I presented a detailed analysis of what happened on Volatility Black Monday:
https://artursepp.com/2018/02/15/lessons-from-the-crash-of-short-volatility-etfs/
the feedback is welcome

Amin, thank you for the kind words.Best Regards

<t>Amin, I assume that you are trying to model the probability distribution for the two-dimensional process p(S,V,t). You have to specify four boundaries. I suggest the following ones:1) p_{S}(S,V,t)|_{S=0}=0,2) p_{V}(S,V,t)|_{V=0}=0,These are reflecting boundaries - the diffusion is reflected at ze...

<t>Alan, it will definitely be very interesting to read your book.Are there any reasons to assume that jump intensity is stochastic? It complicates the pricing problem adding the third dimension. I have played with such models, but haven't found any significant improvement compared with stoch. volat...

<t>QuoteOriginally posted by: AlanJohnny, thanks for the plug.I sometimes see a used copy available from amazon.Otherwise, I am working on a vol 2, and when I print that,say by year-end or next spring, then I'll also do a second printing ofvol. 1.regards,alanHi Alan,It is nice to have a vol 2 of you...

<t>I cannot derive this PDE using the standard delta-hedging strategy, but the following probabilistic considerations can be applied.Let S denote asset price. S_t is a stochastic process (an exponential Brownian motion in the Black-Scholes world) with transition density function w(S,t;S',t'), S \in ...

khairoo,You can find local volatility formula in terms of implied volatility function as well as its derivation in this projectBest Regards

In Dupire's world, the local volatility \sigma(S,T) means the future volatility at state S and time T such that the current vanilla prices are matched.

<t>>I have tried Kou's version as well, but the results are exactly the same!Nevertheless, I assume that the second term has to be accounted for. You use quite large theta1. Recall that the second root beta2>theta1. In your example theta1=12.6 so that the second term with exp(-beta2*x)<exp(-theta1*x...

<t>Hi Anton,I took a look at your presentation. It is very informative. I have a question.Eq 9 has four real (unique) roots on intervals (-infinity, -theta2), (theta2, 0), (0,theta1), (theta1, infinity)Next you introduce the Laplace transform of the FTP T_beta: eq 10. Why you use only one root beta1...

<t>Thank you, AlanI agree on tractability of exponential jumps, but it seems that Lipton's approach is quite tricky. A more transparent approach is needed... I'm waiting for your articles.Both log-normal and log-exponential jumps can fit the smile, they even produce approximately the same risk param...

<t>Hi Alan,I came across your recent talk "Path-dependent Options under Jump-Diffusions". It is really interesting. I have a few questions to you...Can your results be applied to the case double-barriers?Is it possible to incorporate rebates into your formulas?Have you succeeded in implementing Mert...

<t>Hi Alan,thank you so much. I checked some papers by Boyarchenko-Levendorskii and luckily found out the relevant formulas for general processes. Now I understand the whole point.I very appreciate your book and your papers. We all gained much insight from your work and hope you will continue provid...

Hi Alan,I'm eager to read your articles.I still wonder whether I can work out the explicit expression for q_+ given below eq (11) in Lipton's paper using the fluctuation identity he reports on page 150? Is it a simple calculation of integrals or is there any trick?Thanks