Related papers: Volatility has to be rough

This paper concerns a local volatility model in which volatility takes two possible values, and the specific value depends on whether the underlying price is above or below a given threshold value. The model is known, and a number of…

We exploit a continuous time random walk description of stock prices to obtain a fast and accurate evaluation of their volatility from intraday data. We show that financial markets are usefully described as open physical systems. Indeed we…

In this paper, we develop a general rough volatility model for commodities that provides an automatic calibration of the initial term structure of the futures prices and an appropriate treatment of the Samuelson effect. After the…

We study, both analytically and numerically, an ARCH-like, multiscale model of volatility, which assumes that the volatility is governed by the observed past price changes on different time scales. With a power-law distribution of time…

Deep learning methods have become a widespread toolbox for pricing and calibration of financial models. While they often provide new directions and research results, their `black box' nature also results in a lack of interpretability. We…

Working on different aspects of algorithmic trading we empirically discovered a new market invariant. It links together the volatility of the instrument with its traded volume, the average spread and the volume in the order book. The…

We derive an explicit asymptotic approximation for the implied volatilities of Call options written on bonds assuming the short-rate is described by an affine short-rate model. For specific affine short-rate models, we perform numerical…

The volatility characterizes the amplitude of price return fluctuations. It is a central magnitude in finance closely related to the risk of holding a certain asset. Despite its popularity on trading floors, the volatility is unobservable…

Option prices encode the market's collective outlook through implied density and implied volatility. An explicit link between implied density and implied volatility translates the risk-neutrality of the former into conditions on the latter…

This paper derives explicit formulas for both the small and large time limits of the implied volatility in the minimal market model. It is shown that interest rates do impact on the implied volatility in the long run even though they are…

We consider microstructure as an arbitrary contamination of the underlying latent securities price, through a Markov kernel $Q$. Special cases include additive error, rounding and combinations thereof. Our main result is that, subject to…

In this paper, we focus on the estimation of historical volatility of asset prices from high-frequency data. Stochastic volatility models pose a major statistical challenge: since in reality historical volatility is not observable, its…

We show that typical behaviors of market participants at the high frequency scale generate leverage effect and rough volatility. To do so, we build a simple microscopic model for the price of an asset based on Hawkes processes. We encode in…

We study specific nonlinear transformations of the Black-Scholes implied volatility to show remarkable properties of the volatility surface. Model-free bounds on the implied volatility skew are given. Pricing formulas for the European…

Estimating volatility from recent high frequency data, we revisit the question of the smoothness of the volatility process. Our main result is that log-volatility behaves essentially as a fractional Brownian motion with Hurst exponent H of…

The robust option pricing problem is to find upper and lower bounds on fair prices of financial claims using only the most minimal assumptions. It contrasts with the classical, model-based approach and gained prominence in the wake of the…

We consider economic obstacles that limit the reliability and accuracy of value-at-risk (VaR). Investors who manage large market transactions should take into account the impact of the randomness of large trade volumes on predictions of…

The drift burst hypothesis postulates the existence of short-lived locally explosive trends in the price paths of financial assets. The recent U.S. equity and treasury flash crashes can be viewed as two high-profile manifestations of such…

We consider the robust pricing and hedging of American options in a continuous time setting. We assume asset prices are continuous semimartingales, but we allow for general model uncertainty specification via adapted closed convex…

We study the dynamics of the normal implied volatility in a local volatility model, using a small-time expansion in powers of maturity T. At leading order in this expansion, the asymptotics of the normal implied volatility is similar, up to…