On general semi-closed-form solutions for VIX derivative pricing

Most pricing methods for VIX futures and European VIX options rely on the existence of the squared VIX moment generating function. Yet this function does not exist for some state-of-the-art option pricing models, which prevents their widespread use. This letter presents a semi-closed-form solution for European VIX option prices based on the squared VIX characteristic function. When coupled with a new, alternative VIX futures pricing formula, the VIX option pricing method requires only the evaluation of a single integral, making its implementation very efficient. These pricing formulas are applicable to a wide class of models—virtually all exponentially affine models in the literature, among others—as the characteristic function always exists. We also test our newly proposed pricing methodologies against usual benchmarks in the literature and report that they lead to more efficient and accurate prices.