes the rest of the equation work”. At that point… how much value are you really getting from the rest of the equation?
The parameter (sigma) is the historical volatility (stdev of annualized returns). Implied volatility is what you get if you run the formula backwards and input the observed price to solve for volatility. In practice though many people use implied volatility as the input making the whole thing circular.
How does this square with "past market returns are do not (entirely) determine future market returns"? Surely the same applies to the historical stddev?
Earlier quoted context omitted.
Volatility is a bit more predictable than price. And there are more complex formulae that also model volatility rather than treat it as a constant.
If volatility is predictable, it would quickly be traded until it became unpredictable and unprofitable.
Actual volatility (not implied!) is much easier to predict than price.
It’s also much more difficult to trade than price changes. So your intuition about this is correct though.
It is not super difficult to predict tomorrows volatility sign (up/down compared to today) with +60% success. Even textbook GARCH models do well here.
If you could do that with the price, you’d quickly become filthy rich.