A New Approach to Modeling the Dynamics of Implied Distributions : Theory and Evidence from the S&P 500 Options

This paper presents a new approach to modeling the dynamics of implied distributions. First, we obtain a parsimonious description of the dynamics of the Samp;P 500 implied cumulative distribution functions (CDFs) by applying Principal Components Analysis. Subsequently, we develop new arbitrage-free Monte-Carlo simulation methods that model the evolution of the whole distribution through time as a diffusion process. Our approach generalizes the conventional approaches of modeling only the first two moments as diffusion processes, and it has important implications for smile-consistent option pricing and for risk management. The out-of-sample performance within a Value-at-Risk framework is examined