Examining the volatility skew in the South African equity market using risk-neutral historical distributions

Is it really paid for sustainable development? The economic significance of firms' green practice

“…14. Out-of-the-money skew (OTM_SKEW) equals the average implied volatility of call options and put options minus the implied volatility of OTM put options (De Araújo & Maré, 2006). According to the hypothesis in this paper, out-of-the-money skew is expected to be negatively correlated with ESGEnv.…”

“…According to the hypothesis in this paper, option bid‐ask spread is expected to be negatively correlated with ESGEnv. At‐the‐money skew ( ATM_SKEW ) is equal to the implied volatility of call options minus the implied volatility of put options (Gauthier & Rivaille, 2009). According to the hypothesis in this paper, at‐the‐money skew is expected to be negatively correlated with ESGEnv. Out‐of‐the‐money skew ( OTM_SKEW ) equals the average implied volatility of call options and put options minus the implied volatility of OTM put options (De Araújo & Maré, 2006). According to the hypothesis in this paper, out‐of‐the‐money skew is expected to be negatively correlated with ESGEnv. Implied volatility‐realized volatility spread ( IV_RV_SPREAD ) is equal to the average of the IVs of the ATM call and put options at time t minus the realized volatility calculated by the daily returns of the previous month (Bollerslev et al, 2011).…”

Modelling South African single-stock futures option volatility smiles

“…There is also a one-to-one correspondence between the structure of the implied volatility curve and the riskneutral density, with a left-biased smile shape corresponding to a heavy-tailed and negatively skewed risk-neutral returns distribution. It is mathematically and economically appropriate to assume that the riskneutral density is some deformation of the physical density (see de Araujo and Mare (2006), Brunner and Hafner (2003) and others). Although this part of the problem is supposedly obvious, it is neither easy to test, nor straightforward to reconcile with the statistical distributional characteristics of the underlying asset.…”

“…Of those conducted, de Araujo and Mare (2006) examined the volatility skew using risk-neutral historical distributions and Bonney, Shannon, and Uys (2008) did a principle component analysis of the Top40 volatility skew. Kotze and Joseph (2009) generated an implied volatility surface by fitting a quadratic deterministic function to data from ALSI index options.…”