Related papers: L\'evy processes as weak limits of rough Heston mo…
We study small time bounds for transition densities of convolution semigroups corresponding to pure jump L\'evy processes in $\mathbb{R}^{d}$, $d \geq 1$, including those with jumping kernels exponentially and subexponentially localized at…
This work extends the variance reduction method for the pricing of possibly path-dependent derivatives, which was developed in (Genin and Tankov, 2016) for exponential L\'evy models, to affine stochastic volatility models (Keller-Ressel,…
We provide a detailed importance sampling analysis for variance reduction in stochastic volatility models. The optimal change of measure is obtained using a variety of results from large and moderate deviations: small-time, large-time,…
In this manuscript we analyze the weak convergence rate of a discretization scheme for the Heston model. Under mild assumptions on the smoothness of the payoff and on the Feller index of the volatility process, respectively, we establish a…
Recent empirical studies suggest that the volatilities associated with financial time series exhibit short-range correlations. This entails that the volatility process is very rough and its autocorrelation exhibits sharp decay at the…
The purpose of this paper is to analyze the distribution distance between random vectors derived from the magnitude of the analytic wavelet transform of the squared envelopes of Gaussian processes and their large-scale limits. When the…
The asymptotic solution of the inviscid Burgers equations with initial potential $\psi$ is closely related to the convex hull of the graph of $\psi$. In this paper, we study this convex hull, and more precisely its extremal points, if…
Pricing derivatives goes back to the acclaimed Black and Scholes model. However, such a modeling approach is known not to be able to reproduce some of the financial stylized facts, including the dynamics of volatility. In the mathematical…
We consider stochastic control systems affected by a fast mean reverting volatility $Y(t)$ driven by a pure jump L\'evy process. Motivated by a large literature on financial models, we assume that $Y(t)$ evolves at a faster time scale…
We consider a fractional version of the Heston volatility model which is inspired by [16]. Within this model we treat portfolio optimization problems for power utility functions. Using a suitable representation of the fractional part,…
Most of the empirical studies on stochastic volatility dynamics favor the 3/2 specification over the square-root (CIR) process in the Heston model. In the context of option pricing, the 3/2 stochastic volatility model is reported to be able…
L\'{e}vy processes with completely monotone jumps appear frequently in various applications of probability. For example, all popular stock price models based on L\'{e}vy processes (such as the Variance Gamma, CGMY/KoBoL and Normal Inverse…
In quantitative finance, modeling the volatility structure of underlying assets is vital to pricing options. Rough stochastic volatility models, such as the rough Bergomi model [Bayer, Friz, Gatheral, Quantitative Finance 16(6), 887-904,…
In this paper, we show an approximation in law, in the space of the continuous functions on $[0,1]^2$, of two-parameter Gaussian processes that can be represented as a Wiener type integral by processes constructed from processes that…
The dynamics of the Hamiltonian mean field model is studied in the context of continuous time random walks. We show that the sojourn times in cells in the momentum space are well described by a L\'evy truncated distribution. Consequently…
This paper presents a methodology to introduce time-dependent parameters for a wide family of models preserving their analytic tractability. This family includes hybrid models with stochastic volatility, stochastic interest-rates, jumps and…
Let $\xi$ be a L\'{e}vy process and $I_\xi(t):=\int_{0}^te^{-\xi_s}\mathrm{d} s$, $t\geq 0,$ be the exponential functional of L\'{e}vy processes on deterministic horizon. Given that $\lim_{t\to \infty}\xi_t=-\infty$ we evaluate for general…
We propose new nonparametric estimators of the integrated volatility of an It\^{o} semimartingale observed at discrete times on a fixed time interval with mesh of the observation grid shrinking to zero. The proposed estimators achieve the…
In contrast to their seemingly simple and shared structure of independence and stationarity, L\'evy processes exhibit a wide variety of behaviors, from the self-similar Wiener process to piecewise-constant compound Poisson processes.…
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…