Monte carlo simulation: Brownian motion

[Fullperson]

I have downloaded S&P prices, how do I find annual drift?

[DharmikJ]

great video! Even though I studied this in uni, I was a bit shaky in answering this question in an interview but now feel more confident about it! thanks a lot :)

[pgthanki]

This is a great Video. Thanks so much David Harper.

[AnkitMichael]

Cool :)

[thanhvuueh]

How can I compute Var with changing price in Monte Carlo method. it is easy to calculate var in Historical

[fvgdfbdokd]

Gah, you should go in complete detail. Pull no punches dammit, I didn't spend the last 6 years studying physics for naught! ;)

[neb967]

Do you know of any other pricing dynamics other than GBM that you can utilise for these simulations...?

Perhaps something with a distribution that incorporates heavier tails...?

I find the Gaussian bell-curve a bit false.

I get taught by Dr Alexander at ICMA though btw.

[jokermant]

Hi @bionicturtledotcom, is this the same approach to simulate Monte Caro VaR for a portfolio?

[luisxtm]

Very good video explanation, all the formulas match with the ones I have on my notes. We can use the Drift value (Expected return) from CAPM model and Stock Volatility calculated using GARCH.

[nahaymath]

Just curious: as an undergraduate in chemical engineering at the University of Delaware in the 1980s, I got a VERY rigorous education in mathematical modelling - i.e. in coming up with one's OWN models (of the physical world). That training completely altered my way of thinking and inspired my passion for inventing new models of events.

I assume and hope that students today are still taught in math and engineering classes to invent models, in addition to studying the work of others.

[LondonBoy2006]

@nahaymath No they are not, just memorize the book to get a 2.1 or 1st. (UCL University Of London).

[TommyMarxable]

@nahaymath In math and engineering, yes. In finance, no. Most people who use this have no idea of the fundamental principles they are applying.

[ids180genius]

@TommyMarxable Actually, the GBM process is considered a "random walk" which is actually the most appropriate model for the market without getting into agent based modelling. So, in finance, YES. The Black Scholes option pricing formula was also derived from a geometric Brownian Motion assumption and through the use of Ito's lemma fwi....

[TommyMarxable]

@ids180genius Fantastic regurgitation. If you read the thread, I was saying most people in the finance world who use Black Scholes have no idea how it works (of course they'll have read the finance 301 textbook, case in point). I wasn't knocking the model itself. In engineering and physics fields there is no pre-packaged excel spreadsheet you can buy on the internet to solve the problems you find there.

[nahaymath]

The hard thing is modelling justice. That requires formal logic, predicate calculus, the concept of contradictions. The notion of: if player P (bankers, gets all the rewards for a transaction but none of the risk), while player Q (ordinary poor Joe) is forced to be punished if HE is caught commiting fraud, then over time, P will take away far more from Q than Q from P. It's a negative sum game for Q.

The fault is never math modelling & formalization. It's in the person doing the modelling,

[nahaymath]

@nahaymath .. or, more specifically, deliberately misapplying models with tons of wrong assumptions, the number one assumption being that all players act honestly and keep their promises.

[777wt]

maybe should we blame the banksters and CDS? to create the big scam of crisis!

[bionicturtledotcom]

@pzedful I can't argue with somebody who is careful with their comments; i.e., 1/[norm.s.dist( -5 , true)*2] = ~ 1.7 million, indeed!

... I agree with you, but i still like using the normal b/c it is a common building. This video isn't about the distribution per se, it's about the GBM in MCS, as a drift + random process. So, why complicate with a detour on the problems of normal? Where to draw the line; e.g., the i.i.d. assumption (i.e no mean reversion/autocorrelation) is also a problem?

[777wt]

IS it the reason why we got economic crisis ? with shit formula !

[bionicturtledotcom]

@777wt honestly you should blame the copula not MCS, IMO. If folks ran more simulations, it might have helped

[BOomster86]

@777wt no

[bionicturtledotcom]

@pzedful it's normal just by definition of GBM. MCS can use any distributional assumption. Why? physics envy, of course. Exactly why? because i wanted to share and it's the first MCS I learned. Caveat emptor. I am not defending it. Models simplify, that's what they do. A toy train is not a train, but it may still have something to offer about the train-ness of trains.

[nahaymath]

@bionicturtledotcom Thank you, pzedful, for asking this question, and thank you bionicturtledotcom for answering it so well. (Nearly) everyone loves the normal distribution so much because it really involves only 2 free parameters: the average (1st moment) and variance (2nd moment). I never like to assume normal distribution (ND). I prefer to make up my own.

