Ito's Lemma

[@yannicknovacek5566]

You actually explain it like a human being, thank you

[@pilusass]

This is the first time, I got someone who explained this Ito's lemma in layman's terms and your explanations make so much sense. Thank you, prof. I now have some understanding of what Ito's Lemma is and how it is applicable.

[@andyboadu3891]

Thanks Very much. I thought of dropping my financial economics class because of How my Prof thought this topic. I was so lost, but I am now at home. Good work

[@gerardomoscatelli9035]

Just one detail Mu is not the interest rate as said in the video at @0:58 but the expected rate of return or the mean if we talk about a normal distribution. Many Thanks for this video, excellent complete explanation, finally understood the mysterious origins of Black Scholes !

[@gipsi5]

Thank you very very very much. After 1 term of stochastic calculus and a bunch of other subjects I still didn't understand why we use Ito's formula. Then I tried finding the answer on the internet and no use - Try typing in the google "why we use Ito's formula" - no reasonable answer. Then I read chapters about Ito from most referenced books and still couldn't understand it until this lecture. You explained it so simple and reasonable. I am looking forward to the rest of you videos.

[@paulportesi]

The absolute best explanation of Ito's Lemma on the net. Fact!

[@razadaza9651]

I have to agree, passed my quant finance exams last year thanks to this..

[@hyuming2577]

this is actually the best geometric Brownian motion video after i went through +10 videos and try to understand lol. much appreciated

[@ruturajpatwardhan9133]

Superb explanation. I have tried multiple videos and books but understood it through your video. Thank you so much.

[@tiptavo]

Excellent step-by-step explanation that helps you to grasp the core idea behind Ito's lemma. Thank you so much!

[@SuperReddevil23]

Best Explanation of Ito's Lemma on the planet. Professor you are a saviour

[@airstr1ke]

Thank you, this was incredibly intuitive to understand, and it feels like a fundamental step in understanding more complex derivative functions. Very helpful!!

[@coopernfsps]

Great video! I have an oral exam including basics of ito's lemma coming up, and this lecture really contains all the relevant information I need to be able to bring across! Thank you!

[@Topbitcoinexchanges]

What a simple and nice explanation of Ito's lemma. My prof didn't explain it this simply so it's very helpful the steps he tkaes in this video. highly recommended!!

[@hneifield]

Thank you. Clear explanation and extremely helpful. Keep posting these videos, they help us a lot. Great job.

[@fbruvik]

My brain hurts.

[@stephendavis3821]

for real!

[@MsMangaholics]

Mr Byrne, you have saved me academic life

[@wow5212]

i have reached a point in maths where not seeing the proof might not be such a bad idea

[@delphinehintz7819]

This was so helpful! Thank you so much for explaining everything at a very accessible level.

[@manishsrivastava2992]

Brilliant & simple explanation of Ito's Lemma. Thank you!

[@jorgegonzalez-ec5fl]

This guy is really good at explaining

[@Ysefl]

This is just amazing! Great work! Thank you!

[@manavbansal1230]

Man , He is a Hero !!

[@gipsi5]

I won't comment on the math part because I wasn't paying that much attention to it but I think you have to agree that he explained pretty well in common language why we use Ito's formula. Just an example, professor that was teaching stoch calculus course at my program didn't even know what X(t) could represent in real life. She was pure mathematician and didn't care about financial part of stochastic. This resulted un majority of people not knowing how to use it. So tell me what is better.

[@SalsaTiger83]

I think the benefit is that you can define the shape of the probability density function of G over time, given just G over the stock price and a process for the stock price.

[@shakibishfaq8627]

You are my hero! Forget batman, superman and the avengers. You are my hero.

[@Lucian86]

An Introduction to the Mathematics of Financial Derivatives, author. Neftci...very good intro book about stochastic calculus

[@pablovelazquez1903]

Thank you for your explanation. Highly appreciated.

