I have a question about the Ito's integral. You say that the Ito Integral in the integral of a random variable with respect to Brownian motion correct? But what exactly is that? For example, if you integrate a velocity function what the answer IS is the total distance traveled. Or more generally multiple the y-axis by the x-axis and it is the total of what ever that product is. So what exactly IS the answer you get from performing Ito's Integration?
“We expect the share price to grow as time goes because the more shares we have the more it grows e.g if it doubles then it will follow an exponential manner”. No dude, if it doubles over time its just linear y=2x 😅 Exponential is because we want the share price to not have negative values and grow with the risk free interest rate. The whole idea of brownian motion by the way is NOT that we expect the share to grow, but that it will have the same probability of up and down movement like a random walk. Geometric brownian motion has this growth just because it follows the risk free interest rate.
if the volatility is = 0 then the stock price will behave like a Risk free investment (bond), if you invest your money on risk free assests, your wealth will grow exponentialy with a constant rate of return.
It kind of is being "added" to e^(alpha*t)... The key is to think about laws of indices: the "randomness" is still following an exponential shape so should be e^(beta*Bt). Thus, when we put it together we have e^(alpha*t) x e^(beta*Bt). So because the bases are the same and being multiplied, we add in the powers: e^(alpha*t + beta*Bt) The reason why we MULTIPLY them together rather than add: e^(alpha*t) x e^(beta*Bt) rather than e^(alpha*t) + e^(beta*Bt) Think about transformations of graphs... Effectively our starting function is f(x)=e^(alpha*t) which is the familiar smooth exponential function ADDING e^(beta*Bt) would TRANSLATE our original f(x) vertically: f(x) + b where I've just called b our e^(beta*Bt) But that's not what's happening here; instead our f(x) is being pushed and pulled up and down... so STRETCHED in the vertical direction. A stretch applied vertically corresponds to MULTIPLYING f(x) by a value: b x f(x) where, again, b is just e^(beta*Bt) (granted, it's not a single stretch like we're used to but the Bt bit in e^(beta*Bt) will take care of that because it will change its value depending on what time we're at so will stretch it by a different amount at every time) So b x f(x) = f(x) x b = e^(alpha*t) x b = e^(alpha*t) x e^(beta*Bt) = e^(alpha*t + beta*Bt) Hopefully that's a little clearer now :)
Have systematic strats profited off of these assumptions over the past years because? A) the assumptions are sound or B) central banks have inflated financial market Security prices move because of human action, phraseology. Not because of Brownian motion. You will figure it out one of these days, its going to hurt.
I was looking for weeks for a simple explanation like this! So relieved that I finally understood what the term actually means...Big thanks! 🙌🙌🙌
Best simple and concise explanation that I could find on CZcams - thank you!
thanks for such a simple explanation. I was struggling with brownian motion for quite a long time. Your video really helped to understand.
The simplest explanation for Brownian Motion! Thanks a lot
Great Video mate!You just saved me hours of research cheers!
Mans really said at 7:30 "you don't really need to understand the maths" WHAT ELSE ARE WE SUPPOSED TO DO
I have a question about the Ito's integral. You say that the Ito Integral in the integral of a random variable with respect to Brownian motion correct? But what exactly is that? For example, if you integrate a velocity function what the answer IS is the total distance traveled. Or more generally multiple the y-axis by the x-axis and it is the total of what ever that product is. So what exactly IS the answer you get from performing Ito's Integration?
Thank you thank you thank you! Finally I understand BM
great video!
Great video. Very well explained
Thank you sooo much! It is really clear and does help me a lot!
wow. amazing. thanks mate
Thank you so much!!!!!
This amazing
That "share prices grow exponentially" explanation is non sense. The exponential factor is about compounding interest/return in continuous time
That's true. But despite some of his mistakes, this guy is still a really good teacher
yes but das okay. He managed to keep me stick around and follow along unlike MITCourseware Dry jokes lectures.
Logarithmic which is exponential otherwise long price action gets stuck in consolidation.
you are a champion human
what is the correlation function of a geometric Brownian motion ?
Thank you
You're just a good bloke
Beta can be roughly approximated by (Correlation of X,M * Std. Dev.X)/(Std. Dev.M)... where X equals your security in question, and M is the market.
at 7:56, why isnt it alpha * t + beta * B(t) ?
how do we know that Bt~N(0,t) whats the theory behind it. do u explain it somewhere
“We expect the share price to grow as time goes because the more shares we have the more it grows e.g if it doubles then it will follow an exponential manner”. No dude, if it doubles over time its just linear y=2x 😅 Exponential is because we want the share price to not have negative values and grow with the risk free interest rate. The whole idea of brownian motion by the way is NOT that we expect the share to grow, but that it will have the same probability of up and down movement like a random walk. Geometric brownian motion has this growth just because it follows the risk free interest rate.
why assume that prices grow exponentially?
if the volatility is = 0 then the stock price will behave like a Risk free investment (bond), if you invest your money on risk free assests, your wealth will grow exponentialy with a constant rate of return.
Great fucking video mate.
@3:45 why does beta * Beta T equals a mean of 0?
Why beta*Bt is added to alpha*t instead of being added to e^alpha*t? thank you.
It kind of is being "added" to e^(alpha*t)...
The key is to think about laws of indices: the "randomness" is still following an exponential shape so should be e^(beta*Bt).
Thus, when we put it together we have e^(alpha*t) x e^(beta*Bt).
So because the bases are the same and being multiplied, we add in the powers: e^(alpha*t + beta*Bt)
The reason why we MULTIPLY them together rather than add:
e^(alpha*t) x e^(beta*Bt) rather than e^(alpha*t) + e^(beta*Bt)
Think about transformations of graphs...
Effectively our starting function is
f(x)=e^(alpha*t)
which is the familiar smooth exponential function
ADDING e^(beta*Bt) would TRANSLATE our original f(x) vertically:
f(x) + b
where I've just called b our e^(beta*Bt)
But that's not what's happening here; instead our f(x) is being pushed and pulled up and down... so STRETCHED in the vertical direction. A stretch applied vertically corresponds to MULTIPLYING f(x) by a value:
b x f(x)
where, again, b is just e^(beta*Bt)
(granted, it's not a single stretch like we're used to but the Bt bit in e^(beta*Bt) will take care of that because it will change its value depending on what time we're at so will stretch it by a different amount at every time)
So b x f(x) = f(x) x b = e^(alpha*t) x b
= e^(alpha*t) x e^(beta*Bt) = e^(alpha*t + beta*Bt)
Hopefully that's a little clearer now :)
Have systematic strats profited off of these assumptions over the past years because?
A) the assumptions are sound or
B) central banks have inflated financial market
Security prices move because of human action, phraseology. Not because of Brownian motion. You will figure it out one of these days, its going to hurt.
7:09 it’s Beta * Brownian Motion and not Beta * t
Var(kx)=k^2var(x) not k2x anyways thanks
He says Var(kX) = (K^2).a and a = Var(X)
So it's totally correct!
my bad then