I have not got a clue who he is but his lecture is the best way to explain a difficult subject. Not many people can stand on his feet, think and solve problem in front of the students.
@hansa91598 ай бұрын
Your lectures are heaven-sent
@tomminterbobby11 жыл бұрын
I actually understand all your videos. I highly recommend them
@coopernfsps7 жыл бұрын
Thank you for this great explanation!
@WineHot741 Жыл бұрын
If you are still active well you should know that after 12 years this video is helping a lot. I wish you were my professor
@rockYhre11 жыл бұрын
I am really enjoying this video, thanks for sharing!
@oxtherider12 жыл бұрын
thank you so much for this lecture!
@k_anu72 ай бұрын
You are a very good teacher!
@nigarmutallimova84612 жыл бұрын
Thank you! Great explanations
@Ressuu12 жыл бұрын
Thanks! Really good explanation!
@rayhanain63949 жыл бұрын
When he modifies a standard walk to a brownian motion, why is Ri equal to the square root of t/n? Maybe i don't understand what Ri really is because im thinking that Ri is the normal random variable score that occurs at increment i.
@samhkelleysr11 жыл бұрын
Prof. Bill, It might be helpful, when explaining your random walk Markovian Martingales, where the expectation is zero (50/50 probability) to turn your coin toss slide sideways. It then becomes a histogram with a mean of approximately zero. Good lecture.
@dilish170711 жыл бұрын
This is awesome!
@Hugo-Cheung10 жыл бұрын
this is so good
@abhishekbayara73335 жыл бұрын
Thanks for such a nice explanation
@nnigam0078 жыл бұрын
This is very good video and very helpful to understand basic of BM. thanks prof bill. thank you so much. one request, if you upload video on BSM, solve equation starting from basic i.e "x-w(1/delta)" to D1 and D2. thank you
@faustocant93814 жыл бұрын
Cool material!!
@ramasum12 жыл бұрын
Thanks great lecture!
@jcomden8 жыл бұрын
Nice Lecture :)
@mattrixx90199 жыл бұрын
I think it's interesting how he adds letters to stochastic, instead he's fantastically stoked! Stoke-tastic! Also, Wiener is pronounced with a V (Vee-ner). I realize they are just implications of the local vernacular, but it always makes me jump a little bit when he says them. Overall, a great high-level overview for non-mathematicians.
@kevinshao91482 ай бұрын
Thanks for the great video! One question please may I: 27:51 how did you derive that diffusion equation of dx at the top? Do you have another lecture for the details of derivation? Many thanks!
@kweweli78219 жыл бұрын
interesting video, thanks a lot .
@davidjohansson14164 жыл бұрын
So considering martingale "older values" is as "gamblers fallacy"? Expecting a coin to become "fair" in the direction opposite to what it has already shown... if that makes any sense?
@dominikb1211 жыл бұрын
So a= constant as inteterst rate in a bank/bond and b is what? beta of the stock?
@chrish3542 жыл бұрын
Great lecture, loved your examples very straightforward to understand
@SonGoku-uv4pk8 ай бұрын
This is really good
@joaoadelinoribeiro147011 жыл бұрын
great class, even for me (I´m a lready familiar with brownian motions). By the way, the third name contributing to the Black-Scholes model is Merton, not Morton.
@michaeljbarkman10 жыл бұрын
great video
@stimpen1210 жыл бұрын
But how do I model the Wiener process. Say I have a value for b and want to simulate a Wiener process. What do I do with b? Do I run a random number generator picking a number from the normal distribution and then take it times b? And then do that again with the previous result and take it times a new random number from a normal distribution? What would the characteristics of the normal distribution be that I should use for the random numbers? Expected value =0 and what about the variance, I did not really understand that part. It´s only t? But what is t? Is it years? Say I want to model a stockprice over a day should I use 1/365 then? And to simulate a Wiener process I crank up the number of observations on a day to say 1 000 000 to simulate that the n in t/n goes to infinity?
@youtubismystic11 жыл бұрын
There is no implication between martingale and Markovian. You should remove the note on the slide shown around the 6th minute stating that all martingales are Markovian and make sure you do not mix up both concepts as they are distinct.
@kidbornbrat18122 жыл бұрын
Thank you Sir.
