Cornelis W. Oosterlee

Reports and Publications, sorted

PDEs Discretization

  • `An ENO-based Method for Second-Order Equations and Application to the Control of Dike Levels.' (with S.P. van der Pijl).

    Computational Finance

    The SABR Model (with Bin Chen)

  • `Efficient unbiased simulation scheme for the SABR stochastic volatility model.' (with B. Chen, J.A.M van der Weide).
  • `Analytic approximation to constant maturity swap convexity correction in a multi-factor SABR model.' (with B. Chen, S. van Weeren) to appear Int. J. Theoret. Applied Finance.

    Hybrid Financial Derivatives (with Lech Grzelak)

  • `On cross-currency models with stochastic volatility and correlated interest rates.' (with L. Grzelak) submitted 2010.
  • `An equity-interest rate hybrid model with stochastic volatility and the interest rate smile.' (with L. Grzelak) submitted 2010.
  • `On the Heston model with stochastic interest rates.' (with L. Grzelak) submitted 2009.
  • `Extension of stochastic volatility models with Hull-White interest rate process.' (with L.A. Grzelak and S. van Weeren) Quant. Finance, to appear 2010/2011.

    Risk Management; Saddlepoint Approximation (with Xinzheng Huang)

  • `Saddlepoint approximations for expectations.' (with X. Huang) submitted.
  • `Generalized Beta regression models for random Loss-Given-Default.' (with X. Huang) submitted.
  • `Nonnegative matrix factorization of a correlation matrix.' (with P. Sonneveld, J.J.I.M. van Kan and X. Huang) Linear Algebra and Its Applications 431: 334-349 (2009).
  • `Adaptive integration for multi-factor portfolio credit loss models.' (with X. Huang), J. Comp. Appl. Math. 231: 506-516 (2009).
  • `Computation of VaR and VaR contribution in the Vasicek portfolio credit loss model.' (with X. Huang, M.A.M. Mesters) J. of Credit Risk 3(3): 75 -96 (2007).
  • `Higher order saddlepoint approximations in the Vasicek portfolio credit loss model.' (with X. Huang, J.A.M. van der Weide) J. Comp. Finance 11(1): 93 - 113 (2007).

    Fourier Option Pricing Methods (with Fang Fang, Bowen Zhang)

  • `Pricing options under stochastic volatility with Fourier cosine expansions.' (with F. Fang) submitted 2010.
  • `Acceleration of option pricing technique on Graphics Processing Units.' (with B. Zhang).
  • `An Efficient Pricing Algorithm for Swing Options Based on Fourier Cosine Expansions.' (with B. Zhang).
  • `Fast valuation and calibration of credit default swaps under Le'vy dynamics.' (with F. Fang, H. J"onsson, W. Schoutens) Journ. Comp. Finance, to appear 2010.
  • `Pricing early-exercise and discrete barrier options by Fourier-cosine series expansions.' (with F. Fang) Numerische Mathematik 114: 27-62 (2009).
  • `A novel pricing method for European options based on Fourier-cosine series expansions.' (with F. Fang) SIAM J. Sci. Comput. 31: 826-848 (2008).
  • `Multi-asset option pricing using a parallel Fourier-based technique.' (with C.C.W. Leentvaar) J. Comp. Finance 12(1): 1-26 (2008).
  • `A Fast and Accurate FFT-Based Method for Pricing Early-Exercise Options under L'evy Processes.' (with R. Lord, F. Fang, F. Bervoets) SIAM J. Sci. Comput. 30: 1678-1705 (2008).

    PDE Option Pricing Methods (with Coen Leentvaar, Ariel Almendral)

  • `On coordinate transformation and grid stretching for sparse grid pricing of basket options.' (with C.C.W. Leentvaar) J. Comp. Appl. Math. 222: 193-209 (2008).
  • `Accurate American option pricing by grid stretching and high order finite differences.' (with C.C.W. Leentvaar, X.Huang) unpublished.
  • `Accurate Evaluation of European and American Options Under the CGMY Process'. (with A. Almendral), SIAM J. Sci Comput. 29: 93-117 (2007).
  • `On American options under the Variance Gamma process'. (with A. Almendral). Applied Math. Finance 14(2): 131-152 (2007).
  • `Highly Accurate Evaluation of European and American Options Under the Variance Gamma Process.' (with A. Almendral) J. Comp. Finance 10 (1), 21-42 (2006).
  • `Numerical valuation of options with jumps in the underlying.' Applied Num. Math. 53, 1-18 (2005).
  • `TVD, WENO and blended BDF discretizations for Asian options.'(with J.C. Frisch and F.J. Gaspar) Comp. Vis. Science, 6, 131-138 (2004).
  • `On multigrid for linear complementarity problems with application to American-style options.' Electr. Trans. on Num. Anal., 15, 165-185 (2003).

    Multigrid Development

    Poro-Elasticity Equations (with Francisco Gaspar et al.)

