Volatility Jumps

On the Stochastic Properties of Carbon Futures Prices

“…The evidence in Figures 2 and 3 strongly invalidates models including a continuous martingale. Similar to the analysis of the VIX in Todorov and Tauchen (2011) or Internet data in Todorov and Tauchen (2010), our results show that the carbon futures price data for the period under investigation cannot be generated from a stochastic process including a Brownian motion (as the activity index is not flat at all or near to be flat around a value of 2).…”

Realized Laplace Transforms for Estimation of Jump Diffusive Volatility Models

“…There is also some evidence for smaller, more vibrant price-level jumps, as predicted by models built on Lévy processes with so-called Blumenthal-Getoor indexes above zero. 2 This evidence is documented by Jacod (2009a, 2010) for liquid equity prices, by Todorov and Tauchen (2010) for index options prices, see also the references therein.…”

“…It might be thought that a way around this problem is to use volatility-sensitive financial derivatives, e.g., options, but that is not generally the case. As noted by Todorov and Tauchen (2010), a market-based volatility index based on a portfolio of option prices such as the VIX is actually two-level convolution of the 1 See, for example, Shephard (2004, 2006), Ait-Sahalia and Jacod (2009b), among many others, with evaluations of jump tests in Huang and Tauchen (2005), and quite comprehensively in Theodosiou and Zikes (2009).…”

Inferring Volatility Dynamics and Risk Premia from the S&P 500 and VIX Markets

“…4 The specification of jumps is of importance. , Todorov and Tauchen (2011) and Jacod and Todorov (2010) find striking evidence for co-jumps in S&P 500 returns and in the VIX. See also Eraker (2004), Broadie et al (2007), Cont and Kokholm (2013).…”