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Volumn 25, Issue 1, 2005, Pages 87-112

Robust numerical methods for contingent claims under jump diffusion processes

Author keywords

Implicit discretization; Iterative solution; Jump diffusion

Indexed keywords

COSTS; DIFFUSION; ECONOMICS; FAST FOURIER TRANSFORMS; ITERATIVE METHODS;

EID: 11444268256     PISSN: 02724979     EISSN: None     Source Type: Journal    
DOI: 10.1093/imanum/drh011     Document Type: Article
Times cited : (185)

References (43)
  • 1
    • 34848819098 scopus 로고    scopus 로고
    • The obstacle problem for nonlinear Integra-differential equations arising in option pricing
    • Istituto pre le Applicazioni del Calcolo 'M. Piconé', Rome
    • AMADORI, A. L. (2003) The obstacle problem for nonlinear Integra-differential equations arising in option pricing. Working Paper, Istituto pre le Applicazioni del Calcolo 'M. Piconé', Rome.
    • (2003) Working Paper
    • Amadori, A.L.1
  • 2
    • 84993897212 scopus 로고
    • Jump diffusion option valuation in discrete time
    • AMIN, K. I. (1993) Jump diffusion option valuation in discrete time. J. Finance, 48, 1833-1863.
    • (1993) J. Finance , vol.48 , pp. 1833-1863
    • Amin, K.I.1
  • 3
    • 0000264693 scopus 로고    scopus 로고
    • Jump-diffusion processes: Volatility smile fitting and numerical methods for option pricing
    • ANDERSEN, L. & ANDREASEN, J. (2000) Jump-diffusion processes: Volatility smile fitting and numerical methods for option pricing. Rev. Deriv. Res., 4, 231-262.
    • (2000) Rev. Deriv. Res. , vol.4 , pp. 231-262
    • Andersen, L.1    Andreasen, J.2
  • 4
    • 0002666379 scopus 로고    scopus 로고
    • The equity option volatility smile: An implicit finite difference approach
    • ANDERSEN, L. B. G. & BROTHERTON-RATCLIFFE, R. (1998) The equity option volatility smile: An implicit finite difference approach. J. Comput. Finance, 1, 3-37.
    • (1998) J. Comput. Finance , vol.1 , pp. 3-37
    • Andersen, L.B.G.1    Brotherton-Ratcliffe, R.2
  • 5
    • 0040517321 scopus 로고    scopus 로고
    • Empirical performance of alternative option pricing models
    • BAKSHI, G., CAO, C. & CHEN, Z. (1997) Empirical performance of alternative option pricing models. J. Finance, 52, 2003-2049.
    • (1997) J. Finance , vol.52 , pp. 2003-2049
    • Bakshi, G.1    Cao, C.2    Chen, Z.3
  • 6
    • 0041753938 scopus 로고    scopus 로고
    • Convergence of numerical schemes for degenerate parabolic equations arising in finance
    • (L. C. G. Rogers & D. Talay, eds). Cambridge: Cambridge University Press
    • BARLES, G. (1997) Convergence of numerical schemes for degenerate parabolic equations arising in finance. Numerical Methods in Finance (L. C. G. Rogers & D. Talay, eds). Cambridge: Cambridge University Press, pp. 1-21.
    • (1997) Numerical Methods in Finance , pp. 1-21
    • Barles, G.1
  • 7
    • 84977707224 scopus 로고
    • The crash of '87: Was it expected? the evidence from options markets
    • BATES, D. S. (1991) The crash of '87: Was it expected? The evidence from options markets. J. Finance, 46, 1009-1044.
    • (1991) J. Finance , vol.46 , pp. 1009-1044
    • Bates, D.S.1
  • 8
    • 0030534228 scopus 로고    scopus 로고
    • Jumps and stochastic volatility: Exchange rate processes implicit in Deutsche mark options
    • BATES, D. S. (1996) Jumps and stochastic volatility: Exchange rate processes implicit in Deutsche mark options. Rev. Financial Studies, 9, 69-107.
