Characteristic function-based factor modelling of affine jump diffusions

We develop a framework to analyse affine jump diffusions using factor modelling techniques, offering a novel method to study which and how many risk factors drive the price process of a single asset. We use information contained in options to construct observations on the characteristic function of the underlying price process without having to specify a parametric model. We form a linear factor model out of these observations, and extract the factors using principal component analysis. We propose a criterion for the number of risk factors based on the eigenvalues of the sample covariance matrix of the constructed factor model. We analyse the finite-sample performance in a Monte Carlo study. An empirical application suggests that the main factors underlying S&P 500 index options are the index price and a process related to the volatility, which jointly explain well over 90% of the variation regardless of the choice of tuning parameters. Comparing the results when using options with a variety of maturities to the results when using only monthly options, we find evidence for an additional factor, necessary to explain the term-structure in option prices. This could be explained by a two-factor volatility model, but also by the presence of jumps.