Eckhard Platen (University of Technology Sydney)
Thursday, July 12, 2018 - 18:00
Technische Universität Berlin, Institut für Mathematik
Strasse des 17. Juni 136, 10623 Berlin, MA 313, 3. Etage
Stochastische Analysis und Stochastik der Finanzmärkte
HU Berlin, TU Berlin, BMS, ECMath
The paper derives an endogenous model for the long-term dynamics of a well-diversified equity index with rough volatility, the S&P500. It assumes that the index is a proxy of the respective growth optimal portfolio, the variance of its increments evolves in some market time proportionally to the index value and the derivative of market time is a linear function of the squared derivative of a smoothed proxy of the single driving Brownian motion. The resulting model is highly tractable, allows almost exact simulation and leads beyond classical finance theory. Its parameters are estimated via a novel martingale inference method, which employs higher-strong order, implicit approximations of the increments of the system of stochastic differential equations.
submitted by Jean Downes (downes@math.tu-berlin.de)