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Weak Approximation of Stochastic Differential Equations and Application to Derivative Pricing

Citations

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Cited by:

  1. Ahdida, Abdelkoddousse & Alfonsi, Aurélien, 2013. "A mean-reverting SDE on correlation matrices," Stochastic Processes and their Applications, Elsevier, vol. 123(4), pages 1472-1520.
  2. Masahiro Nishiba, 2013. "Pricing Exotic Options and American Options: A Multidimensional Asymptotic Expansion Approach," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 20(2), pages 147-182, May.
  3. Ofelia Bonesini & Emilio Ferrucci & Ioannis Gasteratos & Antoine Jacquier, 2024. "Rough differential equations for volatility," Papers 2412.21192, arXiv.org.
  4. Christian Bayer & Peter K. Friz & Paul Gassiat & Jorg Martin & Benjamin Stemper, 2020. "A regularity structure for rough volatility," Mathematical Finance, Wiley Blackwell, vol. 30(3), pages 782-832, July.
  5. Christian Bayer & Peter Friz & Ronnie Loeffen, 2010. "Semi-Closed Form Cubature and Applications to Financial Diffusion Models," Papers 1009.4818, arXiv.org.
  6. Denis Belomestny & Tigran Nagapetyan, 2014. "Multilevel path simulation for weak approximation schemes," Papers 1406.2581, arXiv.org, revised Oct 2014.
  7. Syoiti Ninomiya & Yuming Ma, 2025. "A new architecture of high-order deep neural networks that learn martingales," Papers 2505.03789, arXiv.org, revised Jun 2025.
  8. Christian Bayer & Peter K. Friz, 2013. "Cubature on Wiener space: pathwise convergence," Papers 1304.4623, arXiv.org.
  9. Rey, Clément, 2019. "Approximation of Markov semigroups in total variation distance under an irregular setting: An application to the CIR process," Stochastic Processes and their Applications, Elsevier, vol. 129(2), pages 539-571.
  10. Christian Bayer & Peter K. Friz & Paul Gassiat & Joerg Martin & Benjamin Stemper, 2017. "A regularity structure for rough volatility," Papers 1710.07481, arXiv.org.
  11. Riu Naito & Toshihiro Yamada, 2024. "Deep high-order splitting method for semilinear degenerate PDEs and application to high-dimensional nonlinear pricing models," Digital Finance, Springer, vol. 6(4), pages 693-725, December.
  12. Syoiti Ninomiya & Yuji Shinozaki, 2025. "A high-order recombination algorithm for weak approximation of stochastic differential equations," Papers 2504.19717, arXiv.org, revised May 2025.
  13. Jürgen Geiser, 2020. "Iterative and Noniterative Splitting Methods of the Stochastic Burgers’ Equation: Theory and Application," Mathematics, MDPI, vol. 8(8), pages 1-28, July.
  14. Kenichiro Shiraya & Akihiko Takahashi & Masashi Toda, 2009. "Pricing Barrier and Average Options under Stochastic Volatility Environment," CIRJE F-Series CIRJE-F-682, CIRJE, Faculty of Economics, University of Tokyo.
  15. Kenichiro Shiraya & Akihiko Takahashi & Masashi Toda, 2010. "Pricing Barrier and Average Options under Stochastic Volatility Environment," CIRJE F-Series CIRJE-F-745, CIRJE, Faculty of Economics, University of Tokyo.
  16. Mariko Ninomiya, 2011. "Sde Weak Approximation Library (Sde Wa) (Version 1.0)," CARF F-Series CARF-F-274, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
  17. Aur'elien Alfonsi & Edoardo Lombardo, 2022. "High order approximations of the Cox-Ingersoll-Ross process semigroup using random grids," Papers 2209.13334, arXiv.org, revised Apr 2023.
  18. Kazuhiro Yoshikawa, 2015. "An Approximation Scheme for Diffusion Processes Based on an Antisymmetric Calculus over Wiener Space," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 22(2), pages 185-207, May.
  19. Susana Alvarez Diez & Samuel Baixauli & Luis Eduardo Girón, 2019. "Valoración de Opciones Call Asiáticas Promedio Aritmético bajo Movimiento Browniano Logístico," Working Papers 46, Faculty of Economics and Management, Pontificia Universidad Javeriana Cali.
  20. Shigeto Kusuoka & Mariko Ninomiya & Syoiti Ninomiya, 2012. "Application Of The Kusuoka Approximation To Barrier Options," CARF F-Series CARF-F-277, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
  21. Philipp Doersek & Eskil Hansen, 2012. "High order splitting schemes with complex timesteps and their application in mathematical finance," Papers 1210.5392, arXiv.org.
  22. Aur'elien Alfonsi & Edoardo Lombardo, 2024. "High order approximations and simulation schemes for the log-Heston process," Papers 2407.17151, arXiv.org, revised Dec 2024.
  23. Anis Al Gerbi & Benjamin Jourdain & Emmanuelle Cl'ement, 2015. "Ninomiya-Victoir scheme: strong convergence, antithetic version and application to multilevel estimators," Papers 1508.06492, arXiv.org, revised Oct 2015.
