Abstract

This paper presents a new approach to modeling the dynamics of implied distributions. First, we obtain a parsimonious description of the dynamics of the S&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 Þrst two moments as diffusion processes, and it has important implications for ”smileconsistent” option pricing and for risk management. The out-of-sample performance within a Value-at-Risk framework is examined.

Citations