Subordinated Binomial Option Pricing with Stochastic Arrival Intensity and Untraded Underlying Asset

Abstract

We extend the subordinated binomial option pricing model with stochastic arrival intensity (Chang, Chang and Lu, 2010) to allow for untraded underlying assets by using matching futures prices to imply out the underlying asset values. We empirically apply the model to VIX option pricing vis-à-vis the original model with constant arrival intensity (Chang, Chang and Tian, 2006) using a two-year set of daily VIX options and futures data to specifically examine the efficacy of adding stochastic arrival intensity and untraded underlying assets.  We find that the extended version significantly outperforms the original model both in sample and out-of-sample in terms of the MSE, with pricing error reduction about 37% and 32%, respectively, and additionally the outperformance is robust to the selection of the constant arrival intensity level.  We attribute the outperformance to the extended model’s incorporation of the stylized effects of mean-reversion and clustering in intensity arrivals as well as of the information content conveyed by the matching futures prices.