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What is Vega for a derivative when the volatility of the underlying asset stochastic process itself?

When the value of the derivative is $V_d$ vegais $\partial V_d/\partial\sigma$. Consider for instance SABR or Heston where $\sigma$ is a stochastic process, and then I don't understand the mathematics and intuition behind $\partial\sigma$. Can someone help me understand?

Wannebe
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    Some related posts https://quant.stackexchange.com/questions/55641/how-to-calculate-vega-in-stochastic-vol https://quant.stackexchange.com/questions/40984/vega-of-exotic-options – nbbo2 Oct 05 '21 at 08:10

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