Thanks for the amazing video.. I was about to start with the book Dynamic Hedging and Statistical Consequences of Fat Tails... This seems a very good general into 🙂
The relationship between the Weiner differential component and the error term in a statistical model is brilliant. Seems like they have different roles but it's conceptually the exact same thing. Good content Dimitri
I, too, wish this was taught more approachable for people with statistical background. The "mean and nasty" teacher story at 16:20 rings a bell.. :) For me, the key intuition with that SDE was that it was for a Geometric Brownian Motion, meaning that it was a multiplicative process (unlike ARIMA which is inherently additive). And so the the distribution was log-normal, which is the "normal" for the multiplicative domain. I.e. Gibrat's law being similar to CLT. I wish that connection was made earlier, then the Black Scholes derivation would be easier to understand.
Thank you, I’m an mfe student and I think a lot of programs are lacking on bringing time series and stochastic calculus together! Thank you for giving some intuition on how these things relate. Have a good one!
Awesome! Dmitri, please keep doing this kind of videos about different areas of quant finance topics and your perspective on them. Examples of practical application, associated challenges, common mistakes and consequences could also be great. Thanks for the interesting content!
As a Financial Mathematics major, your professor probably used quadratic variation to show that terms (dt^2) were 0. Taylor Series and quadratic variation are the bedrocks to Ito formula, so it makes sense that your professor used to to prove the Black-Scholes PDE.
Thank you for the video, but there are some inaccuracies. The W_t is not independent of the past. It is a Martingale and a Markov process. It is only non overlaping increments of W_t which are independent of each other. There are other things, but that was the one worth mentioning
Dimitri what is the best method for making data stationary? We use log-transformation and simple differencing for our projects, I was wondering if it is this simple in the industry too. ...and brilliant video. Thanks
Dimitri I'm researching about the topic of my dissertation. What's your take on SABR model? Are they used in the industry now? What other stochastic volatility/risk models do you recommend? And what are the other areas or topics that have "momentum" now? Sorry I'm so confused... and you're the only real quant that I know.
I think wrt Brownian motion, that it was the motion of a water droplet very close to boiling on a hot plate. I think it was also Einstein of all people who first captured that motion with equations, if my history is right. I just realised that SDEs are distinct from normal DEs in that the notion of a derivative implies smoothness when zoomed into the function, but SDEs do not. I have a feeling that derivatives of the itô process would look basically the same as the itô process - in that they'd diffuse and drift in like. Do you have a proof of dx_t in the itô process? I take it that dx_t means the same thing as it does in bog standard calculus.
White means the spectrum is flat in other words it describes correlation properties of a process. Gaussian means that increments/changes are distributed according to Gaussian distribution. Hence a process could white and not gaussian, or gaussian and not white. AGWN: additive gaussian white noise is a popular choice as it mimics the effect of many random processes that occur in nature.
I think this is brilliant if understood from an intuitive perspective, however, stochastic calculus is pure mathematics, hence absolute - it is based on definitions. It cannot be reduced to intuition.
Thanks for the amazing video.. I was about to start with the book Dynamic Hedging and Statistical Consequences of Fat Tails... This seems a very good general into 🙂
The relationship between the Weiner differential component and the error term in a statistical model is brilliant. Seems like they have different roles but it's conceptually the exact same thing. Good content Dimitri
I, too, wish this was taught more approachable for people with statistical background. The "mean and nasty" teacher story at 16:20 rings a bell.. :) For me, the key intuition with that SDE was that it was for a Geometric Brownian Motion, meaning that it was a multiplicative process (unlike ARIMA which is inherently additive). And so the the distribution was log-normal, which is the "normal" for the multiplicative domain. I.e. Gibrat's law being similar to CLT. I wish that connection was made earlier, then the Black Scholes derivation would be easier to understand.
Thank you, I’m an mfe student and I think a lot of programs are lacking on bringing time series and stochastic calculus together! Thank you for giving some intuition on how these things relate. Have a good one!
I didn't realize it until I had been working in the industry for a year. It would have made grad school easier.
Awesome! Dmitri, please keep doing this kind of videos about different areas of quant finance topics and your perspective on them. Examples of practical application, associated challenges, common mistakes and consequences could also be great. Thanks for the interesting content!
This kind of videos are amazing. It would be great to have more videos like this
Terrific!
Keep going Dimitri
Dear Dimitri,
Thank you so much for such a beautiful video
Thanks! I figured I would do something a little different since the recent videos have opinion ones.
As a Financial Mathematics major, your professor probably used quadratic variation to show that terms (dt^2) were 0. Taylor Series and quadratic variation are the bedrocks to Ito formula, so it makes sense that your professor used to to prove the Black-Scholes PDE.
Thank you for the video, but there are some inaccuracies. The W_t is not independent of the past. It is a Martingale and a Markov process. It is only non overlaping increments of W_t which are independent of each other. There are other things, but that was the one worth mentioning
Such a succinct explanation!
Thanks!
This was absolutely amazing, thank you
Thanks! I try to create unique views for topics like this.
@DimitriBianco Great to see a statistical view regarding these topics. I hope you make more; looking forward to them.
Dimitri what is the best method for making data stationary? We use log-transformation and simple differencing for our projects, I was wondering if it is this simple in the industry too.
...and brilliant video. Thanks
Seasonal differencing is another approach which is often overlooked. A common issue is mis reading the ADF test, Rho vs Tau.
Dimitri I'm researching about the topic of my dissertation. What's your take on SABR model? Are they used in the industry now? What other stochastic volatility/risk models do you recommend? And what are the other areas or topics that have "momentum" now?
Sorry I'm so confused... and you're the only real quant that I know.
I think wrt Brownian motion, that it was the motion of a water droplet very close to boiling on a hot plate. I think it was also Einstein of all people who first captured that motion with equations, if my history is right.
I just realised that SDEs are distinct from normal DEs in that the notion of a derivative implies smoothness when zoomed into the function, but SDEs do not. I have a feeling that derivatives of the itô process would look basically the same as the itô process - in that they'd diffuse and drift in like.
Do you have a proof of dx_t in the itô process? I take it that dx_t means the same thing as it does in bog standard calculus.
amazing video as always!
White means the spectrum is flat in other words it describes correlation properties of a process. Gaussian means that increments/changes are distributed according to Gaussian distribution. Hence a process could white and not gaussian, or gaussian and not white. AGWN: additive gaussian white noise is a popular choice as it mimics the effect of many random processes that occur in nature.
I think this is brilliant if understood from an intuitive perspective, however, stochastic calculus is pure mathematics, hence absolute - it is based on definitions. It cannot be reduced to intuition.
hey , have watched you watched Quantpy youtube channel it looks interesting and it would be interesting listening to your opinions😇
I have seen the channel but never watched a video.
You’re going to talk about the wiener process and not make a single joke about the name? 😂
Very interesting video though!
@Ryan I've wondered the correct pronunciation. I've had professors use a few different ones. It makes sense given it isGerman.
Haha...
Would you recommend the book “Introduction to Time Series and Forecasting”, Peter J. Brockwell
Richard A. Davis?
I haven't read that book. Maybe I'll add it to my, to-read list.