BFS 2002

Contributed Talk

This paper first investigates the dynamics of implied probability density functions (PDFs) and the dynamics of implied cumulative distribution functions (CDFs). Subsequently, it presents new algorithms for simulating their evolution through time. Understanding the dynamics of implied distributions is essential for effective risk management, for ''smile-consistent'' arbitrage pricing with stochastic volatility, and for economic policy decisions. We investigate the number and shape of shocks that drive implied PDFs and CDFs by applying Principal Components Analysis (PCA). Performing PCA on CDFs provides us with easier to interpret results. Under a variety of criteria, two components are identified. The first component affects the location of the implied distribution while the second affects its variance and kurtosis.
The proposed algorithms are arbitrage-free and they can be implemented easily. The only inputs that they require are the known initial implied PDF and the PCA output.