On Randomization of Affine Diffusion Processes with Application to Pricing of Options on VIX and S&P 500

TL;DR

This paper introduces Randomized Affine Diffusion models that incorporate exogenous stochasticity into parameters, enhancing flexibility and calibration speed for pricing options on VIX and S&P 500, while maintaining computational efficiency.

Contribution

It proposes a novel RAnD framework that generalizes affine diffusion models by randomizing parameters, enabling better fit to market data and efficient option pricing.

Findings

RAnD models improve calibration speed and accuracy.

The method maintains analytical tractability for characteristic functions.

Application to S&P 500 and VIX options demonstrates practical advantages.

Abstract

The class of Affine (Jump) Diffusion (AD) has, due to its closed form characteristic function (ChF), gained tremendous popularity among practitioners and researchers. However, there is clear evidence that a linearity constraint is insufficient for precise and consistent option pricing. Any non-affine model must pass the strict requirement of quick calibration -- which is often challenging. We focus here on Randomized AD (RAnD) models, i.e., we allow for exogenous stochasticity of the model parameters. Randomization of a pricing model occurs outside the affine model and, therefore, forms a generalization that relaxes the affinity constraints. The method is generic and can apply to any model parameter. It relies on the existence of moments of the so-called randomizer- a random variable for the stochastic parameter. The RAnD model allows flexibility while benefiting from fast calibration and well-established, large-step Monte Carlo simulation, often available for AD processes. The article will discuss theoretical and practical aspects of the RAnD method, like derivations of the corresponding ChF, simulation, and computations of sensitivities. We will also illustrate the advantages of the randomized stochastic volatility models in the consistent pricing of options on the S&P 500 and VIX.