Estimating the roughness exponent of stochastic volatility from discrete observations of the realized variance

no code implementations • 5 Jul 2023 • Xiyue Han, Alexander Schied

We consider the problem of estimating the roughness of the volatility in a stochastic volatility model that arises as a nonlinear function of fractional Brownian motion with drift.

A limit theorem for Bernoulli convolutions and the $Φ$-variation of functions in the Takagi class

no code implementations • 4 Feb 2021 • Xiyue Han, Alexander Schied, Zhenyuan Zhang

We consider a probabilistic approach to compute the Wiener--Young $\Phi$-variation of fractal functions in the Takagi class.

Probability Classical Analysis and ODEs

A central bank strategy for defending a currency peg

no code implementations • 2 Aug 2020 • Eyal Neuman, Alexander Schied, Chengguo Weng, Xiaole Xue

We model this situation through a continuous-time market impact model of Almgren--Chriss-type with drift, in which the exchange rate is a diffusion process controlled by the price impact of the central bank's intervention strategy.

An FBSDE approach to market impact games with stochastic parameters

no code implementations • 19 Dec 2019 • Samuel Drapeau, Peng Luo, Alexander Schied, Dewen Xiong

We analyze a market impact game between $n$ risk averse agents who compete for liquidity in a market impact model with permanent price impact and additional slippage.