Spanning and Derivative-Security Valuation

The Valuation of Volatility Options

“…The relevance of this model is motivated by i substantial empirical evidence supporting the EGARCH model of Nelson 1991 see Engle and Ng 1993, Danielsson 1994, Hentschel 1995 and ii the fact that EGARCH converges to a gaussian process that is mean reverting in the log and thus matches our MRLP speci cation. 3 In this context we show that the hedging behaviors of European-and American-style options di er quite drastically. It is of particular interest to note that the European call option, unlike its 2 For example, in December 1995, a volatility index, the VDAX was introduced by the German Futures and Options Exchange.…”

“…It is of particular interest to note that the European call option, unlike its 2 For example, in December 1995, a volatility index, the VDAX was introduced by the German Futures and Options Exchange. 3 Some of the most common choices of volatility speci cation display mean reversion in volatility levels. Recent empirical studies, however, indicate that such models may be misspeci ed Nandi 1998 .…”

Good and Bad Variance Premia and Expected Returns

“…For this purpose, we utilize the method developed by Bakshi and Madan (2000) and Bakshi, Kapadia, and Madan (2003) to infer the moments of the risk-neutral return distribution from the cross-section of option prices in a model-free way.…”

“…Our proxies for the good and bad variance premia correspond to the differences between the good and bad implied and realized variance of returns. Good (bad) implied variance measures the conditional risk-neutral expectation of the 1-month squared positive (negative) log equity return, computed from option prices as in Bakshi and Madan (2000) and Bakshi, Kapadia, and Madan (2003). We also compute the good and bad realized variance measures using the high-frequency return data, following Barndorff-Nielsen, Kinnebrock, and Shephard (2010).…”

Realized Skewness

“…As Bakshi and Madan (2000) show, any general claim can be replicated by a portfolio of vanilla options; the replicating portfolio for the third moment claim is…”