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The class of Affine (Jump) Diffusion (AD) has, due to its closed formcharacteristic function (ChF), gained tremendous popularity among practitionersand researchers. However, there is clear evidence that a linearity constraintis insufficient for precise and consistent option pricing. Any non-affine modelmust pass the strict requirement of quick calibration -- which is oftenchallenging. We focus here on Randomized AD (RAnD) models, i.e., we allow forexogenous stochasticity of the model parameters. Randomization of a pricingmodel occurs outside the affine model and, therefore, forms a generalizationthat relaxes the affinity constraints. The method is generic and can apply toany model parameter. It relies on the existence of moments of the so-calledrandomizer- a random variable for the stochastic parameter. The RAnD modelallows flexibility while benefiting from fast calibration and well-established,large-step Monte Carlo simulation, often available for AD processes. Thearticle will discuss theoretical and practical aspects of the RAnD method, likederivations of the corresponding ChF, simulation, and computations ofsensitivities. We will also illustrate the advantages of the randomizedstochastic volatility models in the consistent pricing of options on the S&P500 and VIX.

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