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An Intuitive Explanation of Black–Scholes

gregorygundersen.com

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Re: An Intuitive Explanation of Black–Scholes

#11

Post by rubyn00bie »

pfdietz wrote: post #3
ComplexSystems wrote: post #2

If 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.

I used to think charting was bullshit for day and swing trading. Because on paper it sure seems to be, but in reality so many other players are also charting that it becomes useful and somewhat predictive. Largely because you’re all using the same signals. Sure it’s impossible difficult to time things perfectly, but perfect is the enemy of profit. You don’t need to catch the absolute bottom and you don’t need to catch the absolute top.

Specific to Black-Sholes the best option plays, when going long, are the ones which have incorrect assumptions about the volatility of the underlying. You can have far outta the money options, absolutely print, with a sufficient spike in the underlying. Even if the strike price will never be met (though you’ll also give that back if you ride them to expiration or let things settle down).

Re: An Intuitive Explanation of Black–Scholes

#12

Post by stackghost »

ComplexSystems wrote: post #2

If 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.

Indeed, hence the meme "stocks only go up". There's a grain of truth to the meme, though. The safest bet I can think of to make is that, on average, the S&P 500 will be higher in the future than today. Obviously there are temporary down trends but on a time horizon of years to decades I can't think of a safer bet.

Re: An Intuitive Explanation of Black–Scholes

#13

Post by nicolapede »

ComplexSystems wrote: post #2

If 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. Just look at equations 6 and 7 in the link. The expected value of the move can be either positive or negative depending on the model parameters.

Re: An Intuitive Explanation of Black–Scholes

#14

Post by pigeons »

stackghost wrote: post #12
ComplexSystems wrote: post #2

If 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.

Indeed, hence the meme "stocks only go up". There's a grain of truth to the meme, though. The safest bet I can think of to make is that, on average, the S&P 500 will be higher in the future than today. Obviously there are temporary down trends but on a time horizon of years to decades I can't think of a safer bet.

However the company stocks included in the S&P 500 aren't the same.

Re: An Intuitive Explanation of Black–Scholes

#15

Post by tel »

ComplexSystems wrote: post #2

If 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.

Generally these parameters are unknown and the drift parameter is often quite a bit smaller than the volatility. As a consequence, you cannot be sure your investment is secure and its value is likely to wobble significantly in the short term even if it ultimately produces value in the long term.

If you actually knew that the drift on a certain investment was positive, you still have to be prepared to survive the losses you might accumulate on the way to profit. The greater the volatility the more painful this process can be. If you can just sock away your investment and not look at it for a long time it will become more valuable. On a day-to-day time scale, as an actual human watching this risky bet you've made wobble back and forth, it can require a lot of fortitude to remain invested even as the value dips significantly.

Re: An Intuitive Explanation of Black–Scholes

#16

Post by yieldcrv »

the creators of Black-Scholes destroyed their options selling fund based on their flawed belief that everyone else had mispriced options, or the black swan possibility should have been part of the formula

also Black-Scholes doesnt factor in the liquidity of the underlying asset, in modern times I think this is relevant in determining the utility of an options contract

there are other options pricing formulas

Re: An Intuitive Explanation of Black–Scholes

#18

Post by smabie »

ComplexSystems wrote: post #2

If 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.

Why? the mean can be negative?

Re: An Intuitive Explanation of Black–Scholes

#19

Post by smabie »

stackghost wrote: post #12
ComplexSystems wrote: post #2

If 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.

Indeed, hence the meme "stocks only go up". There's a grain of truth to the meme, though. The safest bet I can think of to make is that, on average, the S&P 500 will be higher in the future than today. Obviously there are temporary down trends but on a time horizon of years to decades I can't think of a safer bet.

Safer bet would be to hold short term treasures.

Re: An Intuitive Explanation of Black–Scholes

#20

Post by smabie »

yieldcrv wrote: post #16

the creators of Black-Scholes destroyed their options selling fund based on their flawed belief that everyone else had mispriced options, or the black swan possibility should have been part of the formula also Black-Scholes doesnt factor in the liquidity of the underlying asset, in modern times I think this is relevant in determining the utility of an options contract there are other options pricing formulas

LTCM wasn't really an options selling fund though selling equity options did become a big trade for them

Also they were more of advisors in the fund then anything else

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