[@veselintilev7446]

You sir, are great! Does anyone have the presentation in a pdf or something good for printing?

[@Lucian86]

The reason why you can't use standard calculus is because you can't define an integral with respect to a WInner process since, as the professor pointed out, the functions is too irregular as W(i)-w(i-1) gets smaller and smaller.....Behind Ito's Lemma there's Ito integral which explains well this issue and how can it be integrated

[@gerardomoscatelli9035]

In other words if you have a a time-series of daily log returns and calculate the mean = mu, this is the expected mean log return of your stock. Not an interest rate but the specific mean rate of return of this stock calculated historically

[@jonesr227]

It's not clear to me at all why the drift rate, mu, of a stock time series is referred to as the interest rate in the video. The US stock market has an historical drift rate of 8% -> 0.08. The interest rate has been less than, say, 3% -> 0.03 for a long time.

[@racontur]

You are confusing terms here, interest rates is a general term in finance. In this case he was just referring to the expected returns on the stock which is also an interest rate. So Interest rates are just expected payments possibly in the future that every asset is expected to pay back relative to the initial principal. If an asset has no interest, it's not worth investing in.

[@rafiqderafew2136]

Awesome..... You saved my exam....

[@emit_etinif]

From a Stoc.Calc perspective, this hurts a little. From an intuition perspective, it’s refreshing! A little intuition on why standard calculus doesn’t apply: We want a reasonable ’white noise’ process with continuous sample paths, to model the stochastic behavior. i.e. we want (W_t) to satisfy: i) W_t is independent wrt. W_k for all t,k not equal. ii) (W_t) is stationary. That is, the joint distributions are independent of t, for all t. iii) E[W_t] = 0 for all t Turns out the only process with continuous sample paths, satisfying i) ii) and iii) is a Brownian Motion! However, though continuous everywhere, Brownian motion is no where differentiable. Thus standard calculus doesn’t apply. (It is in fact a measurability problem. There’s no measurable processes with continuous sample paths satisfying i) and ii), but a Brownian Motion)

[@sakuranooka]

Ok, now we have transformed the original equation, but we still haven't solved neither the original nor the transformed equation. Where does Ito's lemma actually help us solve the equation(s)?

[@variousmentalproblems]

is there an error in the variance formula at 14:54? There shouldn't be a b^2 on the outside, right?

[@faustocant9381]

Pretty cool work! You're the best!!

[@M4laoWei]

ure sooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo much better than my lecturer! THANK YOU SIR!

[@bendirval3612]

This is good, despite you changing notation several times.

[@sylsylee]

Hi, this is a fantastic video, thanks for sharing it.

[@frecklematt]

"we're not going to go over the proof of this" K BYYYEEEEEEEE

[@wenzhang365]

This is very helpful, thank you professor.

[@wecanmakeit7174]

Thank you sooo much, this made sooo much sense!!🙏🏻☺️☺️☺️

[@AndrewCharles1]

So good. Just soo good. Watch all the way until 15:20 and at that point, you will finally get the entire thing. You will have a matrix moment at that point.

[@stimpen12]

The formula at 36:40. Like what do I use the dz term for? Expected value is 0 so when is it usable. If I ever would need to calculate or use dz then what is it? If I want to simulate dz what is the function for doing so? Right now it feels a bit abstract. But saw there is a separate video on Brownian Motion (Wiener process) so have to check that one out as well.

[@tinggu5545]

You can use dz for calculating the expected volatility. dz~N(0,t).

[@danielswenson1226]

stimpen12 yes, E(dz) = 0 but, E(dz^2) = Var(dz) = dt

[@danielswenson1226]

Ting Gu no… dz ~ N(0, dt)

[@airstr1ke]

+stimpen12 The easiest way to think about it is simulation 10,000 draws of a standard normal variable, i.e. a number from a uniform random distribution with mean 0 and standard deviation 1.

