Abstract
So far, we have looked at two modelling approaches to explain the implied volatility smile: local volatility and stochastic volatility. If we choose a stochastic volatility approach, we have seen that there are many possible models, each having the ability to generate a smile. This is rather unsatisfactory since it leaves us wondering which approach or which particular model we should use. There are further questions we have touched on but not yet answered. What if our stochastic volatility model does not perfectly match our smile at all strikes? As we only have a small number of stochastic volatility parameters, what can we do about getting the smile right at a number of different expiry dates? Do all the contracts we care about even have well-defined prices in the model we choose?KeywordsStochastic VolatilityImplied VolatilityBarrier OptionLocal VolatilityVolatility SurfaceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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