On randomization of affine diffusion processes with application to pricing of options on VIX and S&P 500

The class of Affine (Jump) Diffusion [8] (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-a...

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Vydáno v:Applied mathematics and computation Ročník 508; s. 129598
Hlavní autor: Grzelak, Lech A.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Inc 01.01.2026
Témata:
Bates
Heston
Quantization
RAnD method
Randomized affine-diffusion
S&P 500
Short maturity options
Stochastic collocation
Stochastic parameters
VIX
Stochastic collocation
VIX
S&P 500
Short maturity options
RAnD method
Quantization
Stochastic parameters
Bates
Randomized affine-diffusion
Heston
ISSN:0096-3003
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Shrnutí:The class of Affine (Jump) Diffusion [8] (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. •Introduces a flexible framework for randomizing affine diffusion models.•Demonstrates efficient pricing of options on VIX and S&P 500.•Captures complex implied volatility surfaces with improved fit.•Generalizes Heston and Bates models through distributional extensions.•Supports rapid calibration with strong numerical stability.
ISSN:0096-3003
DOI:10.1016/j.amc.2025.129598