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I'm interested in the areas surrounding Stochastic Volatility Modelling. I've read up on the main models that are prominent in the literature (Hull White, Heston, SABR) but I was wondering what the other issues facing this field are.

Incorporating Stochastic Volatility makes an incomplete model and I've read a few papers on how one may potentially counteract this incompleteness. This also leads from the fact that there could be more than one EMM which turns the asset price process into a martingale, so I have also read up on choosing an optimal measure which is closest to the real world measure.

Does anyone know about other areas like the two I have mentioned which would be good to read up on to solidify my understanding of Stochastic Volatility?

Thanks!

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  • $\begingroup$ I would not say that market is uncomplete. From my point of view, stochastic volatility models assume you can buy a call option $C(T,K_0)$ on the market, then you can hedge a call option $C(T,K)$ with $K\neq K_0$. $\endgroup$ – MJ73550 Jun 6 '16 at 12:10
  • $\begingroup$ @MJ73550 I see what you mean. But IMHO it's incomplete in the sense you could well use different instruments to perform the volatility hedge (e.g. a variance swaps or whatever), each strategy is associated to a certain "market price of volatility risk", hence a different model. $\endgroup$ – Quantuple Jun 6 '16 at 14:17
  • $\begingroup$ @Dabshffabjvs could you insert the reference of the article which tells you how to choose an "optimal measure" which resembles the real world measure? $\endgroup$ – Quantuple Jun 6 '16 at 14:19
  • $\begingroup$ @Quantuple netegrate.com/index_files/Research%20Library/Catalogue/… $\endgroup$ – Dabshffabjvs Jun 6 '16 at 22:32
  • $\begingroup$ @Quantuple netegrate.com/index_files/Research%20Library/Catalogue/… $\endgroup$ – Dabshffabjvs Jun 6 '16 at 22:35
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Great reads to further explore and better understand stochastic volatility models are the series of articles "Smile Dynamics" by Lorenzo Bergomi.

As the name indicates the idea is to study stochastic volatility models not only as "smile models" (in the sense that SV models can be used to capture the state of the vanilla market by correctly accounting for implied volatility term structure and skew = static picture) but also as "smile dynamics models" (in the sense that they embed a view on the evolution of that vanilla market).

Smile Dynamics I

Smile Dynamics II

Smile Dynamics III

Smile Dynamics IV

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