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Old Nov 3rd 2017, 08:15 AM   #1
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Difference between Einsteins Brownian Motion and Geometric brownian motion.

We all know this. Even a fifth grader knows that brownian motion measures distance. Distance is change in position. This is similar to geometric brownian motion which measures change in stock price. Now as a fifth grader would tell you there is one more similarity. One part of the formula of Brownian Motion measures the mean squared displacement which is similar to variance concept in quantitative finance. Which leads us to standard deviation. So mean squared displacement is similar to standard deviation. But this is only the shock part. How does the first part namely drift compare with Einsteins formulation of brownian motion?

If the above is not correct then tell me how was drift and shock derived from original brownian motion equation? Tell me the similarity between brownian motion formula of Einstein and geometric brownian motion formula. If possible tell me about black scholes model. Being from a finance background I studied black scholes model. But didnt go deep. Now I am thinking deeply.

As Salman Khan says "You can learn anything". I believe I can learn anything. Is Salman Khan right when he says so?
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Old Nov 3rd 2017, 08:28 AM   #2
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Originally Posted by avito009 View Post
We all know this. Even a fifth grader knows that brownian motion measures distance. Distance is change in position. This is similar to geometric brownian motion which measures change in stock price. Now as a fifth grader would tell you there is one more similarity. One part of the formula of Brownian Motion measures the mean squared displacement which is similar to variance concept in quantitative finance. Which leads us to standard deviation. So mean squared displacement is similar to standard deviation. But this is only the shock part. How does the first part namely drift compare with Einsteins formulation of brownian motion?

If the above is not correct then tell me how was drift and shock derived from original brownian motion equation? Tell me the similarity between brownian motion formula of Einstein and geometric brownian motion formula. If possible tell me about black scholes model. Being from a finance background I studied black scholes model. But didnt go deep. Now I am thinking deeply.

As Salman Khan says "You can learn anything". I believe I can learn anything. Is Salman Khan right when he says so?
Anyone can learn just about anything provided they are willing to put in the time and effort to do so. I've been studying for about 15 years to try and grapple with string field theory

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Old Nov 3rd 2017, 08:47 AM   #3
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Originally Posted by avito009 View Post
We all know this. Even a fifth grader knows that brownian motion measures distance. Distance is change in position.
Really? That's what they teach? I shudder to think what teachers have in mind when the say such things.

Brownian motion is defined as the random motion of particles suspended in a fluid. See: https://en.wikipedia.org/wiki/Brownian_motion

Originally Posted by avito009 View Post
Distance is change in position.
W
Where did you get that idea? That's not what distance is. Distance is the measure of how far apart two points in space is.

Originally Posted by avito009 View Post
This is similar to geometric brownian motion which measures change in stock price.
See: https://en.wikipedia.org/wiki/Geometric_Brownian_motion
Geometric Brownian motion is a the continuous-time stochastic process in which the logarithm of the randomly varying quantity follows a Brownian motion.

Originally Posted by avito009 View Post
... similar to variance concept in quantitative finance.
Variance is a concept that comes from probability and statistics theory.
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Old Nov 3rd 2017, 10:04 AM   #4
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My estimation.

I am not sure as to what brownian motion formula measures as I couldnt find much on internet. I searched as to what it measures but couldnt find out clearly.

In one place it was mentioned that Einstein couldnt measure distance travelled by a single particle so he found distance travelled by all particles collectively. Thats why I said the formula measures distance.

Also I asked my friend as to what was the meeting point between physics and finance. How was physics used in finance? What was the link? So he told me it was brownian motion. Brownian motions links physics to finance. Statistical physics that is.
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Old Nov 3rd 2017, 11:38 AM   #5
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Let's start with a correct statement.


Brownian motion was not discovered by Einstein.

It was discovered by ....well..... Brown.





History: Brownian motion was discovered by the biologist Robert Brown [2] in 1827. While Brown was studying pollen particles float- ing in water in the microscope, he observed minute particles in the pollen grains executing the jittery motion.
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Old Nov 6th 2017, 10:11 AM   #6
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Originally Posted by avito009 View Post
I am not sure as to what brownian motion formula measures as I couldnt find much on internet. I searched as to what it measures but couldnt find out clearly.

In one place it was mentioned that Einstein couldnt measure distance travelled by a single particle so he found distance travelled by all particles collectively. Thats why I said the formula measures distance.

Also I asked my friend as to what was the meeting point between physics and finance. How was physics used in finance? What was the link? So he told me it was brownian motion. Brownian motions links physics to finance. Statistical physics that is.
Brownian motion is not a measure of anything. Its simply what is observed. See the link at Wikipedia that I posted.
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