Related papers: The fractional volatility model and rough volatili…
In this article, we give some existence and smoothness results for the law of the solution to a stochastic heat equation driven by a finite dimensional fractional Brownian motion with Hurst parameter $H>1/2$. Our results rely on recent…
We use princiles of fuzzy logic to develop a general model representing several processes in a system's operation characterized by a degree of vagueness and/or uncertainy. Further, we introduce three altenative measures of a fuzzy system's…
Modeling of phenomena such as anomalous transport via fractional-order differential equations has been established as an effective alternative to partial differential equations, due to the inherent ability to describe large-scale behavior…
We price European options in a class of models in which the volatility of the underlying risky asset depends on the short rate of interest. Our study results in an explicit pricing formula that depends on knowledge of a characteristic…
We introduce fractional Brownian motion processes (fBm) as an alternative model for the turbulent index of refraction. These processes allow to reconstruct most of the refractive index properties, but they are not differentiable. We…
This article presents a new continuous-time modelling framework for multivariate time series of counts which have an infinitely divisible marginal distribution. The model is based on a mixed moving average process driven by L\'{e}vy noise -…
This paper discusses and summarizes some results on complex variables that are very useful in fractional-order systems analysis and design, specifically when the system is analyzed in the frequency domain. The author hopes that this…
We investigated the quality of forecasting of fractional Brownian motion, and new method for estimating of Hurst exponent is validated. Stochastic model of the time series in the form of converted fractional Brownian motion is proposed. The…
When modelling time series, it is common to decompose observed variation into a "signal" process, the process of interest, and "noise", representing nuisance factors that obfuscate the signal. To separate signal from noise, assumptions must…
"Noise-induced volatility" refers to a phenomenon of increased level of fluctuations in the collective dynamics of bistable units in the presence of a rapidly varying external signal, and intermediate noise levels. The archetypical…
The recently developed rough Bergomi (rBergomi) model is a rough fractional stochastic volatility (RFSV) model which can generate more realistic term structure of at-the-money volatility skews compared with other RFSV models. However, its…
Many mathematical models utilize limit processes. Continuous functions and the calculus, differential equations and topology, all are based on limits and continuity. However, when we perform measurements and computations, we can achieve…
In this article we look at stochastic processes with uncertain parameters, and consider different ways in which information is obtained when carrying out observations. For example we focus on the case of a the random evolution of a traded…
Using Malliavin Calculus techniques, we derive closed-form expressions for the at-the-money behaviour of the forward implied volatility, its skew and its curvature, in general Markovian stochastic volatility models with continuous paths.
Volatility is the canonical measure of financial risk, a role largely inherited from Modern Portfolio Theory. Yet, its universality rests on restrictive efficiency assumptions that render volatility, at best, an incomplete proxy for true…
We study a class of semi-implicit Taylor-type numerical methods that are easy to implement and designed to solve multidimensional stochastic differential equations driven by a general rough noise, e.g. a fractional Brownian motion. In the…
Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the…
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…
We study the fundamental problem of the calculus of variations with variable order fractional operators. Fractional integrals are considered in the sense of Riemann-Liouville while derivatives are of Caputo type.
In this paper, a pricing formula for volatility swaps is delivered when the underlying asset follows the stochastic volatility model with jumps and stochastic intensity. By using Feynman-Kac theorem, a partial integral differential equation…