In a tractable stochastic volatility model, we identify the price of the smile as the price of the unspanned risks … traded in SPX option markets. The price of the smile reflects two persistent volatility and skewness risks, which imply a …-form and structural models of stochastic volatility …

In electricity markets, futures contracts typically function as a swap since they deliver the underlying over a period … averaging results in geometric swap price dynamics. Our framework allows for including typical features as the Samuelson effect …, seasonalities, and stochastic volatility. In particular, we investigate the pricing procedures for electricity swaps and options in …

portfolios. This paper proposes a new estimation and inference framework for these option-implied term structures that addresses … nonparametric. New confidence intervals quantify the term structure estimation error. The framework is applied to estimating the …

We develop a discrete-time stochastic volatility option pricing model, which exploits the information contained in high …-frequency data. The Realized Volatility (RV) is used as a proxy of the unobservable log-returns volatility. We model its dynamics by … competing time-varying (i.e. GARCH-type) and stochastic volatility pricing models. The pricing improvement can be ascribed to …

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 …

This paper provides empirical evidence that volatility markets are integrated through the time-varying term structure … of variance risk premia. These risk premia predict the returns from selling volatility for different horizons, maturities … significance from the no-arbitrage prices and bounds implied by the variance swap market. The paper examines these pricing errors …

advantages: i) ensures nonnegative interest rates, ii) easily accommodates unspanned factors affecting volatility and risk …, volatility, and risk premium dynamics — including when interest rates are close to the zero lower bound …

market, volatility and jump risks, and observation error of time changes. To operationalize the models, we use volume …

straddles; second, we estimate the PVR in a Heston (1993) stochastic-volatility model. In both cases, the estimation is … more negative and its term structure is steeper when volatility is high. These findings are inconsistent with calibrations …

option prices on both markets. We find that including VIX option prices in the model estimation allows better identification … of the parameters driving the risk-neutral conditional distributions and term structure of volatility, thereby enhancing … the estimation of the variance risk premium. We gain new insights on the properties of the premium's term structure and …