We provide an efficient swaption volatility approximation for longer maturities and tenors, under the lognormal forward …-LIBOR model. In particular, we approximate the swaption volatility with a mean update of the spanning forward rates. Since the …

Chicago Board Options Exchange (CBOE) volatility index (VIX) options. Our methodology is analytically tractable and yet … modeling the stochastic co-volatility factor can significantly improve the in-sample fitting results due to the improved …

log-returns and their volatility with the aim of analysing which risk factors and which distribution features provide a …-returns and volatility offer the best trade-off between model performance and parsimony …

significant price jump component in variance swap rates. A model-based analysis shows that investors' willingness to ensure … against volatility risk increases after a market drop. This effect is stronger for short horizons and more persistent for long …

In this paper, we propose a new Heston based stochastic volatility model for stock price and option pricing, which not … only captures the volatility smile, but also naturally captures the stochastic volatility of volatility. It's more …

We develop a new efficient and analytically tractable method for estimation of parametric volatility models that is …-day data into the Realized Laplace Transform of volatility, which is a model-free and jump-robust estimate of daily integrated … empirical Laplace transform of the unobservable volatility. The estimation then is done by matching moments of the integrated …

implied volatility smile and the risk neutral density function is tested on SPX options …

Volatility clustering, long-range dependence, non-Gaussianity and anomalous scaling are all well-known stylized facts …