Keynote speakers of the JEF'2020 Conference

Title:  Contrast estimation of general locally stationary processes using coupling

Summary: This talk aims at providing statistical guarantees for a kernel based  estimation of time varying parameters driving the dynamic of very generals classes of local stationary processes.  We consider coupling arguments in order to extend the results of Dahlhaus to the local stationary version of the  infinite memory processes. The estimators are computed as localized M-estimators of any contrast satisfying appropriate regularity conditions.

We prove the uniform consistency and pointwise asymptotic normality of such kernel based estimators. We apply our results to usual contrasts such as least-square, least absolute value, or quasi-maximum likelihood contrasts. Various local-stationary  processes as ARMA, AR(∞), GARCH, ARCH(∞), ARMA-GARCH, LARCH(∞) ….  and  integer valued processes are also considered. Numerical experiments demonstrate the efficiency of the estimators on both simulated and real data sets such as log-returns of financial index.

Title: Fractional Brownian models in finance, and option pricing with a martingale method for path-dependent PDEs         

Summary: The first half of this presentation will provide a brief introduction to a continuous-time framework for high-frequency stochastic volatility modeling in finance, including the use of fractional Brownian motion (fBm), and how it relates to rough volatility and long-memory models. These processes, which are highly non-Markovian, defy standard attempts at computing objects such as hedging-based option prices. In the presentation’s second part, we will provide a brief overview of a new technique for path-dependent PDEs, which allows to express option prices as conditional expectations based on the entire path of a martingale component of the underlying fBm-type process. In a dynamic setting, this requires a concatenation of the observed path up to the current time with a specific observable curve derived from the distribution of the future paths. The application to option pricing and hedging in a financial market with rough volatility, uses critically the fact that forward variances are quoted in the said market. (This is joint work with Jianfeng Zhang from the University of Southern California).