Thanks Brian! Indeed it has been a journey, made even more enjoyable by your continued support! PS: You can see we are building up nicely to the Variance Gamma!
extraordinary. Have seen the previous video on (several ways) to derive Dupire PDE, excellent as well. Haven't completed this one, hope some comments on pricing behaviour for path dependent exotics (hopefully as a function of time to maturity?) Thank you so much
Thanks @Tianrong Wang! We set their values equal to each other so that they reproduce the same price, their underlying processes are different. Hope this helps!
Hello, for the third part, the subtitle in the intro is Relationship between local and Black Scholes’ time-dependent implied vol. I believe it should be Relationship between constant bs implied vol and Black Scholes’ time-dependent implied vol? thanks!
Ah it is easy! if you take derivative of the whole PDE wrt a variable, and then interchange the derivatives, then we get the same PDE for the derivative of price.
Hello, your content is so excellent: could you please do a session on the SABR model? It is so difficult to find accessible and readable content on SABR online...
Yes this is on the list, and high on the priority list. We were planning to do it a year ago, but being a specialised (i.e., small!) channel, google/yt feedback sends us astray, but we do get there eventually!
@@quantpie something to visualize it, how the derivatives isolate certain points in the Volatility structure. I'm learning Volatility trading right now and withe vega charm etc it sometimes gets confusing. Would be a great help if the second and third derivatives would be visualized in the presentation. How to for example see a visual edge for stivky delta on the vol surface. I can link a video to some calculus videos that helped me a lot where the guy visualizes it. I don't want to link it on yoyr channel without your permission
Hi, on the proof of the dollar gamma being a martingale - I believe it is only valid if the underlying stock follows the Black Scholes dynamics. In your proof, you use that the dollar gamma function V(t,x) obeys the black scholes PDE with constant vol Sigma, which is correct, but then if you define a process Z_t = V(t, S_t ) where S_t is a process that has not the same vol Sigma that is in the PDR - then there is no guarantee the drift of Z_t will be 0.0. On the contrary, if S_t follows a BS process with the vol SIgma then yes the drift of Z_t will be 0.0. I believe here we are talking about a process S_t with a local volatility and therefore V(t,S_t) is not necessarily a martingale
Man, I feel like we have really come a long way since 7-8 months ago. Bravo as always quantpie :-).
Thanks Brian! Indeed it has been a journey, made even more enjoyable by your continued support! PS: You can see we are building up nicely to the Variance Gamma!
One of the best and more detailed explanations....congratulations guys..you're the best. ...keep going
Thanks @Herve Franck for the kind words! as always!
You're ability in "market speak" combined with your mathematical insight is uncanny.
thank you for the kind words! many thanks!
Amazing and very clear explanation
Best quant ever !
thank you!!
extraordinary. Have seen the previous video on (several ways) to derive Dupire PDE, excellent as well. Haven't completed this one, hope some comments on pricing behaviour for path dependent exotics (hopefully as a function of time to maturity?) Thank you so much
May I ask why CKT and CBS are different? In 11:15 they are actually the same right? But when constructing the portfolio you assume they are different?
Thanks @Tianrong Wang! We set their values equal to each other so that they reproduce the same price, their underlying processes are different. Hope this helps!
Hello, for the third part, the subtitle in the intro is Relationship between local and Black Scholes’ time-dependent implied vol. I believe it should be Relationship between constant bs implied vol and Black Scholes’ time-dependent implied vol? thanks!
Hi, Can you explain why at 31:00, if V Tilda satisfy Black PDE, then V Tilda's derivative satisfy this PDE too?
Ah it is easy! if you take derivative of the whole PDE wrt a variable, and then interchange the derivatives, then we get the same PDE for the derivative of price.
Hello, your content is so excellent: could you please do a session on the SABR model? It is so difficult to find accessible and readable content on SABR online...
Yes this is on the list, and high on the priority list. We were planning to do it a year ago, but being a specialised (i.e., small!) channel, google/yt feedback sends us astray, but we do get there eventually!
Please do SABR!
This is priceless..
thank you!!
This is great, could you put in graphics in between the transformation
Hello and many thanks for the comment! Soz don’t fully follow, could you provide a bit more detail please?
@@quantpie something to visualize it, how the derivatives isolate certain points in the Volatility structure. I'm learning Volatility trading right now and withe vega charm etc it sometimes gets confusing. Would be a great help if the second and third derivatives would be visualized in the presentation. How to for example see a visual edge for stivky delta on the vol surface. I can link a video to some calculus videos that helped me a lot where the guy visualizes it. I don't want to link it on yoyr channel without your permission
@@ControlTheGuh thanks! got it!!
Hi, on the proof of the dollar gamma being a martingale - I believe it is only valid if the underlying stock follows the Black Scholes dynamics. In your proof, you use that the dollar gamma function V(t,x) obeys the black scholes PDE with constant vol Sigma, which is correct, but then if you define a process Z_t = V(t, S_t ) where S_t is a process that has not the same vol Sigma that is in the PDR - then there is no guarantee the drift of Z_t will be 0.0. On the contrary, if S_t follows a BS process with the vol SIgma then yes the drift of Z_t will be 0.0. I believe here we are talking about a process S_t with a local volatility and therefore V(t,S_t) is not necessarily a martingale
What's the point of constructing a portfolio with longing a market price call and shorting a bs call？
Excellent! Can you do Local Stochastic Volatility?
many thanks!! Sure!
Can you give me an articles of your explanation please
😊 23:38
That's just wizardry...