Publications

Book

Karel in 't Hout: Numerical Partial Differential Equations in Finance Explained. Palgrave Macmillan (2017).

This book provides a first, basic introduction into the valuation of financial options via the numerical solution of partial differential equations (PDEs). It provides readers with an easily accessible text explaining main concepts, models, methods and results that arise in this approach. In keeping with the series style, emphasis is placed on intuition as opposed to full rigor, and a relatively basic understanding of mathematics is sufficient. The book provides a wealth of examples, and ample numerical experiments are given to illustrate the theory. The main focus is on one-dimensional financial PDEs, notably the Black-Scholes equation. The book concludes with a detailed discussion of the important step towards two-dimensional PDEs in finance.

Articles

K.J. in 't Hout: An efficient numerical method for American options and their Greeks under the two-asset Kou jump-diffusion model. Submitted for publication (2024).

K.J. in 't Hout: A note on the numerical approximation of Greeks for American-style options. Math. Comp. Simul. (2024).

K.J. in 't Hout and P. Lamotte: Efficient numerical valuation of European options under the two-asset Kou jump-diffusion model. J. Comp. Finan. 26, 101–137 (2023).

K.J. in 't Hout and J. Snoeijer: Numerical valuation of American basket options via partial differential complementarity problems. Mathematics 9(13), 1498 (2021).

K.J. in 't Hout and J. Snoeijer: Numerical valuation of Bermudan basket options via partial differential equations. Int. J. Comp. Math. 98, 829–844 (2021).

L. Boen and K.J. in 't Hout: Operator splitting schemes for the two-asset Merton jump-diffusion model. J. Comp. Appl. Math. 387, 112309 (2021).

L. Boen and K.J. in 't Hout: Operator splitting schemes for American options under the two-asset Merton jump-diffusion model. Appl. Numer. Math. 153, 114–131 (2020).

L. von Sydow, S. Milovanović, E. Larsson, K.J. in 't Hout, M. Wiktorsson, C.W. Oosterlee, V. Shcherbakov, M. Wyns, A. Leitao, S. Jain, T. Haentjens, J. Waldén: BENCHOP – SLV: the BENCHmarking project in Option Pricing – Stochastic and Local Volatility problems. Int. J. Comp. Math. 96, 1910–1923 (2019).

K.J. in 't Hout and J. Toivanen: ADI schemes for valuing European options under the Bates model. Appl. Numer. Math. 130, 143–156 (2018).

W. Hundsdorfer and K.J. in 't Hout: On multistep stabilizing correction splitting methods with applications to the Heston model. SIAM J. Sci. Comp. 40, A1408–A1429 (2018).

M. Wyns and K.J. in 't Hout: An adjoint method for the exact calibration of stochastic local volatility models. J. Comp. Sci. 24, 182–194 (2018).

K.J. in 't Hout and R.L. Valkov: Numerical study of splitting methods for American option valuation. In: "Novel Methods in Computational Finance", eds. M. Ehrhardt, M. Günther, E.J.W. ter Maten, Springer, 373–398 (2017).

A. Arrarás, K.J. in 't Hout, W. Hundsdorfer and L. Portero: Modified Douglas splitting methods for reaction-diffusion equations. BIT 57, 261–285 (2017).

K.J. in 't Hout and M. Wyns: Convergence of the Modified Craig-Sneyd scheme for two-dimensional convection-diffusion equations with mixed derivative term. J. Comp. Appl. Math. 296, 170–180 (2016).

A. Cuyt, O. Salazar Celis, M. Lukach and K.J. in 't Hout: Analytic models for parameter dependency in option price modelling. Numer. Algor. 73, 15–31 (2016).

Karel in 't Hout and Jari Toivanen: Application of operator splitting methods in finance. In: "Splitting Methods in Communication, Imaging, Science, and Engineering", eds. R. Glowinski, S. J. Osher and W. Yin, Springer, 541–575 (2016).

T. Haentjens and K.J. in 't Hout: ADI schemes for pricing American options under the Heston model. Appl. Math. Finan. 22, 207–237 (2015).

Karel in 't Hout and Maarten Wyns: Convergence of the Hundsdorfer-Verwer scheme for two-dimensional convection-diffusion equations with mixed derivative term. AIP Conf. Proc. 1648, 850054 (2015).

Karel in 't Hout and Radoslav Valkov: Numerical solution of a two-asset option valuation PDE by ADI finite difference discretization. AIP Conf. Proc. 1648, 020007 (2015).

K.J. in 't Hout and K. Volders: Stability and convergence analysis of discretizations of the Black-Scholes PDE with the linear boundary condition. IMA J. Numer. Anal. 34, 296–325 (2014).

K.J. in 't Hout and C. Mishra: Stability of ADI schemes for multidimensional diffusion equations with mixed derivative terms. Appl. Numer. Math. 74, 83–94 (2013).

T. Haentjens and K.J. in 't Hout: Alternating direction implicit finite difference schemes for the Heston-Hull-White partial differential equation. J. Comp. Finan. 16, 83–110 (2012).

K.J. in 't Hout and K. Volders: Stability of central finite difference schemes for the Heston PDE. Numer. Algor. 60, 115–133 (2012).