  24. Yusuke Morimoto & Makiko Sasada, 2015. "Algebraic Structure of Vector Fields in Financial Diffusion Models and its Applications," Papers 1510.02013, arXiv.org, revised Dec 2015.
  25. Akiyama, Naho & Yamada, Toshihiro, 2024. "A weak approximation for Bismut’s formula: An algorithmic differentiation method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 216(C), pages 386-396.
  26. Mariko Ninomiya & Syoiti Ninomiya, 2009. "A new higher-order weak approximation scheme for stochastic differential equations and the Runge–Kutta method," Finance and Stochastics, Springer, vol. 13(3), pages 415-443, September.
  27. Jean-Franc{c}ois Chassagneux & Junchao Chen & Noufel Frikha, 2022. "Deep Runge-Kutta schemes for BSDEs," Papers 2212.14372, arXiv.org.
  28. Abdelkoddousse Ahdida & Aur'elien Alfonsi, 2011. "A Mean-Reverting SDE on Correlation matrices," Papers 1108.5264, arXiv.org, revised Feb 2012.
  29. Riu Naito & Toshihiro Yamada, 2024. "Deep Kusuoka Approximation: High-Order Spatial Approximation for Solving High-Dimensional Kolmogorov Equations and Its Application to Finance," Computational Economics, Springer;Society for Computational Economics, vol. 64(3), pages 1443-1461, September.
  30. Arturo Kohatsu-Higa & Salvador Ortiz-Latorre & Peter Tankov, 2012. "Optimal simulation schemes for L\'evy driven stochastic differential equations," Papers 1204.4877, arXiv.org.
  31. Susana Alvarez Diez & Samuel Baixauli & Luis Eduardo Girón, 2019. "Valoración de opciones call asiáticas Promedio Aritmético usando Taylor Estocástico 1.5," Working Papers 44, Faculty of Economics and Management, Pontificia Universidad Javeriana Cali.
  32. Lenkšas, A. & Mackevičius, V., 2015. "Weak approximation of Heston model by discrete random variables," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 113(C), pages 1-15.
  33. Benjamin Jourdain & Mohamed Sbai, 2013. "High order discretization schemes for stochastic volatility models," Post-Print hal-00409861, HAL.
  34. Mackevičius, Vigirdas, 2010. "On weak approximations of CIR equation with high volatility," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(5), pages 959-970.
  35. Hocquet, Antoine & Vogler, Alexander, 2023. "An application of the multiplicative Sewing Lemma to the high order weak approximation of stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 165(C), pages 183-217.
  36. Goodell, John W. & Kumar, Satish & Lim, Weng Marc & Pattnaik, Debidutta, 2021. "Artificial intelligence and machine learning in finance: Identifying foundations, themes, and research clusters from bibliometric analysis," Journal of Behavioral and Experimental Finance, Elsevier, vol. 32(C).
  37. Aur'elien Alfonsi & Ahmed Kebaier, 2021. "Approximation of Stochastic Volterra Equations with kernels of completely monotone type," Papers 2102.13505, arXiv.org, revised Mar 2022.
  38. Al Gerbi, A. & Jourdain, B. & Clément, E., 2018. "Asymptotics for the normalized error of the Ninomiya–Victoir scheme," Stochastic Processes and their Applications, Elsevier, vol. 128(6), pages 1889-1928.
  39. Al Gerbi Anis & Jourdain Benjamin & Clément Emmanuelle, 2016. "Ninomiya–Victoir scheme: Strong convergence, antithetic version and application to multilevel estimators," Monte Carlo Methods and Applications, De Gruyter, vol. 22(3), pages 197-228, September.
  40. Rey Clément, 2017. "Convergence in total variation distance of a third order scheme for one-dimensional diffusion processes," Monte Carlo Methods and Applications, De Gruyter, vol. 23(1), pages 1-12, March.
  41. Abdelkoddousse Ahdida & Aur'elien Alfonsi, 2010. "Exact and high order discretization schemes for Wishart processes and their affine extensions," Papers 1006.2281, arXiv.org, revised Mar 2013.
  42. Abdelkoddousse Ahdida & Aurélien Alfonsi, 2013. "A Mean-Reverting SDE on Correlation matrices," Post-Print hal-00617111, HAL.
  43. Aur'elien Alfonsi, 2023. "Nonnegativity preserving convolution kernels. Application to Stochastic Volterra Equations in closed convex domains and their approximation," Papers 2302.07758, arXiv.org, revised Oct 2024.
  44. Dupret, Jean-Loup & Barbarin, Jérôme & Hainaut, Donatien, 2021. "Impact of rough stochastic volatility models on long-term life insurance pricing," LIDAM Discussion Papers ISBA 2021017, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
  45. Abdelkoddousse Ahdida & Aurélien Alfonsi, 2013. "Exact and high order discretization schemes for Wishart processes and their affine extensions," Post-Print hal-00491371, HAL.
  46. Alfonsi, Aurélien, 2025. "Nonnegativity preserving convolution kernels. Application to Stochastic Volterra Equations in closed convex domains and their approximation," Stochastic Processes and their Applications, Elsevier, vol. 181(C).
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