Related papers: On the difference between the volatility swap stri…
We introduce a notion of regularized total variation on an interval for continuous functions with unbounded variation. The definition of regularized total variation is obtained from that of total variation by subtracting a penalty for the…
In stochastic Volterra rough volatility models, the volatility follows a truncated Brownian semi-stationary process with stochastic vol-of-vol. Recently, efficient VIX pricing Monte Carlo methods have been proposed for the case where the…
In this paper we derive lower bounds in minimax sense for estimation of the instantaneous volatility if the diffusion type part cannot be observed directly but under some additional Gaussian noise. Three different models are considered. Our…
This paper examines how shocks to currency volatilities predict exchange rates. Using option-implied volatilities, we construct a dynamic, directed network of volatility connections. Currencies that transmit more volatility shocks, which…
In the Black-Scholes model, the absence of arbitrages imposes necessary constraints on the slope of the implied variance in terms of log-moneyness, asymptotically for large log-moneyness. The constraints are used for example in the SVI…
Following closely the construction of the Schrodinger bridge, we build a new class of Stochastic Volatility Models exactly calibrated to market instruments such as for example Vanillas, options on realized variance or VIX options. These…
In this paper we study the Fourier estimator of Malliavin and Mancino for the spot volatility. We establish the convergence of the trigonometric polynomial to the volatility's path in a setting that includes the following aspects. First,…
This paper investigates the pricing and hedging of variance swaps under a $3/2$ volatility model. Explicit pricing and hedging formulas of variance swaps are obtained under the benchmark approach, which only requires the existence of the…
We introduce a pathwise integration for Volterra processes driven by L\'evy noise or martingale noise. These processes are widely used in applications to turbulence, signal processes, biology, and in environmental finance. Indeed they…
We study the relationship between price spread, volatility and trading volume. We find that spread forms as a result of interplay between order liquidity and order impact. When trading volume is small adding more liquidity helps improve…
Rough volatility models are continuous time stochastic volatility models where the volatility process is driven by a fractional Brownian motion with the Hurst parameter smaller than half, and have attracted much attention since a seminal…
The volatility of financial instruments is rarely constant, and usually varies over time. This creates a phenomenon called volatility clustering, where large price movements on one day are followed by similarly large movements on successive…
This paper presents closed-form analytical formulas for pricing volatility and variance derivatives with nonlinear payoffs under discrete-time observations. The analysis is based on a probabilistic approach assuming that the underlying…
We consider a microstructure model for a financial asset, allowing for price discreteness and for a diffusive behavior at large sampling scale. This model, introduced by Delattre and Jacod, consists in the observation at the high frequency…
This paper investigates short-term behaviors of implied volatility of derivatives written on indexes in equity markets when the index processes are constructed by using a ranking procedure. Even in simple market settings where stock prices…
We consider a process $X_t$, which is observed on a finite time interval $[0,T]$, at discrete times $0,\Delta_n,2\Delta_n,\ldots.$ This process is an It\^{o} semimartingale with stochastic volatility $\sigma_t^2$. Assuming that $X$ has…
In recent joint papers the authors of this note solved a famous problem remained open for many years and proved that for arbitrary contractions with trace class difference there exists an integrable spectral shift function, for which an…
This study investigates the short-term asymptotic behavior of the implied volatility surface (IVS), with a particular focus on the at-the-money (ATM) skew and curvature, which are key determinants of the IVS shape and whose are widely…
In this paper, we propose a nonparametric way to test the hypothesis that time-variation in intraday volatility is caused solely by a deterministic and recurrent diurnal pattern. We assume that noisy high-frequency data from a discretely…
According to the volatility feedback effect, an unexpected increase in squared volatility leads to an immediate decline in the price-dividend ratio. In this paper, we consider the properties of stock price dynamics and option valuations…