    • (1996) Rev. Financial Studies , vol.9 , pp. 69-107
    • Bates, D.S.1
  • 9
    • 0034512163 scopus 로고    scopus 로고
    • Resolvent conditions and bounds on the powers of matrices, with relevance to the numerical stability of initial value problems
    • BOROVYKH, N. & SPUKER, M. N. (2000) Resolvent conditions and bounds on the powers of matrices, with relevance to the numerical stability of initial value problems. J. Comput. Appl. Math., 125, 41-56.
    • (2000) J. Comput. Appl. Math. , vol.125 , pp. 41-56
    • Borovykh, N.1    Spuker, M.N.2
  • 10
    • 11344295984 scopus 로고    scopus 로고
    • Convergence of numerical schemes for viscosity solutions to Integra-differential degenerate parabolic problems arising in financial theory
    • to appear
    • BRIANI, M., LA CHIOMA, C. & NATALINI, R. (2003) Convergence of numerical schemes for viscosity solutions to Integra-differential degenerate parabolic problems arising in financial theory. Numer. Math., to appear.
    • (2003) Numer. Math.
    • Briani, M.1    La Chioma, C.2    Natalini, R.3
  • 11
    • 0141564564 scopus 로고    scopus 로고
    • Application of the fast Gauss transform to option pricing
    • BROADIE, M. & YAMAMOTO, Y. (2003) Application of the fast Gauss transform to option pricing. Manag. Sci., 49, 1071-1088.
    • (2003) Manag. Sci. , vol.49 , pp. 1071-1088
    • Broadie, M.1    Yamamoto, Y.2
  • 12
    • 0002478877 scopus 로고    scopus 로고
    • Reconstructing the unknown local volatility function
    • COLEMAN, T. F., Li, Y. & VERMA, A. (1999) Reconstructing the unknown local volatility function. J. Comput. Finance, 2, 77-102.
    • (1999) J. Comput. Finance , vol.2 , pp. 77-102
    • Coleman, T.F.1    Li, Y.2    Verma, A.3
  • 14
    • 11444254254 scopus 로고    scopus 로고
    • Finite difference methods for option pricing in jump-diffusion and exponential Levy models
    • École Polytechnique, Paris, France
    • CONT, R. & VOLTCHKOVA, E. (2003) Finite difference methods for option pricing in jump-diffusion and exponential Levy models. Working Paper, École Polytechnique, Paris, France.
    • (2003) Working Paper
    • Cont, R.1    Voltchkova, E.2
  • 15
    • 84967708673 scopus 로고
    • User's guide to viscosity solutions of second order partial differential equations
    • CRANDALL, M. G., ISHII, H. & LIONS, P. L. (1992) User's guide to viscosity solutions of second order partial differential equations. Bull. Am. Math. Soc., 27, 1-67.
    • (1992) Bull. Am. Math. Soc. , vol.27 , pp. 1-67
    • Crandall, M.G.1    Ishii, H.2    Lions, P.L.3
  • 16
    • 2442536011 scopus 로고    scopus 로고
    • A penalty method for American options with jump diffusion processes
    • D'HALLUIN, Y., FORSYTH, P. A. & LABAHN, G. (2004) A penalty method for American options with jump diffusion processes. Numer. Math.. 97, 321-352.
    • (2004) Numer. Math. , vol.97 , pp. 321-352
    • D'Halluin, Y.1    Forsyth, P.A.2    Labahn, G.3
  • 17
    • 4944257158 scopus 로고    scopus 로고
    • Robust numerical methods for contingent claims under jump diffusion processes
    • University of Waterloo, Canada
    • D'HALLUIN, Y., FORSYTH, P. A. & VETZAL, K. R. (2003) Robust numerical methods for contingent claims under jump diffusion processes. Working Paper, University of Waterloo, Canada.
    • (2003) Working Paper
    • D'Halluin, Y.1    Forsyth, P.A.2    Vetzal, K.R.3
  • 18
