Related papers: Volatility has to be rough
Using a large dataset on major FX rates, we test the robustness of the rough fractional volatility model over different time scales, by including smoothing and measurement errors into the analysis. Our findings lead to new stylized facts in…
We present a number of related comparison results, which allow to compare moment explosion times, moment generating functions and critical moments between rough and non-rough Heston models of stochastic volatility. All results are based on…
The question of the volatility roughness is interpreted in the framework of a data-reconstructed fractional volatility model, where volatility is driven by fractional noise. Some examples are worked out and also, using Malliavin calculus…
This note continues investigation of randomness-type properties emerging in idealized financial markets with continuous price processes. It is shown, without making any probabilistic assumptions, that the strong variation exponent of…
We introduce a new class of continuous-time models of the stochastic volatility of asset prices. The models can simultaneously incorporate roughness and slowly decaying autocorrelations, including proper long memory, which are two stylized…
In this chapter we first briefly review the existing approaches to hedging in rough volatility models. Next, we present a simple but general result which shows that in a one-factor rough stochastic volatility model, any option may be…
The relationship between price volatilty and a market extremum is examined using a fundamental economics model of supply and demand. By examining randomness through a microeconomic setting, we obtain the implications of randomness in the…
In this paper we study short-time behavior of the at-the-money implied volatility for Inverse European options with fixed strike price. The asset price is assumed to follow a general stochastic volatility process. Using techniques of the…
We present small-time implied volatility asymptotics for Realised Variance (RV) and VIX options for a number of (rough) stochastic volatility models via large deviations principle. We provide numerical results along with efficient and…
The implied volatility skew has received relatively little attention in the literature on short-term asymptotics for financial models with jumps, despite its importance in model selection and calibration. We rectify this by providing…
In this paper, we study the relationship between the short-end of the local and the implied volatility surfaces. Our results, based on Malliavin calculus techniques, recover the recent $\frac{1}{H+3/2}$ rule (where $H$ denotes the Hurst…
Single index financial market models cannot account for the empirically observed complex interactions between shares in a market. We describe a multi-share financial market model and compare characteristics of the volatility, that is the…
Econophysics and econometrics agree that there is a correlation between volume and volatility in a time series. Using empirical data and their distributions, we further investigate this correlation and discover new ways that volatility and…
This paper expands traditional stochastic volatility models by allowing for time-varying skewness without imposing it. While dynamic asymmetry may capture the likely direction of future asset returns, it comes at the risk of leading to…
In the information-based approach to asset pricing the market filtration is modelled explicitly as a superposition of signals concerning relevant market factors and independent noise. The rate at which the signal is revealed to the market…
The observation of power laws in the time to extrema of volatility, volume and intertrade times, from milliseconds to years, are shown to result straightforwardly from the selection of biased statistical subsets of realizations in otherwise…
We present an empirical study examining several claims related to option prices in rough volatility literature using SPX options data. Our results show that rough volatility models with the parameter $H \in (0,1/2)$ are inconsistent with…
The notion of market impact is subtle and sometimes misinterpreted. Here we argue that impact should not be misconstrued as volatility. In particular, the so-called ``square-root impact law'', which states that impact grows as the…
The problem of non-stationarity in financial markets is discussed and related to the dynamic nature of price volatility. A new measure is proposed for estimation of the current asset volatility. A simple and illustrative explanation is…
This paper formulates a model of utility for a continuous time framework that captures the decision-maker's concern with ambiguity about both volatility and drift. Corresponding extensions of some basic results in asset pricing theory are…