Simplified: Girsanov Theorem for Brownian Motion (Change of Probability Measure)

Рет қаралды 24,828

3 жыл бұрын

Explains the Girsanov’s Theorem for Brownian Motion using simple visuals. Starts with explaining the probability space of brownian motion paths, and once the probability measure is introduced, then shows how the change of probability measure looks like visually. The video ends with outlining the relationship between conditional expectation under the two measures.

Пікірлер: 47

@aidenshen8343 2 жыл бұрын

The professor recommends the video to us! Thanks!

@quantpie 2 жыл бұрын

it is very kind of them! You're welcome!

@abigail-sothoth362 3 жыл бұрын

The best video I have found on Girsanov Theorem. Thank you so much!

@quantpie 3 жыл бұрын

You're very welcome! thank you!

@thiminhthinguyen6414 Жыл бұрын

Your visualization is truly amazing. I have had a hard time constructing the probability measure of Brownian motion in my head and thanks to your explanation, it is clear to me now.

@AlexRodriguez-bt5jb 3 жыл бұрын

So grateful for you and this channel. Thank you so much for your work

@quantpie 3 жыл бұрын

You’ re welcome! Thank you!

@bramgriffioen5436 9 ай бұрын

Thank you so much!! Really resourceful explanation, to get some insights into this abstract formula !

@StratosFair Жыл бұрын

Wonderful explanation of Girsanov's theorem

@uminhtetoo 10 ай бұрын

Thank you so much for sharing, Sir.

@mariuslotz8896 3 жыл бұрын

Thanks, easy to understand

@hbbexxter4666 3 жыл бұрын

Fantastic. Absolutely fantastic! You bring stochastic calculus to life and make it finally understandable for mortal people as well.

@quantpie 3 жыл бұрын

Many thanks for the kind words!!

@jxliu6375 3 жыл бұрын

Love the video! Thanks!

@quantpie 3 жыл бұрын

Glad you enjoyed it! You're welcome!

@adokoka 2 жыл бұрын

Clean explanation!

@quantpie 2 жыл бұрын

Glad it was helpful! many thanks!

@sheldonjallen 3 жыл бұрын

That was awesome! Thank you for that patient, cogent explanation!

@quantpie 3 жыл бұрын

thank you!

@qiguosun129 5 ай бұрын

Great ! thanks!

@milinds4161 3 жыл бұрын

The very best intuitive explanation on the net. Thanks so much!

@quantpie 3 жыл бұрын

Thank you!!

@williamqiu1917 Жыл бұрын

You mentioned in the video that we don't need to worry about the sigma algebra too much. But the problem always hugged me a little, can't the sigma algebra be too small for something we are describing or is there a theorem stating for any problem we can find a suitable sigma algebra.

@devyash313 3 жыл бұрын

Very intuitive explanation. Thank you!

@quantpie 3 жыл бұрын

Glad it was helpful!

@user-wc7em8kf9d 3 жыл бұрын

Amazing explanation! Thank you so much for this.

@quantpie 3 жыл бұрын

thanks! You're very welcome!

@vitalimueller6209 3 жыл бұрын

You have great content, well done

@quantpie 3 жыл бұрын

Thank you so much 👍

@War4Skills 3 ай бұрын

Hi, thank you for the great video, it truly made me understand the concept of changing probability measures way easier. I never knew it was actually that straightforward! Is it possible to share your slides? I would like to take notes on them if you don't mind :)

@curisity 3 жыл бұрын

Amazing explanation !

@quantpie 3 жыл бұрын

Thank you!!

@yanisbarillon3597 Жыл бұрын

First, thanks for your video it's quite clear to relate with practical and visual example. But around 7 min you said that the proba that the brownian pass through the 3 gates is the product because of independance but there is only independance of Wt2-Wt1 with Wt1 not of Wt2 with Wt1 isn't it ? (So my question is : Is there an error or am I missing something)

@peterpaton7817 11 ай бұрын

The independence between the brownian increments (the change in the process between these times)

@abhinavsaxena2388 2 жыл бұрын

I am new to computational finance. With so many videos, suggest should be the first 5 topics to view ?

@quantpie 2 жыл бұрын

thanks! Just replied to your other comment, apologies for the slow response!

@ajith009100 3 жыл бұрын

Hi, great content ! I lost a bit at 17:34, how did you get at the dQ/dP = exp(-2.5W -0.5*2.5*t^2) ?

@Beacher1085 3 жыл бұрын

Check at 18:40, bottom right-hand side. You know μ from previous step. (He's applying Nadon-Rikodym derivative. en.m.wikipedia.org/wiki/Girsanov_theorem)

@quantpie 3 жыл бұрын

thanks!

@yanisbarillon3597 Жыл бұрын

At 18:46 you made a mistake on the sign of the term in t in the radon nikodyn dQ/dP density but really thank you good explanation

@ROni_ROmio 3 жыл бұрын

Thanks bro, could you do video about le new FMM Foward Market Model and explain the changes VS LMM please,..? Many Thanks

@quantpie 3 жыл бұрын

thanks! it is on the to do list!

@fabioniski3316 3 жыл бұрын

Yes a video on the FMM from the quantpie would be a huge hit.

@NA-rq5dw 3 жыл бұрын

Should it not be -2.5dt?

@quantpie 3 жыл бұрын

Whereabout please? dW has drift zero under P, drift of -2.5 under Q. The tilde version has drift zero under Q, so under Q you will to add 2.5 to dW to get the tilde version. Does that answer your question?

@danielmcdouall4056 3 жыл бұрын

@@quantpie I think they mean the dt coefficient for the dWt tilde. The gradient is downward sloping so should the vale not be negative?

@danielmcdouall4056 3 жыл бұрын

value*