, which is defined as the ratio between the realized volatility and trading volume and which refines the popular price impact … measure proposed by Amihud (2002). In our model, both price volatility and market liquidity are assumed to follow stochastic … processes in continuous time. In this setting, characterized by stochastic volatility and liquidity, we prove that the realized …

We study an extension of the Heston stochastic volatility model that incorporates rough volatility and jump clustering … phenomena. In our model, named the rough Hawkes Heston stochastic volatility model, the spot variance is a rough Hawkes … the log returns and the square of the volatility index can be computed explicitly in terms of solutions of deterministic …

Exact simulation schemes under the Heston stochastic volatility model (e.g., Broadie-Kaya and Glasserman-Kim) suffer …

model extended with stochastic volatility. For both cases, we can achieve high-precision results (with average errors around …

In this paper, we show that a time-dependent local stochastic volatility (SLV) model can be reduced to a system of …

We develop a novel method to decompose a straddle into a volatility risk portfolio and a jump risk portfolio. The …. We use the straddle decomposition to analyze the volatility risk premium and the jump risk premium embedded in a straddle … volatility risk portfolio persistently generates positive returns during earnings announcement periods …

The Black-Scholes model, which is widely used to price financial options, assumes that volatility is constant as a … function of strike price. However when market option prices are used to infer the volatility that is implied by those prices … that the volatility smile is “real” in the sense that volatility and price change are correlated through the degree of …

Derivatives, especially equity and volatility options, contain valuable and oftentimes essential information for … estimating stochastic volatility models. Absent strong assumptions, their typically highly nonlinear pricing dependence on the … jointly accounts for stock returns as well as prices of equity and volatility options. Finally, we provide numerical results …

, leading to the so called "unspanned stochastic volatility puzzle". Additional volatility factors seem to be needed to explain … volatility from a nonparametric perspective …