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Alternative models than Black-Scholes?

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I got hammered in a seminar last evening.

The Morgan-Stanley Doctor said people no longer use simple Black-Scholes setting in Wall Street. They add in Heston Volatility Model to capture the irregular up and downs of price movement.

This is a real blow since the whole book of Shreve turns immature before I even finish it.

Beside that, I found Variance-Gamma model, the so called levy-process model also very popular in academia.

I am really confused now so please help me find a book or source that explains either model explicitly so that I can price and delta hedge a very complex exotic option. Thanks.
 
Shreve mentions the Heston volatility model, and I believe there is a problem in chapter 6 dealing with it. Its not horribly difficult to augment B.S. with stochastic volatility.
 
DStahl said:
Shreve mentions the Heston volatility model, and I believe there is a problem in chapter 6 dealing with it. Its not horribly difficult to augment B.S. with stochastic volatility.
Click to expand...
would you plz be more precise about that?
 
I agree that if you haven't finished reading Shreve yet, then you should. Most everything you learn from it will remain useful. Think of the material therein as a necessary condition, not a sufficient condition.

Regarding Levy Processes, etc., I think the best intro book (but finish Shreve or equivalent first) is:
"Financial modelling with Jump Processes" by Rama Cont & Peter Tankov
http://www.cmap.polytechnique.fr/~rama/Jumps/
Very good on intuition and connecting everything with finance -- it actually motivates the why of Levy Processes (what are the financial reasons to use them in modeling), not just the how (which is often an unfortunate phenomenon in the academic papers, some of which seem to use math for math sake).
 
DStahl said:
Exercise 6.7
Click to expand...

Unfortunately, in that exercise, the boundary condition (6.9.29) is wrong and the others are and probably not correct as well AFAIK.

One needs to look at the Feller condition and Fichera PDE theory.
 
Polter said:
I agree that if you haven't finished reading Shreve yet, then you should. Most everything you learn from it will remain useful. Think of the material therein as a necessary condition, not a sufficient condition.

Regarding Levy Processes, etc., I think the best intro book (but finish Shreve or equivalent first) is:
"Financial modelling with Jump Processes" by Rama Cont & Peter Tankov
http://www.cmap.polytechnique.fr/~rama/Jumps/
Very good on intuition and connecting everything with finance -- it actually motivates the why of Levy Processes (what are the financial reasons to use them in modeling), not just the how (which is often an unfortunate phenomenon in the academic papers, some of which seem to use math for math sake).
Click to expand...
I am enjoying working through Shreve-2, though it's more about the BSM-world. I chanced upon Rama Cont's book today, that uses the char. func of the stoch process and shows how to price derivatives in markets with jumps; this should make a great follow-up of Shreve.
 
2 factor PDE
 

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