An Empirical Comparison of Affine and Non-Affine Models for Equity Index Options

Abstract

The existing literature on equity index option valuation largely focuses on affine models because they lead to closed-form solutions for option prices. This paper investigates the empirical shortcomings associated with affine models, using data on S&P500 call options. We find that the root mean squared dollar error for a simple non-affine continuous-time stochastic volatility model is 25-27% lower than that of the benchmark continuous-time affine stochastic volatility model in- and out-of-sample. The analytical convenience of affine option valuation models therefore comes at a price, and non-affine models ought to be investigated more extensively. We also compare the empirical performance of affine and non-affine discrete-time models. While the performance of the discrete-time non-affine model is similar to that of the continuous-time non-affine model, the discrete-time affine model outperforms the continuous-time affine model. We provide some intuition for these findings. At the methodological level, our analysis uses a novel technique based on the Auxiliary Particle Filter. This technique allows for an analysis of option valuation models using options data that imposes consistency with underlying equity returns. It is straightforward to implement and it can be used in a variety of applications and on various loss functions.