[nahaymath]

@bionicturtledotcom LOL! Great explanation. It's amazing how strongly those who do applied simulations get wed to their favorite probability distribution functions, because THOSE were the ones they were taught in school. No shame! I am just as easily attached to the distributions I learned studying for my actuarial exams. The great value of doing research is it forces one to be creative and to consider all conceivable probability functions.

[caetans]

nice video!! how can I get Value at rik from your example?

[WarrenEdwardBuffet]

Is there a way I could let excel do this monte carlo simulation 100 times in a row with all the results simultaneously displayed on a single chart?

[bionicturtledotcom]

@WarrenEdwardBuffet sure, you'd just extend the XLS i used above to 100 rows. If you request in our forum (click on our YT channel header), I'll share you my copy (I don't think YT lets me link directly...)

[WarrenEdwardBuffet]

@bionicturtledotcom Yeah, I have done that already. I was just so excited to try it out because I heart a lot about the monte carlo simulation but no one taught us during our studies. Thanks anyways! I will be subscribing, great channel.

[remo1200]

thanks for the reply, the matter is that I have to find the expected return for a different excercise. thanks for your time, anyway, man.

[remo1200]

Hi, how do you get the drift????

[bionicturtledotcom]

@remo1200 as slipknotpsychoman noticed, I made a mistake in the drift. First, the annual drift of 10% is merely an input assumption (nothing necessary about that). Second, the daily drift should be = (10% - 40%^2/2)/252 = 0.0079%. Or, daily mu = 10%/252 = 0.04%. Daily vol = 40% * SQRT(1/252) = 2.52%. And daily drift = 0.04% - 2.52%^2/2 = 0.0079%.

(by inadvertently deleting the extra 2 in 252, i implicitly assumed an annual drift of 101%)

[maleckicoa1]

@bionicturtledotcom

drift should be a random walk function on excel

[bionicturtledotcom]

@maleckicoa1 This is GBM, the drift is deterministic component and volatility is the stochastic component; i.e., RAND() scales the volatility

[KeshaWW]

previously did not believe that so many stupid people

[remynz]

Do you have any examples with correlated variables using choleski ordering..

[dicieromike]

Hi David--

In your example - prices evolve log normally - median return (vol factored) is not equal to mean return.

Mike

[bionicturtledotcom]

@dicieromike yes understood and i agree the "mean" is imprecise.... but the input cell is Greek "mu" (not mu - 1/2 variance^2). I do not think I would label mu as "median return." I was just trying to identify the best label for mu given that, IMO, neither "mean return" nor "median return" is precise.

[bionicturtledotcom]

@dicieromike (of course i meant 1/2 variance below). I checked Hull: he calls mu "Expected return on stock per year" ... so i am liking "Exp return" or just "drift" ; i.e., no median or mean. thanks for the insight!

[dicieromike]

Hi David--

Aren'y you using a median (geometric) return?

Mike

[bionicturtledotcom]

@dicieromike great observation. I think i did mislabel but it should be: drift (return). You are totally correct that under the GBM, the use of the return (mu) as an INPUT gets to the distributional median with (mu - var^2/2) rather than mean with (mu). I guess we could, confusingly, also call this a geometric rather than arithmetic mean. In summary, I find "mean" ambiguous. Which is a way of agreeing with you that it is a bad label. But i think i like "return" (mu) rather than median. thoughts?

[bionicturtledotcom]

@dicieromike it just occurred to me, unless i have confused myself, that what is typically called a "geometric mean" is equivalent to the distributional "median" (i.e., ex ante lognormal) ... if you know better or agree, i'd love to hear how i could have that wrong?

[dicieromike]

Hi David--

Aren't you using median (geometric) dirft? Your cell is labeled 'mean'.

Thanks,

Mike

[MissJookie]

Very simple and good explanation, thanks !

[brunetto345]

bravissimo, complimenti

[SPW1981]

Thanks for all your videos. They are really helpful. You explain very well.

[quacka101]

this be for nerds and geeks me thinks.

[Volver1234]

If it be NERD, I proudly am :D

[ajnaqvi86]

What would be the modification of the methodology in this simulation if you would look at a simple portfolio of stocks instead of a singular asset?

[gitgitgitgitgit]

Hi, did you find an answer? I'm also interested.

[Riverdale270]

this really comes in handy for my masterthesis, thanks a bunch!

[slipknotpsychoman]

you deleted the end 2 of the 252 drift daily on accident

[bionicturtledotcom]

yes, thank you for noting that, I did mistakenly change the 252 to 25. I appreciate your help on that point. David

[wooddog007]

@slipknotpsychoman ... i noticed this too. wish BT would fix it in a new example.

[sudeepdoon]

All the videos from the user are very good and are very helpful..

:)