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Lorenzo


Total Posts: 7
Joined: Jan 2016
 
Posted: 2016-01-22 09:37
Hello everybody, my book has just come out.
It's about 500 pages long and covers a host of smile modeling issues, from local volatility to multi-asset stochastic volatility.



Please visit my website www.lorenzobergomi.com for a table of contents and two sample chapters:
- Introduction
- Local volatility

I'll be happy to have your feedback.
Lorenzo

radikal


Total Posts: 253
Joined: Dec 2012
 
Posted: 2016-01-22 17:25
Chapter 2 definitely covers a LOT of ground. Even as a reasonably non-math-afraid quant nerd, it's dense for me even being very familiar with all this stuff. (Ran skew rv books in lots of stuff)

I don't think is a negative; it's a pretty thorough summary of a lot of the issues w.r.t local vol with the caveats:

- No real coverage of translating back to implied probability space which is, at least personally, really useful when talking about cross-asset type opportunities (Comparing probability mass is sometimes easier)

- What about non-linear time models? (Like skew premium near event or how to think of assymetric dt schemes)

- Implementation of a lot of this stuff is non-trivial. Would be nice to have code examples to go along with the examples even if just high-level non-optimized.

I can see owning this as a reference, but I'm kind of more in the market for something a bit more concrete.


There are no surprising facts, only models that are surprised by facts

Lorenzo


Total Posts: 7
Joined: Jan 2016
 
Posted: 2016-01-23 17:32
Thanks Radikal for your opinion.

Concrete comes in different grades. Personally, I prefer to work with implied vols - vanilla or otherwise - than with probabilities.

Sure, I don't provide code for solving the 1d pricing PDE of the LV model -- you'llfind this in any math finance textbook -- but I provide more precious stuff: formulas for sizing up the dynamics of implied vols in the LV model, which are very simple and can be implemented in XL/VB.

Lorenzo

chiral3
Founding Member

Total Posts: 4986
Joined: Mar 2004
 
Posted: 2016-01-23 20:10
Lorenzo - your book was on my desk when I got into work earlier this week. You've spent quite a bit of time thinking about these things through the years, more than many, and I look forward to reading it.

I've developed some of the work from the Smile Dynamics series. In the end I've often implemented simpler, more practical methods, because I've been less interested in what the price *should be* compared to where it is trading, right or wrong.

Nonius is Satoshi Nakamoto. 物の哀れ

Lorenzo


Total Posts: 7
Joined: Jan 2016
 
Posted: 2016-01-24 10:47
Hi Chiral3 - you'll see there's much more stuff than the material in the SD series - hope you'll like it.

Nonius
Founding Member
Nonius Unbound
Total Posts: 12666
Joined: Mar 2004
 
Posted: 2016-02-04 21:34
Holy Shit. I never thought I'd see Lorenzo Bergomi here. How's SocGen treating you?

Chiral is Tyler Durden

Lorenzo


Total Posts: 7
Joined: Jan 2016
 
Posted: 2016-02-05 10:52
Hi Nonius
Yes I'm alive and kicking! I'm a pretty low-maintenance guy. As long as I'm in a place where
(a) there's the DNA and appetite for trading very exotic things
(b) I can have a meaningful conversation with traders that are hungry for new ways of looking at things and understanding the carry P&L that models materialize
(c) comp is OK
then I'm a happy camper.

numbersix


Total Posts: 299
Joined: Jan 2007
 
Posted: 2016-10-13 08:57
Hi Lorenzo,

Thank you for such a great book. I think it is not only delightful from the quant's perspective, but also, implicitly, from a philosophical perspective, if only because of the recurrent statement, which I personally find fascinating, that there is no such thing as a model (of the behavior of the underlying price) in quantitative finance modeling, but only pricing equations (of the derivative).

I find very exciting that derivatives, for instance vanilla options, should now be considered as underlyings in their own right, and of course I am personally interested in further investigating the philosophical meaning and underpinnings of the corresponding 'market models'.

From the quant point of view, am I right in thinking that the major point of your approach (whose philosophical and methodological implications it remains to investigate) is that any pricing model, or equation, is by necessity subject to recalibration, therefore that what really matters is that the decomposition of the P&L of a derivative's hedged position, after the volatility surface of the vanillas has moved in ways that were not predicted by the initial instance of the pricing equation, or what is called recalibration, still exhibits a form for which break-even is possible, in a totally ex-post fashion?

What fascinates me, philosophically, is that recalibration has become the given and ex-post accounting has, in any case, replaced ex-ante projection. I am aware this may not interest everybody, here, but I would be curious to see the reactions of the philosophers of probability (who are not aware of our quant practice, of course) to such a book. Indeed, I do believe there is a philosophical commitment implicit in your book. I think your book can, and should, also be read from a philosophical point of view, and I am personally interested in the definition of the market that one could extract from a book like yours, which is not just any book, but the epitome of what's being accomplished in the derivatives markets.

Best,
Elie

BSM is not a model and, because it is not a model, no model can surpass it.

numbersix


Total Posts: 299
Joined: Jan 2007
 
Posted: 2016-10-27 01:54
Nobody here either. Pity.

BSM is not a model and, because it is not a model, no model can surpass it.

Lorenzo


Total Posts: 7
Joined: Jan 2016
 
Posted: 2016-11-04 14:16
Hi Elie/Numbersix,

Thank you for your comments on my book, which I just saw. This book cost me so much sleep, that any token of appreciation is gratefully appreciated.

Now, regarding calibration, as I mention in the book's epilogue, it should maybe exist as a word in the dictionary, certainly not as a concept.
Calibration is just a technicality whereby we input in a model's pricing function the prices of financial instruments we use as hedges. When using a multi-asset BS model, no one says they "calibrate" the spot values.
In the local vol model - or in local/stochastic volatility models - the local volatility surface is just a technicality, a byproduct of the existence of a low-dimensional Markov representation of the assets in the model (one-dimensional for the LV model) - nothing to be taken too seriously.

The way finance is taught in master's degree courses is by starting with a process - say diffusive Brownian motion - and then getting to a pricing equation and a pricing function. The problem with this is that aspiring quants take this notion of process - and maybe prediction - seriously.

We should get rid of the notion of process altogether and consider things in the reverse order:
1) We're delta/vega hedged, so our accounting P&L starts with terms of order two and above.
2) Let's be modest and just focus on these second-order greeks.
3) We ask the model to offset P&L contributions from these 2nd order greeks with deterministic theta terms -> we end up with a parabolic pricing equation.

You can decide to interpret the solution of this pricing equation as an expectation of a function of diffusive processes -> that's fine and useful for designing Monte Carlo algos based on the simulation of processes.
Just don't go considering these processes as things that should have a counterpart in reality.

Regards,

Lorenzo
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