K.J. in 't Hout and C. Mishra: Stability of the modified Craig-Sneyd scheme for two-dimensional convection-diffusion equations with mixed derivative term. Math. Comp. Simul. 81, 2540–2548 (2011).

K.J. in 't Hout and J.A.C. Weideman: A contour integral method for the Black-Scholes and Heston equations. SIAM J. Sci. Comp. 33, 763–785 (2011).

Tinne Haentjens, Karel in 't Hout and Kim Volders: ADI schemes with Ikonen-Toivanen splitting for pricing American put options in the Heston model. In: Numerical Analysis and Applied Mathematics, eds. T. E. Simos et. al., AIP Conf. Proc. 1281, 231–234 (2010).

Tinne Haentjens and Karel in 't Hout: ADI finite difference discretization of the Heston-Hull-White PDE. In: Numerical Analysis and Applied Mathematics, eds. T. E. Simos et. al., AIP Conf. Proc. 1281, 1995–1999 (2010).

Karel in 't Hout and Chittaranjan Mishra: A stability result for the Modified Craig-Sneyd scheme applied to 2D and 3D pure diffusion equations. In: Numerical Analysis and Applied Mathematics, eds. T. E. Simos et. al., AIP Conf. Proc. 1281, 2029–2032 (2010).

K.J. in 't Hout and S. Foulon: ADI finite difference schemes for option pricing in the Heston model with correlation. Int. J. Numer. Anal. Mod. 7, 303–320 (2010).

K.J. in 't Hout and K. Volders: Stability of central finite difference schemes on non-uniform grids for the Black-Scholes equation. Appl. Numer. Math. 59, 2593–2609 (2009).

K.J. in 't Hout and B.D. Welfert: Unconditional stability of second-order ADI schemes applied to multi-dimensional diffusion equations with mixed derivative terms. Appl. Numer. Math. 59, 677–692 (2009).

Karel in 't Hout, Joris Bierkens, Antoine P.C. van der Ploeg, Jos in 't panhuis: A semi closed-form analytic pricing formula for call options in a hybrid Heston-Hull-White model. Proceedings of the 58th European Study Group Mathematics with Industry, eds. R.H. Bisseling et. al., Utrecht (2007).

Karel in 't Hout: ADI schemes in the numerical solution of the Heston PDE. In: Numerical Analysis and Applied Mathematics, eds. T. E. Simos et. al., AIP Conf. Proc. 936, 10–14 (2007).

K.J. in 't Hout and B.D. Welfert: Stability of ADI schemes applied to convection-diffusion equations with mixed derivative terms. Appl. Numer. Math. 57, 19–35 (2007).

K.J. in 't Hout and B. Zubik-Kowal: The stability of Radau IIA collocation processes for delay differential equations. Math. Comp. Mod. 40, 1297–1308 (2004).

K.J. in 't Hout and M.N. Spijker: Analysis of error growth via stability regions in numerical initial value problems. BIT 43, 363–385 (2003).

K.J. in 't Hout: On the contractivity of implicit-explicit linear multistep methods. Appl. Numer. Math. 42, 201–212 (2002).

K.J. in 't Hout: Convergence of Runge-Kutta methods for delay differential equations. BIT 41, 322–344 (2001).

K. Engelborghs, T. Luzyanina, K.J. in 't Hout and D. Roose: Collocation methods for the computation of periodic solutions of delay differential equations. SIAM J. Sci. Comp. 22, 1593–1609 (2000).

K.J. in 't Hout and Ch. Lubich: Periodic orbits of delay differential equations under discretization. BIT 38, 72–91 (1998).

K.J. in 't Hout: Stability analysis of Runge-Kutta methods for systems of delay differential equations. IMA J. Numer. Anal. 17, 17–27 (1997).

K.J. in 't Hout: On the stability of adaptations of Runge-Kutta methods to systems of delay differential equations. Appl. Numer. Math. 22, 237–250 (1996).

K.J. in 't Hout: A note on unconditional maximum norm contractivity of diagonally split Runge-Kutta methods. SIAM J. Numer. Anal. 33, 1125–1134 (1996).

K.J. in 't Hout: On the convergence of waveform relaxation methods for stiff nonlinear ordinary differential equations. Appl. Numer. Math. 18, 175–190 (1995).

K.J. in 't Hout: The stability of θ-methods for systems of delay differential equations. Ann. Numer. Math. 1, 323–334 (1994).

K.J. in 't Hout: A new interpolation procedure for adapting Runge-Kutta methods to delay differential equations. BIT 32, 634–649 (1992).

K.J. in 't Hout: The stability of a class of Runge-Kutta methods for delay differential equations. Appl. Numer. Math. 9, 347–355 (1992).

K.J. in 't Hout and M.N. Spijker: Stability analysis of numerical methods for delay differential equations. Numer. Math. 59, 807–814 (1991).

K.J. in 't Hout and M.N. Spijker: The θ-methods in the numerical solution of delay differential equations. In: "The Numerical Treatment of Differential Equations", ed. K. Strehmel, Teubner-Texte zur Mathematik 121, 61–67 (1991).

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