@SuperPrachi11 жыл бұрын
Actually, even if the weather for the last 3 days predicts weather for today, that can still be modeled as a markov process. If each day, there are n possible different states of weather, then the weather for the past 3 days gives n^3 possible states, so the past 3 days can be considered the "current" state, as long as the number of days the next day's weather depends on is finite.
@TheUnknownNexus11 жыл бұрын
Great Video... Next lecture link please?
@animals0feel1pain211 жыл бұрын
Are you sure? I thought all martingales were Markovian? Markovian means that the expected value of the process at any future value depends only on the current value and not on any previous history. Martingales means that the value at any future value is expected to be the current value (and not on any previous history's value).
@SaiRaman11 жыл бұрын
Absolutely ... Amazing teaching ....
@GauchoMwenyewe11 жыл бұрын
black scholes option cost variation formulae...
@user-oe6hb3bc7g3 жыл бұрын
ice cold explanation man!!!! altho at 21:13 you talked about the amount added at each increment is sqrt(t/n), i wonder where does the Normal distribution come in? I thought the amount added at each increment was based on a Normal Distribution but it looks like the amount added (or subtracted??) is sqrt(t/n), a constant. What am I missing?
@thesupersimon9 ай бұрын
i think maybe there should be an 'e' before the sqrt(t/n) so it is e*sqrt(t/n), which e~N(0,1).
@blacksiddis4 жыл бұрын
Good videos but I think you should cite Hull, which your content draws heavily on.
@gutschrimanderson98184 жыл бұрын
Hi Bill, it may be a bit late for me to ask this question, but why exactly should we care about the volatility of a stock when assuming Brownian Motion? The expected value is always going to be 0 if I understand correctly, so shouldn't we just focus on the non-Brownian part of the equation? The factor "b" in the differential equation surely has no influence on the stocks expected value over time, only the factor "a" would be relevant, right?
@gutschrimanderson98184 жыл бұрын
By the way I much enjoyed the video, thanks for uploading!
@thefuckingpearl2 жыл бұрын
Hey so I know I'm too late but the b does matter , since when we predict the future prices of stocks we do have uncertainty regarding its future path of prices so unless and until we have 0 uncertainty and we are absolutely sure of what the future path of the stock price is gonna be (in which case the b=0) b or the volatility of the stock does matter.
@abhisheksaini52172 жыл бұрын
very nice
@TEBA-yd5gm2 жыл бұрын
I need help could u
@miqymike8065 жыл бұрын
nice study
@MissHappyToast8 жыл бұрын
20:48 I don't really understand why Ri = square root of (t/n)? Why is it the square root?
@grrddm8 жыл бұрын
+Dasha Y You can think of Ri as the the standard deviation of each movement (increment). I'm not sure about this statement so don't take my word for it. In an informal way, think of the Var(Ri): Var(Ri) = E[Ri^2] - E^2[Ri]; where E^2[Ri] = 0, E[Ri^2] = t/n -> sd(Ri) = sqrt(Var(Ri)) = sqrt(t/n) On the other hand Since Ri is a martingale: E[Ri^2] = Ri^2 = t/n -> sqrt(Ri) = sqrt(t/n) Hope it helps!
@changantonio8 жыл бұрын
+Dasha Y Me neither... plus if the increments are sqrt(t/n), then the increments are always positive, and E(Si) can never tend to zero. I believe he is actually stating that the stdev(Ri) is sqrt(t/n)... but without really showing why.
@djsocialanxiety16645 жыл бұрын
@@changantonio Maybe I'm too late, but the reason is when you consider a random walk realization Xn with an equal like likely realization of +/-1 , then E[X] is zero, but E[X^2] will equal to x1^2 +x1*x2 + x2^2+x2*x1...etc. here you can see that x1^2 and x2^2 (which correspond to the stepsize N) will equal to 1 regardless if they are +/-1 since they get squared. All the other combination terms f.e. x1*x2 imagine which combinations x1 and x2 could be. both can be 1 in that case the combination would equal to +1, both can be -1 in that case the combination would again be +1, and twice one can be positive and the other negative, where the combination would result in -1, since +1*-1 is negative. So you have 4 combination possibilities with twice +1 and twice -1, which in sum is zero. So all the combination terms equal to zero and only the squared single terms are left, which correspond to the amount of N steps taken - hence E[X^2] = N. Since its a martingale and today is the best estimator for tomorrow X^2 = N and therefore X = sqrt(N).
