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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.
In the swaptions market, for instance quotes are typically for an “at-the-money forward” rate, which makes the first two components zero and all the value is tied to the vol.
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?
Implied volatility is really the standard deviation of the price over time. You can calculate it by look at prices in the market. Then interpolate values. Where banks get funky is that the market for options go out about 3 years, but a banks will write options going out much much further. For those options, they are really just guessing, no matter how much fancy math they do, it's all to dress up a guess. And the tra…
Maybe you mean that “implied volatility is really the implied standard deviation of the price over time”.
How does this square with "past market returns are do not (entirely) determine future market returns"? Surely the same applies to the historical stddev?
Yep. You can make money off of using options as a way of betting on what the volatility measure itself will be. If you think the historical standard deviation is lower than what it will be because of some new change to the company or the world environment, and your view is different from the market's view. It's why sometimes very out of the money call options will paradoxically go up in price after really bad news -…
Great book about all this, 2017 Autobiography: "A Man for All Markets: From Las Vegas to Wall Street, How I Beat the Dealer and the Market"
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?
I would answer- not much.
You can think of BS as a curried function. Since all the other params are fixed, you can curry and get a reduced equation that only depends on IV and underlying. If you do that, then its just - you give me iv and underlying, i give you spot. So, for a given strike(fixed), with the prevailing time left(fixed theta) under current interest rate(fixed), given the underlying, the historical vol gives you the wrong spot. You fudge it until you get the right spot. Call the fudged quantity the IV. Now plot that fudged quantity for a few other strikes and you get a smile. Then you can mess with that smile, plot the vol surface etc but end of the day, does the BS equation matter if the price of spot is going to be off and you have to fudge it with IV ? Its a good question. From an operational standpoint, the equation doesn’t matter. You can use bopm and get a more intuitive price anyways. Traders can trade the iv without knowing what effect BS has on the system.
When I was in 5th grade, they took us to the top of a tall building. We dropped a ball and measured the time it took to hit the ground. So if you square that time and multiply by 5, that’s how tall that building is. At that age I thought wow this is such magic! Then I grew up and reached 8th grade and worked out equations of motion with some basic differential calc, and derived the canonical equation s equals ut plus half at square. So since u is zero and a on planet earth happens to be g which is 9.8, half of which is about 5, that’s why 5t^2.
ok but does this equation matter ? I could have gone my whole life measuring height of buildings without knowing what is gravity.
Fisher black has written some interesting books. For anyone who is interested, check out his Wikipedia page.
If someone is interested in all this, I would strongly recommend looking into Ed Thorp, he discovered pretty much the same thing earlier, but instead of publishing, he made money with the knowledge... Great book about all this, 2017 Autobiography: "A Man for All Markets: From Las Vegas to Wall Street, How I Beat the Dealer and the Market"
Earlier quoted context omitted.
Yep. You can make money off of using options as a way of betting on what the volatility measure itself will be. If you think the historical standard deviation is lower than what it will be because of some new change to the company or the world environment, and your view is different from the market's view. It's why sometimes very out of the money call options will paradoxically go up in price after really bad news -…
Is that a bug in the equation that one could take advantage of?