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Suppose I model an asset $S_1(t)$ under a stochastic volatility model. To price an option on $S_1$, I must assume the existence of an asset $S_2$ that is used to hedge against changes in the volatility of $S_1$.

I suspect that, under reasonable models of market prices, no such asset exists. Are there any assets that come close? How do big hedge funds hedge against changes in volatility?

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  • $\begingroup$ I wanted to include this in the OP, but it is really a separate question: I read a while ago that you can calculate a "price of volatility-risk" using utility functions. I have been unable to find this formula again, but is this something that is actually done in practice? $\endgroup$
    – user60799
    Commented Jan 22, 2022 at 8:10
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    $\begingroup$ Estimating the equity risk premium from utility functions is contentious enough. I doubt this approach is widely used in practice for the variance risk premium. Coval and Shumway (2001, JF) infer price of variance risk from returns of beta-hedged ATM straddles. Carr and Wu (2009, RFS) estimate the price of variance risk from returns of variance swaps. $\endgroup$
    – Kevin
    Commented Jan 22, 2022 at 10:01
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    $\begingroup$ I don't really understand the question. To start with what are $S_1$ and $S_2$? Base assets or derivatives on the same underlier? $\endgroup$
    – user34971
    Commented Jan 22, 2022 at 11:21
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    $\begingroup$ @noob2 So if the question of the OP is what asset does one need to hedge the vol risk of other options, isn't the answer that the required (hedge) asset is another option? I'm stil confused what the question then is. $\endgroup$
    – user34971
    Commented Jan 22, 2022 at 16:14
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    $\begingroup$ Does this question and answer help: quant.stackexchange.com/questions/58521/… $\endgroup$
    – user34971
    Commented Jan 23, 2022 at 9:12

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