Equity index implied volatility functions are known to be excessively skewed in comparison with implied volatility at … index implied volatility from simulating the 30 dimensional return system of all DAX constituents. Option prices are …-dependence coupled with asymmetric correlation response to negative news is essential to explain the index implied volatility skew …

The notion of model-free implied volatility (MFIV), constituting the basis for the highly publicized VIX volatility … more compatible with the related concept of corridor implied volatility (CIV). We provide a comprehensive derivation of the … CIV measure and relate it to MFIV under general assumptions. In addition, we price the various volatility contracts, and …

volatility risk. While pointing out the joint pricing kernel is not identified nonparametrically, we propose model-free estimates … of marginal pricing kernels of the market return and volatility conditional on the VIX. We find that the pricing kernel … present a U-shape. Hence, stochastic volatility is the key state variable responsible for the U-shape puzzle documented in the …

With the innovation of derivatives, the Standard and Poor's (S&P) 500 index -- as an underlying asset of the volatility …. Since the financial crisis of 2008, the degree of market volatility has increased substantially. In addition, a random …

While empirical studies have established that the log-normal stochastic volatility (SV) model is superior to its … depends on the higher order moments of the volatility process. We prove that the second-order leading term is theoretically … valuation of vanilla options. We generalize the affine decomposition to other non-affine stochastic volatility models with …

1/2 classes of volatility processes. Under these models, we study the pricing of European and American VIX options and …-space calculus. The optimal exercise boundary for the volatility is obtained as the unique solution to an integral equation of …

this end, we calibrate the Heston model to a time series of DAX implied volatility surfaces and then price cliquet options …

volatility of the underlying process! This seemingly counterintuitive proposition is driven by a particular feature of Maringale … volatility approaches infinity, the probability of hitting a barrier above the mean goes to zero. Our finding is in contrast to … the common belief that a higher volatility increases all option values. Digital options are observed in a variety of …