Note 05：Volatility Smile（II）

4）Universal Volatility Model
Interestingly，one can combine local volatility model( which regards the volatility as a
function of time and stock price) and stochastic volatility(jump diffusion) model together to construct a universal volatility model (Blacher/Lipton). More parameters, more accuracy...

5) Regime Switch Model
This model admit that the stock price must be modeled by different regimes which are different
parameters. In first sense, this model is not so realistic as even we allow smoothly (in time) swith from a regime to one regime, the market dynamics is not so simple as there is no reason to protect whether the real dynamics is governed by regimes. However, one can implement the above 1) 2) 3) 4) models as different regimes, with the inducement of more parameters, one can surely achieve higher precision.

6) Calibration by exotic option
As we have a lot of models in hand, every one seems to fit the volatility well. How can we do? Of course, directly calibrate the model using exotic option is a good idea.


Then there comes the question. Parameters V.S The Prediction


(to be continue)