  • `Distributive Smoothers in Multigrid for Problems with Dominating Grad-Div Operators.' (with F.J. Gaspar, J.L. Gracia, F.J. Lisbona, P.N. Vabishchevich). Num. Lin. Algebra Appl. 15: 661-683 (2008).
  • `An Efficient Multigrid Solver for a Reformulated Version of the Poroelasticity System.' (with F.J. Gaspar, F.J. Lisbona, P.N. Vabishchevich). Computer Meth. Applied Mech. Engineering, 196: 1447-1457 (2007).
  • `An efficient multigrid solver based on distributive smoothing for poroelasticity equations.' (with R. Wienands, F.J. Gaspar, F.J. Lisbona)
    Computing 73, 99-119 (2004).
  • `A systematic comparison of coupled and distributive smoothing in multigrid for the poroelasticity system.' (with F.J. Gaspar, F.J. Lisbona, R. Wienands), Num. Lin. Algebra Appl. 11, 93-113 (2004).

    Helmholtz Equation (with Yogi Erlangga et al.)

  • `A multigrid-based shifted-Laplacian preconditioner for a fourth order Helmholtz discretization.' (with N. Umetani, S.P. MacLachlan), Num. Lin. Algebra Appl. 16: 603-626 (2009).
  • `A Novel Multigrid Based Preconditioner For Heterogeneous Helmholtz Problems.' (with Y.A. Erlangga, C. Vuik), SIAM J. Sci. Comput. 27: 1471-1492 (2006).
  • `Comparison of multigrid and incomplete LU shifted-Laplace preconditioners for the inhomogeneous Helmholtz equation.' (with Y.A. Erlangga, C. Vuik), Applied Num. Math. 56: 648-666 (2006).
  • `On a class of preconditioners for solving the Helmholtz equation.' (with Y.A. Erlangga, C. Vuik), Applied Num. Math. 50, 409-425 (2004).

    Local Fourier Analysis for Multigrid (with Roman, Scott, Francisco, Carmen, Irad)

  • `Accuracy measures and Fourier analysis for the full multigrid algorithm.' (with C. Rodrigo, F.J. Gaspar and I. Yavneh), to appear in SIAM J. Scient. Comp.
  • `Local Fourier analysis for multigrid with overlapping smoothers applied to systems of PDEs.' (with S.P. MacLachlan), to appear in Num. Lin. Algebra Applications.
  • `A genetic search for optimal multigrid components within a Fourier analysis setting.' (with R. Wienands), SIAM J. Scient. Comp. 24, 924-944 (2002).
  • `On three-grid Fourier analysis for multigrid' (with R. Wienands), SIAM J. Scient. Comp. 23, 651-671 (2001).
  • `Fourier analysis of GMRES(m) preconditioned by multigrid.' (with R. Wienands, T. Washio) SIAM J. Scient. Comp. 22, 582-603 (2000).

    Multigrid Algorithm Development (with Hisham, Scott, Takumi, Francisco)

  • `Algebraic multigrid solvers for complex-valued matrices' (with S.P. MacLachlan), SIAM J. Sci. Comput. 30: 1548-1571 (2008).
  • `Efficient D-Multigrid preconditioners for sparse-grid solution of high dimensional partial differential equations on non-equidistant grid' (with H. bin Zubair), Int. J. Comp. Math., 8: 1129-1147 (2007).
  • `Multigrid for high dimensional elliptic partial differential equations on non-equidistant grid' (with H. bin Zubair, R. Wienands), SIAM J. Sci. Comput. 29: 1613-1636 (2007).
  • `Geometric multigrid with applications to computational fluid dynamics.' (with P. Wesseling) J. Comp. Appl. Math. 128, 311-334 (2001).
  • `Error analysis for a potential problem on locally refined grids.' (with T. Washio), Numer. Math. 86, 539-563 (2000).
  • `Krylov subspace acceleration of nonlinear multigrid with application to recirculating flows.' (with T. Washio), SIAM J. Scient. Comp. 21, 1670-1690 (2000).
  • `Flexible multiple semicoarsening for three dimensional singularly perturbed problems.' (with T. Washio), SIAM J. Scient. Comp. 19, 1646-1666 (1998).
  • `Multigrid line smoothers for higher order upwind discretizations of convection-dominated problems.' (with F.J. Gaspar, T. Washio and R. Wienands) J. Comp. Physics 139, 274-307 (1998).
  • `An evaluation of parallel multigrid as a solver and as a preconditioner for singularly perturbed problems.'(with T. Washio) SIAM J. Scient. Comp. 19, 87-110 (1998).
  • `Krylov subspace acceleration for nonlinear multigrid schemes.' (with T. Washio) Electr. Trans. on Num. Analysis, 6, 271-290 (1997).
  • `A GMRES-based plane smoother in multigrid to solve 3D anisotropic fluid flow problems.' J. Comp. Physics 130, 41-53 (1997).