    • 0033102416 scopus 로고    scopus 로고
    • Nonuniform fast Fourier transform
    • DUIJNDAM, A. & SCHONEWILLE, M. (1999) Nonuniform fast Fourier transform. Geophysics, 64, 539-551.
    • (1999) Geophysics , vol.64 , pp. 539-551
    • Duijndam, A.1    Schonewille, M.2
  • 19
    • 0002004145 scopus 로고
    • Pricing with a smile
    • DUPIRE, B. (1994) Pricing with a smile. Risk, 7, 18-20.
    • (1994) Risk , vol.7 , pp. 18-20
    • Dupire, B.1
  • 20
    • 0142188082 scopus 로고    scopus 로고
    • The impact of jumps in volatility and returns
    • ERAKER, B., JOHANNES, M. & POLSON, N. (2003) The impact of jumps in volatility and returns. J. Finance, 58, 1269-1300.
    • (2003) J. Finance , vol.58 , pp. 1269-1300
    • Eraker, B.1    Johannes, M.2    Polson, N.3
  • 21
    • 0036447626 scopus 로고    scopus 로고
    • Quadratic convergence of a penalty method for valuing American options
    • FORSYTH, P. A. & VETZAL, K. R. (2002) Quadratic convergence of a penalty method for valuing American options. SIAM J. Sci. Comput., 23, 2096-2123.
    • (2002) SIAM J. Sci. Comput. , vol.23 , pp. 2096-2123
    • Forsyth, P.A.1    Vetzal, K.R.2
  • 22
    • 0031526503 scopus 로고    scopus 로고
    • On the stability and convergence of discretizations of initial value PDEs
    • GILES, M. B. (1997) On the stability and convergence of discretizations of initial value PDEs. IMA J. Numer. Anal., 17, 563-576.
    • (1997) IMA J. Numer. Anal , vol.17 , pp. 563-576
    • Giles, M.B.1
  • 24
    • 4944225306 scopus 로고    scopus 로고
    • Pricing American options under variance gamma
    • HIRSA, A. & MADAN, D. (2004) Pricing American options under variance gamma. J. Comput. Finance, 7, 63-80.
    • (2004) J. Comput. Finance , vol.7 , pp. 63-80
    • Hirsa, A.1    Madan, D.2
  • 26
    • 0036698288 scopus 로고    scopus 로고
    • A jump-diffusion model for option pricing
    • Kou, S. G. (2002) A jump-diffusion model for option pricing. Manag. Sci., 48, 1086-1101.
    • (2002) Manag. Sci. , vol.48 , pp. 1086-1101
    • Kou, S.G.1
  • 27
    • 0023453539 scopus 로고
    • Stepsize restrictions for stability in the numerical solution of ordinary and partial differential equations
    • KRAAIJEVANGER, J. F. B. M., LENFERINK, H. W. J. & SPIJKER, M. N. (1987) Stepsize restrictions for stability in the numerical solution of ordinary and partial differential equations. J. Comput. Appl. Math., 20, 67-81.
    • (1987) J. Comput. Appl. Math. , vol.20 , pp. 67-81
    • Kraaijevanger, J.F.B.M.1    Lenferink, H.W.J.2    Spijker, M.N.3
  • 28
    • 84966237981 scopus 로고
    • On the use of stability regions in the numerical analysis of initial value problems
    • LENFERINK, H. W. & SPIJKER, M. N. (1991) On the use of stability regions in the numerical analysis of initial value problems. Math. Comput., 57, 221-237.
    • (1991) Math. Comput. , vol.57 , pp. 221-237
    • Lenferink, H.W.1    Spijker, M.N.2
  • 30
    • 34248474317 scopus 로고
    • Option pricing when underlying stock returns are discontinuous
    • MERTON, R. C. (1976) Option pricing when underlying stock returns are discontinuous. J. Financial Econ., 3, 125-144.
    • (1976) J. Financial Econ. , vol.3 , pp. 125-144
    • Merton, R.C.1
  • 31
    • 2442598068 scopus 로고    scopus 로고
    • The numerical valuation of options with underlying jumps
    • MEYER, G. H. (1998) The numerical valuation of options with underlying jumps. Acta Math. Univ. Comenian., 67, 69-82.
