Model-Free Implied Volatility under Jump-Diffusion Models
The model-free implied volatility (MFIVol) is intended to measure the variability of underlying asset price on which options are written. Analytically, however, it does not measure exactly the variability under jump diffusion. Our extensive empirical study suggests that the approximation error can be as much as about 3%--5% although most samples over the data period exhibit less than 1% errors. Even with the non-negligible errors, the MFIVol may be still considered a valid volatility measure from the perspective of risk-neutral return density, in the sense that it is bounded by the two variability measures as well as reflecting the shape of the risk-neutral density via its higher central moments.
Jump-diffusion model; Model-free Implied Volatility; Risk-neutral probability density; Volatility index (VIX)
C58, C65, G12
Choi, S.M., and Yang, H.T. (2019). "Model-Free Implied Volatility under Jump-Diffusion Models", Review of Economics & Finance, vol.16, no.2, pp. 01-14.