The information content of implied volatility, skewness and kurtosis: empirical evidence from long‐term CAC 40 options

Abstract

Implied standard deviation is widely believed to be the best available forecast of the volatility of returns over the remaining contract life (Jorion, 1995). In this paper, we take this result two steps further to the higher moments of the distribution (skewness and kurtosis) based on a Gram ± Charlier series expansion of the normal distribution (Corrado and Su, 1996) using long-term CAC 40 option prices contract, named PXL. First, we found that implied first moments contain a substantial amount of information for future moments of CAC 40 returns although this amount decreases with respect to the moment's order. Secondly, we found that the different shapes of the volatility smile are consistent with different distribution of the underlying returns. Based on these results, we also observed that including other implied moments significantly improves the out-of-sample pricing performance of the Black ±Scholes, (1973) model.

The hidden martingale restriction in Gram‐Charlier option prices

“…Adroit use of the Edgeworth/Gram-Charlier option pricing framework can be found in Ane (1999) and Jondeau and Rockinger (2000) who adapt the methodology of Madan and Milne (1994) to empirical tests involving S&P 500 index options and Franc/Mark exchange rate options, respectively. CapelleBlancard, Jurczenko, and Maillet (2001) examine the pricing and hedging performance of the Jarrow-Rudd model with CAC 40 index options and Navatte and Villa (2000) test the Corrado-Su model with long-term CAC 40 index options. Chauveau and Gatfaoui (2002) perform simulation experiments comparing their own innovative two-factor option pricing model with the Corrado-Su model.…”

Investigating unusual changes in real-dollar exchange rate

“…As suggested by Beckers (1981), ATM options are better than any other approaches based on weightedaverages. Additionally, these options are usually the most traded instruments, best reproducing market 3 Christensen and Prabhala (1998), Jorion (1995) and Navatte and Villa (2000). 4 As noted by Ahoniemi (2006), predominant studies reject the hypothesis of an unbiased predictor.…”

Fourier inversion formulas for multiple-asset option pricing

“…To illustrate concretely how our pricing formulas work, we develop a simple, theoretically grounded and broadly applicable multivariate model (affine realized variance, or ARV) that captures individual and joint dynamics in several stock 5 For example, Navatte and Villa (2000) demonstrate that the recovered implied moments of the CAC 40 significantly improved out-of-sample pricing performance; Buss and Vilkov (2012) find that using options data to construct implied factor betas significantly outperforms historical betas in the capital asset pricing model; Kempf et al (2014) report substantial portfolio gains when relying solely on the plain vanilla options to calibrate a covariance matrix; Buraschi et al (2014) demonstrate the usefulness of implied correlations in the factor returns construction; and van Binsbergen et al (2012) use well-known put-call parity (Stoll, 1969) to construct a term structure analog of dividend yields for the market portfolio by calibrating implied dividend yields from the option contracts. 6 In Canada, for example, Structured-Retails-Products (2013) report that the notional amount of options written on basket was 2.865 billion CAD, whereas that of single shares was only 16 million CAD in 2013.…”