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How would one go about computing a vega profile of an exotic derivative where the volatility surface is modeled using Gatheral's SVI parameterization? In particular, I am thinking about bumping each of the params up by epsilon and computing a Jacobian for each time slice. So the vega explain would be computed like this:

Consider a time series of SVI parameterizations: $w_t(k;a,b,\rho, m, \sigma)$. Let $\mathscr{V}(t)$ be the vega explain along each slice. Then the vega explain would something like:

$$ \mathscr{V}(t) = \Delta a* \frac{\partial w_t}{\partial a} + \Delta b* \frac{\partial w_t}{\partial b} + \Delta \rho* \frac{\partial w_t}{\partial \rho}+ \Delta m* \frac{\partial w_t}{\partial m}+ \Delta \sigma* \frac{\partial w_t}{\partial \sigma} + \ldots$$

What are your thoughts?

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  • $\begingroup$ How are you calculating the price of the derivative to begin with? $\endgroup$ – will May 12 '18 at 17:26
  • $\begingroup$ PDE pricing model which uses a local vol model. The implied vols use the SVI model. Dupire formula is used to move between implied and local vols $\endgroup$ – John Doe May 12 '18 at 18:02
  • $\begingroup$ So why not try bumping the svi params and looking at the change in your price? Or applying a flat bump to your actual created vols and then repricing? $\endgroup$ – will May 13 '18 at 8:31
  • $\begingroup$ But how much to bump the params? $\endgroup$ – John Doe May 13 '18 at 19:59
  • $\begingroup$ Why not try creating fitting many surfaces, and look at the range of values you get? Or why not try bumping the parameters by a range of values and seeing how (non)linear the price is as a function of the param? $\endgroup$ – will May 13 '18 at 20:06

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