An Intuitive Explanation of Black–Scholes
gregorygundersen.com
An Intuitive Explanation of Black–Scholes
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Re: An Intuitive Explanation of Black–Scholes
#2If you found a stock price that actually follows the geometric Brownian motion pattern this model is built on, wouldn't that basically just print you an infinite amount of money? The expected value of the price movement one time-unit later would be positive.
Re: An Intuitive Explanation of Black–Scholes
#3If you found a stock price that actually follows the geometric Brownian motion pattern this model is built on, wouldn't that basically just print you an infinite amount of money? The expected value of the price movement one time-unit later would be positive.
I think these models are self-defeating, since they stop working when enough people try to exploit them.
Re: An Intuitive Explanation of Black–Scholes
#4If you found a stock price that actually follows the geometric Brownian motion pattern this model is built on, wouldn't that basically just print you an infinite amount of money? The expected value of the price movement one time-unit later would be positive.
The competitive advantage is lessened because everyone knows it already. It’s “priced in” as they say
Re: An Intuitive Explanation of Black–Scholes
#5If you found a stock price that actually follows the geometric Brownian motion pattern this model is built on, wouldn't that basically just print you an infinite amount of money? The expected value of the price movement one time-unit later would be positive.
No, this doesn't imply an "infinite amount of money", it's just a pricing model.
You still need the parameters of the distribution (brownian motion / random walk), and these are unobservable. You can try to estimate them, but there is a lot of practical problems in doing so, primarily that volatility / variance isn't constant.
Re: An Intuitive Explanation of Black–Scholes
#6If you found a stock price that actually follows the geometric Brownian motion pattern this model is built on, wouldn't that basically just print you an infinite amount of money? The expected value of the price movement one time-unit later would be positive.
I think these models are self-defeating, since they stop working when enough people try to exploit them.
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Re: An Intuitive Explanation of Black–Scholes
#7This guy's other notes are also well thought through and written. Thanks for the link.
Re: An Intuitive Explanation of Black–Scholes
#8If you found a stock price that actually follows the geometric Brownian motion pattern this model is built on, wouldn't that basically just print you an infinite amount of money? The expected value of the price movement one time-unit later would be positive.
Yes. That’s basically how the stock market works. If you buy and hold an S&P 500 index fund you can expect to make an infinite amount of money, in an infinite amount of time. But few have the patience for that.
Re: An Intuitive Explanation of Black–Scholes
#9If you found a stock price that actually follows the geometric Brownian motion pattern this model is built on, wouldn't that basically just print you an infinite amount of money? The expected value of the price movement one time-unit later would be positive.
I think these models are self-defeating, since they stop working when enough people try to exploit them.
The opposite.
We have huge numbers of people 'rocking the boat' trying to create say.... a Gamma Squeeze.
The only reason everyone trusts a Gamma Squeeze can happen is because they trust the math in Black Scholes. The may not even understand the math, just trust that the YouTuber who told them about Gamma Squeezes had enough of an understanding
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Today's problem IMO, is now a bunch of malicious players who are willing to waste their money are trying to make 'interesting' things happen in the market, almost out of shear boredom. Rather than necessarily trying to find the right prices of various things.
Knowing that other groups follow say, Black Scholes, is taken as an opportunity to mess with market makers.
Re: An Intuitive Explanation of Black–Scholes
#10If you found a stock price that actually follows the geometric Brownian motion pattern this model is built on, wouldn't that basically just print you an infinite amount of money? The expected value of the price movement one time-unit later would be positive.
This is a pricing model, i.e. what is the value according to the assumptions the model does (which btw are known to be weak for BS) but as anything else the price is what you are going to pay in the market for whatever other reasons.
Imagine you have a model that establishes the price of used cars, it can be really really good but if you go to the market to buy one you will pay whatever is been asked for not what your model says.
EDIT: Although pricing models do not have direct affectation to market prices they do in an indirect manner. To manage risk are needed pricing models which somehow condition market participants and therefore prices indirectly. In the simile with cars, you can buy as many cars as you want at the price you want, but what you do when you have them and if you want to take wise decisions with them you have to know something about their value.