[@stephendavis3821]

thank you so much for this video!!!!!!

[@drdca8263]

Cool! This really is a rather clear explanation!

[@ashroy83]

@skoules who taught you that risk free rate has to be continuous compounded.

[@KeithBassJr.]

this is a great explanation

[@Hamking1]

The extra b^2 should be a (dt). Since we treat everything but dz as a constant we get: (Let @ denote partial) VAR[(@G/@x)*bdz] = ([(@G/@x)*b]^2)*VAR(dz) = Where: dz = epsilon*sqrt(dt) ; where epsilon~N(0,1) RV. If we let dt approach -> 0, it approaches a constant. If we treat it as such we should get: VAR(dz) = VAR(epsilon*sqrt(dt)) = ([sqrt(dt)]^2)*VAR(epsilon) = dt*VAR(epsilon) VAR of a N(0,1) RV is sigma^2 which is 1 in this case, so we get dt*1 Put it all together: ([(@G/@x)*b]^2)dt

[@robinlam5038]

Good video! Very clear actually! What are a and b in ito's lemma? are they always mu_S and sigma_S respectively?

[@ohad157]

The slides are partly from Hull! (:

[@fantasyd1928]

Fantastic! Thanks for sharing!

[@dotted58]

Great explanation. Thank you.

[@kseniyapak3086]

thank u thank u thank u, i finally start understandin!!!

[@loekloekloek]

Best. Explanation. Ever.

[@jac6003]

Pretty cool, nice explanation!

[@Ohiostmrchbandawesom]

The very first slide says "Ito's" not "it's." Were you joking?

[@danielswenson1226]

I went over this a couple of times. I think the answer is wrong. In the answer to the dF equation, there should be no "S" multiplied by the dt term, or the dz term.

[@AndrewCharles1]

So good. Just so good.

[@marosal0707]

quite informal, but very useful in a practical sense.

[@haoyuwang1117]

great lecture. Thank you so much.

[@TheActurialRepository]

Lovely explanation

[@oxtherider]

Thank you for this nice lecture sir.

[@manzb23]

so what is the difference between the SDE and the ito's lemma, as we still have dz

[@LeGekkonidae]

Great explanation! Thanks

[@ambaraba75]

Excellent explanation. Thank you.

[@faryalfatima1713]

how can we apply ito formula on skew brownian motion

[@69erthx1138]

@37:39 unless that risk minded person is a scalp trader using 1 hr to 15 minute charts:-)

[@raginisingh3075]

Excellent explanation. Thanks

[@galymzhankenesbekov2924]

Hi! Which book do you use? Or how can I get an access for full lectures? thanks!

[@manzb23]

hey thanks i understand this..but I'm going to be asked this for my dissertation and they won't accept that as a answer :(

[@mohammedalbanna9413]

lifesaver! thanks!!!

[@nyashagweru4276]

What is the name of that book please

[@ejejejej92]

Thank you for sharing!

[@szpacur]

Legend

[@sonnyskaa]

When you calculated the variance of the ito process at around 14.15 you stated that it is ((partialG/partialx))b)^2 which I understand. But why the extra b^2???

[@aseefzahir3977]

Thank you.

[@Jackson_M5]

As the good book would say, Multifractional Multistable motion or GTFO. Let me preface this by saying, I didnt watch this video. I think a fairly good intro book is Shreve: Stochastic Calc for finance II. Do you disagree, oracle?

[@TheJurgen57]

32.08 - if a guy asked me that stupid question after one hour of explaining, i'd slap him in the face 'stochastically'

[@horacechan9202]

thanks for the video

[@tophych]

good video!

[@oraclecenter]

if you really wanna learn some stochastic calculus then drop the things this video tells you cuz they are totally wrong

[@SalsaTiger83]

Then I guess this is a perfect time to bother your advisor ;-)

[@varun0narang]

Shreve

[@Jackson_M5]

lol He's doing math, wrong :P