Brownian Motion Share Price Modelling

Рет қаралды 9,366

Mathematics with Plymouth University

Күн бұрын

In this short video we describe a mathematical model for share price behaviour over time.
To do this we discuss Brownian motion, which you may know from science lessons, and how it is represented mathematically.
Like all mathematical models, our share price model involves unknown parameters. We explain some theory about how these
parameters can be estimated from data, and we illustrate this estimation using Marks and Spencer’s share prices over time.
We use the Taylor expansion of log(1 + x) to link our estimation process with the concept of relative return. Finally, we mention some drawbacks of the mathematical model
that we have described, and where this model is used in the study of financial markets and the products that derive from them.

Пікірлер: 22

@benjiemejos7246 29 күн бұрын

having a hard time understanding the concept of this model but this man just explained it to me in a simplest way. this is the best video tutorial i've ever seen! Dr. Stander, you are the best!

@user-jm7ct9qj6i Жыл бұрын

Have to admit, this is THE BEST video I have watched that explains the Brownian motion clearly. Thank you!

@renemartinez3014 2 жыл бұрын

Dr. Stander, this is the best, straight to point and most well explained video about Geometric Brownian Motion on KZfaq. Excellent job, congrats.

@kubawyszomirski 6 ай бұрын

So good. The best explanation online.

@muaazkasker5075 3 жыл бұрын

brilliant video that explains brownian motion almost effortlessly! 👏 very helpful

@brunoissler7800 2 жыл бұрын

very didactic! cheers from Brazil!

@anujpatel6438 3 жыл бұрын

Wonderfully explained everything

@motamota8141 3 жыл бұрын

Well done, clearly explained

@dil9112 3 жыл бұрын

Thank you so much.It was very helpful to understand brownian motion.

@anthonychung8112 17 күн бұрын

Hi, Prof . Its really interesting modelling. Could u shows us the coding please

@StevenSmith68828 Жыл бұрын

Always wondered what this was in chem now im balls deep in quantitative finance with no intention to change careers lol

@danielaisabel5096 4 ай бұрын

Grazie mille!

@sunbreezy3935 2 жыл бұрын

Great Video. Would you be able to explain how to simulate geometric brownian motion in R?

@lauralagesse9121 2 жыл бұрын

This is a great video. Please may you tell me how you did the codes. Please may you send them to me!!!

@RARa12812 2 жыл бұрын

So we don't need itos lemma?

@vbg1980 3 жыл бұрын

He didn't tell why there cannot be mixed values for mean and standard deviation (variance); in his assumptions

@mindspectre1 Жыл бұрын

The GBM equation Xt = X0 * exp (mt + s* B) , could some one explain why this doesn't explode since exp of any mean + std * random number is going to be a reallly large number. ie (exp (11+1*.2) is > 59K

@ErdoganCEVHER 3 жыл бұрын

Many thanks. Is there a link to the R code in the video?

@sigangsabaglari3606 2 жыл бұрын

Have you found it?

@sigangsabaglari3606 2 жыл бұрын

Can someone please provide the codes

@TraderZeta 2 ай бұрын

I dont think this is correct. You are claiming that X_t = X_0 *Exp( mu_hat *t -sigma_hat*B_t) is geometric brownian motion? Geometric brownian motion or GBM is the solution to the SDE , dSx = Sx *mu dt + Sx*sigma* d Bx where Sx= Sx_0 *Exp( (mu - sigma^2 / 2) *x + sigma d*Wx) ( check wiki) . Also, the linear drift system is better genearlized by fractional brownian motion i.e. d B_H(x) which is defined by mandlebrot-vonness and where H is the hurst index. Fractional stochastic calculus would better suit the purpose here since it not need be gaussian. The only real application of the linear drift system would be if the dWx was gausian and often its not. Lastly, you are using log returns which have an implied bias of the gassuian, I find percent change works better in calculating returns.

@HitAndMissLab 11 ай бұрын

this is exceedingly inaccurate because it is well known that financial market prices are distributed with fat-tail distribution, not with normal distribution that is unfortunately assumed here.