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Choosing the Target Surface for SLV Leverage Calibration

Article Quant Q&A · Author: Xerium
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Summary

The document asks which implied volatility surface should serve as the target when calibrating the leverage function in a stochastic-local volatility model. It describes a two-stage setup: first calibrate pure Heston parameters, then fit the leverage function. Because the calibrated Heston model may not reproduce the market surface exactly, the question is whether the leverage fit should target market implied volatility or the surface generated by those Heston parameters.

No answer or calibration procedure is provided, so the document does not resolve the choice or give evidence for either approach. It is useful as a statement of a modeling question, but readers will need additional sources to learn the standard calibration method and its assumptions.

Key ideas

  • The question concerns the target surface used to calibrate the SLV leverage function.
  • The proposed sequence calibrates pure Heston parameters before fitting leverage.
  • The document notes that a Heston-generated surface may differ from the market surface.
  • No answer or supporting calibration details are included.

Tags

OptionsVolatilityDerivatives pricing
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# 78199


# In the Stochastic-Local Volatility (SLV/LSV) calibration procedure, which surface is used when calibrating the Leverage function












Before we match the leverage function $L(S_t,t)$ to the implied volatility surface generated from the market, we are supposed to calibrate the pure Heston parameters, $(\theta, \kappa, v_0, \rho, \xi)$. Since the Heston parameters don't usually match the market surface 1:1, the surface generated from the calibrated heston parameters will be different than the market surface (otherwise there would be no need for SLV). Then when calibrating $L(S_t,t)$, do we use the market IV surface, or the surface generated from the Heston parameters we calibrated?

I would think it would still be the market surface, but I am not sure because the parameters are from a different surface...

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