Estimating SVI Parameter Contributions to Options Vega

Summary

The document asks how to explain the vega of an exotic derivative when its volatility surface is represented with Gatheral’s SVI parameterization. It proposes examining changes in each SVI parameter across time slices and approximating the resulting change in implied total variance with a first-order sensitivity calculation. The parameters named are the level, slope, correlation, horizontal shift, and curvature controls of the SVI smile.

The idea is to combine parameter moves with sensitivities to estimate each parameter’s contribution to the surface change, then use that information in a vega explain. The document poses this as a question and supplies no derivation, numerical example, implementation, or empirical comparison. It also leaves open how to map changes in implied variance to the exotic’s price, how to handle parameter constraints and recalibration effects, and whether a local linear approximation is adequate for large moves. Those details would be needed for a complete risk methodology.

Key ideas

• SVI parameters can be bumped individually to estimate sensitivities of a volatility slice.
• A first-order decomposition combines parameter changes with their local sensitivities.
• The proposed calculation concerns implied variance changes and does not specify the full mapping to exotic option value.
• Parameter constraints, recalibration, and the accuracy of linear approximations remain unresolved.

Tags

# Vega with SVI Gatheral bumps


# Vega with SVI Gatheral bumps












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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.