Related papers: Multiscaling and rough volatility: an empirical in…
Based on criteria of mathematical simplicity and consistency with empirical market data, a stochastic volatility model is constructed, the volatility process being driven by fractional noise. Price return statistics and asymptotic behavior…
We empirically analyze the scaling properties of daily Foreign Exchange rates, Stock Market indices and Bond futures across different financial markets. We study the scaling behaviour of the time series by using a generalized Hurst exponent…
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…
Many studies assume stock prices follow a random process known as geometric Brownian motion. Although approximately correct, this model fails to explain the frequent occurrence of extreme price movements, such as stock market crashes. Using…
The Black-Scholes-Merton model is a mathematical model for the dynamics of a financial market that includes derivative investment instruments, and its formula provides a theoretical price estimate of European-style options. The model's…
Diffusion processes driven by Fractional Brownian motion (FBM) have often been considered in modeling stock price dynamics in order to capture the long range dependence of stock price observed in reality. Option prices for such models had…
This paper studies the pricing problem in which the underlying asset follows a non-Markovian stochastic volatility model. Classical partial differential equation methods face significant challenges in this context, as the option prices…
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…
Rough volatility models are known to reproduce the behavior of historical volatility data while at the same time fitting the volatility surface remarkably well, with very few parameters. However, managing the risks of derivatives under…
We study the temporal fluctuations in time-dependent stock prices (both individual and composite) as a stochastic phenomenon using general techniques and methods of nonequilibrium statistical mechanics. In particular, we analyze stock price…
The present paper proposes a new framework for describing the stock price dynamics. In the traditional geometric Brownian motion model and its variants, volatility plays a vital role. The modern studies of asset pricing expand around…
We introduce a canonical way of performing the joint lift of a Brownian motion $W$ and a low-regularity adapted stochastic rough path $\mathbf{X}$, extending [Diehl, Oberhauser and Riedel (2015). A L\'evy area between Brownian motion and…
The aim of this paper is to present a simple stochastic model that accounts for the effects of a long-memory in volatility on option pricing. The starting point is the stochastic Black-Scholes equation involving volatility with long-range…
Pricing of high-dimensional options is one of the most important problems in Mathematical Finance. The objective of this manuscript is to present an original self-contained treatment of the multidimensional pricing. During the past decades…
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 develop a product functional quantization of rough volatility. Since the quantizers can be computed offline, this new technique, built on the insightful works by Luschgy and Pages, becomes a strong competitor in the new arena of…
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…
The research presented in this article provides an alternative option pricing approach for a class of rough fractional stochastic volatility models. These models are increasingly popular between academics and practitioners due to their…
The rough Bergomi (rBergomi) model can accurately describe the historical and implied volatilities, and has gained much attention in the past few years. However, there are many hidden unknown parameters or even functions in the model. In…
This paper advances interest rate modeling in the post-LIBOR era by introducing rough stochastic volatility into the Forward Market Model (FMM). We establish a rigorous asymptotic expansion of swaption implied volatility, connecting the FMM…