Local Volatility Model: Dupire PDE and Valuation/Pricing PDE Derivations and Comparisons
Вставка
- Опубліковано 2 жов 2024
- Introduces the Local Volatility Model, and derives the Dupire PDE using two alternative approaches. Also compares and contrast the Dupire PDE against the Valuation/pricing PDE (this is kinda Black Scholes PDE), and the Fokker Planck Equation
Hi Guys, thank you for your videos..I think it will be also useful to make a videos on the avantages/drawbacks of these models on exotics products like barriere options, Autocall products etc...
Wow, your discussion around 6:00 is totally the result of bias-variance trade-off.
really appreciate your video,that's will better if there is a script of this video for someone who is not good at listening english
Good to see Lorenzo Bergomi's argument explained clearly by this video - Looking forward to see more videos of this especially touch basing the other concepts of stoch vol models.
Hi, really enjoy your detailed explains. But I still have a question: at 22:04, why the expectation of the second term does not have "Q" as the first term? Looking forward to your reply and thank you very much!
thank you, good spot! that is a typo!
Hi, great series of video on financial mathematics! Seems very close to practical use instead of repeating what's in classical textbooks. May I ask whether you summarized these contents from original references paper? Could you please give some reference for the video?
Glad it was helpful! The material is quite standard; however, it is not based on particular book/article. If you take references in the Dupire's original paper, and complement them by those in Gatheral's then that should provide sufficient coverage of the topics covered in this video. many thanks!
HI Guys, Thank you so much for making the life easy. to apply the itos lema to absolute function can you plase name the formula. i couldnt catch it correctly
Thanks! It is called Tanaka Meyer, pls see here- en.m.wikipedia.org/wiki/Tanaka%27s_formula
Can you please share 2nd and 3rd order greeks for learning
HI , thank you for your vid. It is great. I have a question: what is the different between Dupirce 's local vol. model and those model like deterministic form for the vol, for example: CEV model ? Both of them are so- called local vol. model, but I can't relate them to each other. Thank you .
many thanks for the question! One is parametric (kinda assumes a particular functional form with some parameter whose value can be varied to get as close a fit as possible), and the second is non-parametric - it does not have a specific functional form, so shape is driven by the data. Hope this answers your question. Many thanks!
Thank you for this informative and well-explained video - your video has helped me greatly so far with my dissertation. Much appreciated.
You’re welcome! Glad you found it useful! Thanks!
In the local volatility SDE we have the term sigma(t, S), while all the PDE have sigma(T, K). How do these two relate to each other?
hello, could I have your slides please? I am student and I am studying your lecture! its awesome!
Beautifully explained. Also, can you provide the pdf so it will be easy for us to take notes.
As soon as possible! We have received this request many times, but unfortunately formatting the equations in a readable format requires work, and will switch to formatting as soon as we have finished the backlog!
Perfect
the video is wonderful! Which one of the video discusses the jump process?
thanks! We have started introducing jump processes in the Levy process playlist, there are 3 videos which cover different aspects of the Poisson, more videos to follow!
@21:00 Why can you replace d/dT by the partial derivative?
Super wonderful! It's sooo clear and the video is awesome also!
Thank you! Cheers!
Thank you!! How can we tell the Dupire is a forward PDE?
Thanks @Jun Wang! At least two ways to identify forward vs backward PDE in these settings: 1) via the sign of the second derivatives vs time derivative (please compare it to the Black Scholes PDE which is a backward PDE), and 2) via knowledge of the problem: initial vs terminal conditions and what dynamics is the PDE describing - here we have the initial condition S_0-K, and the PDE is in terms of the T (maturity), so it is a forward PDE. Hope it is clearer, but let me know if you have any further questions!
quantpie Thank you so much!
Are you using a textbook? Which one?
Very clear in the explanation. Thank you
Glad it was helpful! You are welcome!
Thanks for sharing!
@M.Y., thank you!!
Great job as always
thanks @Davide!!
fantastic walkthrough, many thanks!
Hi, can u please explain at 25:09 the expectation return nonzero when K=S? a bit confuse here, thanks
i got that at 18:56 haha
Congratulations Guys.. keep going
Thank you @Herve Franck!
Astonishing explanation!
Masterpiece
Amazing as always!! Glad to see vids again :-)
Thanks Brian!!
This is so clear! Very much appreciated! :)
awesome video, and very nice to hear a human voice!!
Glad you liked it! thank you!