# Industry standards for vol control index options

Consider an index of the type:

$$I(t)/I(t-1) = 1+ a(t) (S(t)/S(t-1)-1)+(1-a(t))r(t-(t-1))$$

It is arbitrarily initialized. $$r$$ is the risk free rate.

a(t) is determined piecewise as:

$$a(t)=s_{target}/s_{estimated}$$

Where $$s_{target}$$ is the contractual target vol, something that the client wants the index to be exposed to. $$s_{estimated}$$ is the historically estimated measure of the realized vol of $$S$$.

Now I have a vanilla option on $$I(t)$$. Using a local vol model does not feel sufficient because one needs to model the joint dynamics of $$a$$ (vol) and $$S$$ (spot). Also, if $$a$$ is taken to be a constant, this reduces to somewhat of a cliquet which is sensitive to stochastic volatility.

I am looking for information on the industry/academic standards on how products like these are usually modelled?