Inferring Volatility in the Heston Model and its Relatives -- an Information Theoretical Approach

Abstract

Stochastic volatility models describe asset prices $S_t$ as driven by an unobserved process capturing the random dynamics of volatility ${\sigma }_t$. Here, we quantify how much information about ${\sigma }_t$ can be inferred from asset prices $S_t$ in terms of Shannon's mutual information $I(S_t:{\sigma }_t)$. This motivates a careful numerical and analytical study of information theoretic properties of the Heston model. In addition, we study a general class of discrete time models motivated from a machine learning perspective. In all cases, we find a large uncertainty in volatility estimates for quite fundamental information theoretic reasons.

26 pages, 9 figures. arXiv admin note: text overlap with arXiv:0804.2589 by other authors

References in corpus (3)

• The NumPy array: a structure for efficient numerical computation
• Estimating Mutual Information
• Multiple time scales and the exponential Ornstein-Uhlenbeck stochastic volatility model