Martinghoul, you have recommended stochastic vola models in the past. Can you recommend a stochastic model (with jumps ?) geared towards equities in the public domain that can be [easily ?] calibrated, and has (C#/C++) software that I can run to test it? I know Quantlib has Heston and others, but I find that understanding what the parameters should be and how to calibrate it is hard going. I need a little more hand-holding at this point.
Sire, since I don't really operate in the world of equities, I hesitate to recommend anything. All I can tell you is that the two main variants I use in my domain are SABR and HJM.
SABR and HJM are interest rate models, not used for FX. For Equities, different banks have different models. Heston (in its various forms) is one, but you really don't have to go with stocvol models, unless you are doing something very complicated. Depends on what your objective is? For simple stuff like exchange traded calls/puts/binaries, you can just use simple B-S with a skew and kurtosis parameters and after calibration, it should work fine. Define what your objective is ?
True dat... French, most likely arrogant and probably a graduate of Ecole Polytechnique. I am normally not one for stereotypes, but still...
...with the God-given ability to trade and teach equity derivatives Did you know that you have the choice to be completely covered by French-speaking broker dealers even in Hk, Tokyo, or Singapore? ;-)
Right. I am making a big push to understand more sophisticated models. I have done some extensive research on my own trading, and I have come to a partial conclusion that most of my inaccuracies in replication come from not taking asymmetries in the pdf into consideration, leading to incorrect assumptions in both pricing and hedging in the presence of skew correlation. Finding mis-priced options/spreads in the presence of a model (my own) on top of a volatility model (Black-Scholes). Currently I back out implied volatility from Black-Scholes, which has proven to lead to the inaccuracies explained above. I am confident in my model to statically shed light on an edge, but it is the dynamics that give me problem to hold on to it. Peter Carr example that I describe in this thread is really revealing. Once you have a position, what you perceive as "volatility" is highly dependent on the underlying path, and completely different than if you had a different option position. There is no one definition of vola, only in the presence of a position does it exist. Implied Volatility is measuring something really fleeting, and some sort of average of that fleeting thing on top of that. There is no way to just trade volatility. In the presence of a skew, and a position that has puts and calls and mixes months, you are most definitely trading the underlying, no matter how much you twist and turn. Variance swaps could help to ditch the mean, but they don't exist as a unit for the retail trader, and replication is expensive.
Just my two cents, the problem is even worse, you have to treat the portfolio as one big option, pricing each Call and Put and then adding up the values, does not work. The equations are non-linear, so the solutions do not add. Basically have to value and hence derive the greeks for the portfolio as a whole. Then the vol you use has to be your best guess of what its going to be over the remaining life but adjusted for the way you plan to hedge.