@youtubismystic11 жыл бұрын
2 counter examples: - the Ito integral is a martingale but not Markovian - a biased coin scoring +1 if H and -1 if T. The score is Markovian but not martingale I am happy to provide more explanation if needed. Otherwise check online and the link below. wilmott.com/messageview.cfm?catid=8&threadid=11322
@arrabalimaz6224 жыл бұрын
13:00 for brownian material discussed
@user-oz3id9cr3d7 жыл бұрын
ممكن الترجمة الى العربي وشكرا
@robinlam50385 жыл бұрын
I feel like the definition of Markov Process should be "a sequence of possible events in which the probability of each event depends only on the state attained in the previous event." Simply put, future is independent of the past, given the present. Doesn't this contrast with your slide in 4:25?
@robinlam50385 жыл бұрын
wait, I think there is a difference between a Markov process and a Markov chain.
@gutschrimanderson98184 жыл бұрын
Hi Robin, I believe your definition "[...] each event depends only on the state in the previous event." is slightly flawed. Each event does NOT depend on ANY previous event, not even the one just before it. Each event is completely random. The expected value is solely dependent on the current value, maybe you mixed those two things up. Hope I could help.
@wcottee4 жыл бұрын
Had a question. At 21:13 we talk about the amount added at each increment is sqrt(t/n). Where does the Normal distribution come in? I was thinking that the amount added at each increment was based on a Normal Distribution but it looks like the amount added (or subtracted??) is sqrt(t/n), a constant...What am I missing??? All help appreciated :)
@W-HealthPianoExercises2 жыл бұрын
dW(t) a derivative ? Wiener process is nowhere differentiable...
@majade1312 жыл бұрын
haha wiener
@davidporter67110 жыл бұрын
WIENER!
@Ohiostmrchbandawesom8 жыл бұрын
(Vee-nur)
@auther56645 жыл бұрын
Not bad
@edwardmacnab3542 жыл бұрын
You are never going to understand what Brownian Motion is with Math . You might learn more about math but not Brownian Motion.
@hansa91598 ай бұрын
What makes you say that? What tool do you suggest?
@edwardmacnab3548 ай бұрын
@@hansa9159direct observation with perhaps particles with different flourescent dyes . Different particle sizes . Different tempratures in uv light with high powered microscopes. Vary the parameters. Collect the data. Try to figure out the mathematical relationships between the various variables. there is too much theory and not enough experimenting in the subject of brownian motion
@hansa91598 ай бұрын
Thanks for the insight. Did/do you study physics?
@edwardmacnab3548 ай бұрын
@@hansa9159I did but did not persue it. I'm not made for regular school and it is a lot of work and does not pay well anyway. If you are interested , I am convinced that Brownian Motion is the result of microeddies and microcurrents that .shift and change at very high velocity. The water molecules are not ricocheting around. They are polar for one and water is incompressible for another. There may be tiny ricochets which push and pull at the fully connected water matrix causing it to behave like a complex current carrying whatever is immersed in it , with it. That's my take and it should be verifiable
@L2K4D44L4R10 жыл бұрын
Lamentably, the presenter does not seem to have much clue about his subject and of math in general, he explains things badly if at all, and there are numerous mistakes both in slides and talk. Skip this.
@CompuViz10 жыл бұрын
If so, can you kindly produce a lesson and slides without errors and with better explanations, we as learners would really appreciate that. Meantime I am thankful to Billbyrne that he made all this effort and produced stuff that we all can read from all around the world.
@L2K4D44L4R10 жыл бұрын
CompuViz I'd love to do that, I could do it (I'm a university lecturer on stochastic modelling, among other topics), but I don't have the time. Sorry. I still hope that my comment will help viewers, as well as the lecturer himself, to more realistically assess the quality of this presentation.
@cl1052210 жыл бұрын
I agree with L2K4D44L4R, If this is the first video someone is watching on Brownian process..I am afraid they are going to have lot of misconception about the subject..The section of Martingales esp is very badly explained
@LunaDogStar10 жыл бұрын
L2K4D44L4R being critical can be constructive but I can say what ever I want too without any back up to my claims. I'm a masters of stats student and currently working in a hedge fund and this vid although maybe not perfect did help clear up some concepts for me. thanks to Bill for this.
@Topbitcoinexchanges9 жыл бұрын
L2K4D44L4R Your comment was useless, why would it help anyone trying to learn the subject? You made no specific, concrete critique of the presentation, you just claimed it was wrong. So no, it's not helpful.