Paper: arXiv 2302.12612

Authors: Camilla Damian, Rüdiger Frey

Abstract

In this paper, we focus on the estimation of historical volatility of asset prices from high-frequency data. Stochastic volatility models pose a major statistical challenge: since in reality historical volatility is not observable, its current level and, possibly, the parameters governing its dynamics have to be estimated from the observable time series of asset prices. To complicate matters further, recent research has analyzed the rough behavior of volatility time series to challenge the common assumption that the volatility process is a Brownian semimartingale. In order to tackle the arising inferential task efficiently in this setting, we use the fact that a fractional Brownian motion can be represented as a superposition of Markovian semimartingales (Ornstein-Uhlenbeck processes) and we solve the filtering (and parameter estimation) problem by resorting to more standard techniques, such as particle methods.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 5.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a mathematically sophisticated approach to filtering rough volatility by mapping fractional Brownian motion to a Markovian representation. While mathematically rich and novel in applying particle filtering techniques to this domain, empirical validation remains focused on high-frequency simulations and limited real-data calibration.

Research Flowchart

  flowchart TD
    A[Research Goal: Estimate Rough Volatility from High-Frequency Data] --> B[Data Input: Observable Asset Price Time Series]
    B --> C[Methodology: Represent Fractional Brownian Motion as Superposition of Markovian OU Processes]
    C --> D[Computational Process: Apply Particle Filtering Methods for State & Parameter Estimation]
    D --> E[Key Outcome: Efficient Filtering & Parameter Estimation for Rough Stochastic Volatility]