We price American options using kernel-based approximations of the Volterra Heston model. We choose these approximations because they allow simulation-based techniques for pricing. We prove the convergence of American option prices in the approximating sequence of models towards the prices in the Volterra Heston model. A crucial step in the proof is to exploit the affine structure of the model in order to establish explicit formulas and convergence results for the conditional Fourier--Laplace transform of the log price and an adjusted version of the forward variance. We illustrate with numerical examples our convergence result and the behavior of American option prices with respect to certain parameters of the model.


  1. American options
  2. Volterra Heston model
  3. rough volatility
  4. Riccati--Volterra equations
  5. forward variance
  6. Fourier--Laplace transform

MSC codes

  1. 6060F
  2. 6060G
  3. 9191G

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Information & Authors


Published In

cover image SIAM Journal on Financial Mathematics
SIAM Journal on Financial Mathematics
Pages: 426 - 458
ISSN (online): 1945-497X


Submitted: 22 March 2021
Accepted: 28 January 2022
Published online: 27 April 2022


  1. American options
  2. Volterra Heston model
  3. rough volatility
  4. Riccati--Volterra equations
  5. forward variance
  6. Fourier--Laplace transform

MSC codes

  1. 6060F
  2. 6060G
  3. 9191G



Funding Information

Europlace Institute of Finance
Labex Louis Bachelier
Ecole Polytechnique
Fondation Mathématique Jacques Hadamard https://doi.org/10.13039/501100007493

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