1. The table shows simulation-based averages (1000 runs) of absolute percentage errors 100 � | ? ? Y dense |/Y dense for Y = V, IV, RIX using endpoint volatility (EndPoint), linear regression (LinReg), and RND tail (RND) extrapolation for the base case (Panel A) and crisis scenario (Panel B) with error standard deviation in parentheses;OTM option prices Kput/S0,2000
2. RIX OTM put options only) using trapezoidal integration over dense grids of strikes with ?K/S0 = 0.5%. Estimates ? are obtained from randomly perturbed implied volatility smiles ?noisy,i = ?i (1 + 0.02?), i = 1, . . . , � where ?i are Black and Scholes (1973) implied volatilities computed from Bates (2000) option prices and ? ? N (0, 1). ? are computed from extrapolated moneyness ranges;Y Lo;OTM put options only) based on cubic spline smoothing (RND: with convexity constraints) of strike grids with ?K/S0 = 1%, 2%, 5%. References Ait-Sahalia,1998
3. Robust estimation of risk-neutral moments;M Ammann;Journal of Futures Markets,2019
4. risk-neutral moment estimators: An affine jump-diffusion approach;P Aschakulporn;Journal of Futures Markets,2003