    • (1998) Acta Math. Univ. Comenian. , vol.67 , pp. 69-82
    • Meyer, G.H.1
  • 32
    • 0031677847 scopus 로고    scopus 로고
    • Optimal stopping of controlled jump diffusion processes: A viscosity solution approach
    • PHAM, H. (1998) Optimal stopping of controlled jump diffusion processes: A viscosity solution approach. J. Math. Syst., Estimation Control, 8, 1-27.
    • (1998) J. Math. Syst., Estimation Control , vol.8 , pp. 1-27
    • Pham, H.1
  • 33
    • 0038150517 scopus 로고    scopus 로고
    • Numerical convergence properties of option pricing PDEs with uncertain volatility
    • POOLEY, D. M., FORSYTH, P. A. & VETZAL, K. R. (2003) Numerical convergence properties of option pricing PDEs with uncertain volatility. IMA J. Numer. Anal., 23, 241-267.
    • (2003) IMA J. Numer. Anal. , vol.23 , pp. 241-267
    • Pooley, D.M.1    Forsyth, P.A.2    Vetzal, K.R.3
  • 34
    • 11444254007 scopus 로고    scopus 로고
    • Convergence remedies for non-smooth payoffs in option pricing
    • POOLEY, D. M., VETZAL, K. R. & FORSYTH, P. A. (2003) Convergence remedies for non-smooth payoffs in option pricing. J. Comput. Finance, 6, 25-40.
    • (2003) J. Comput. Finance , vol.6 , pp. 25-40
    • Pooley, D.M.1    Vetzal, K.R.2    Forsyth, P.A.3
  • 35
    • 0011937243 scopus 로고    scopus 로고
    • Fast Fourier transforms for nonequispaced data: A tutorial
    • Chapter 12 (J. J. Benedetto & P. J. S. G. Ferreira, eds). Boston, MA: Birkhauser
    • POTTS, D., STEIDL, G. & TASCHE, M. (2001) Fast Fourier transforms for nonequispaced data: A tutorial. Modern Sampling Theory: Mathematics and Application, Chapter 12 (J. J. Benedetto & P. J. S. G. Ferreira, eds). Boston, MA: Birkhauser, pp. 251-274.
    • (2001) Modern Sampling Theory: Mathematics and Application , pp. 251-274
    • Potts, D.1    Steidl, G.2    Tasche, M.3
  • 36
    • 0000439427 scopus 로고
    • Finite element solution of diffusion problems with irregular data
    • RANNACHER, R. (1984) Finite element solution of diffusion problems with irregular data. Numer. Math., 43, 309-327.
    • (1984) Numer. Math. , vol.43 , pp. 309-327
    • Rannacher, R.1
  • 37
    • 0031476682 scopus 로고    scopus 로고
    • Pricing stock options in a jump-diffusion model with stochastic volatility and interest rates: Applications of Fourier inversion methods
    • SCOTT, L. O. (1997) Pricing stock options in a jump-diffusion model with stochastic volatility and interest rates: Applications of Fourier inversion methods. Math. Finance, 7, 413-426.
    • (1997) Math. Finance , vol.7 , pp. 413-426
    • Scott, L.O.1
  • 39
    • 2442424098 scopus 로고    scopus 로고
    • Numerical valuation of options with jumps in the underlying
    • Delft University of Technology
    • VAZQUEZ, A. A. & OOSTERLEE, C. W. (2003) Numerical valuation of options with jumps in the underlying. Working Paper, Delft University of Technology.
    • (2003) Working Paper
    • Vazquez, A.A.1    Oosterlee, C.W.2
  • 40
    • 0032301587 scopus 로고    scopus 로고
    • Fast approximate Fourier transforms for irregularly spaced data
    • WARE, A. F. (1998) Fast approximate Fourier transforms for irregularly spaced data. SIAM Rev., 40, 838-856.
    • (1998) SIAM Rev. , vol.40 , pp. 838-856
    • Ware, A.F.1
  • 42
    • 11444256473 scopus 로고    scopus 로고
    • Numerical methods for cliquet options
    • University of Waterloo
    • WINDCLIFF, H. A., FORSYTH, P. A. & VETZAL, K. R. (2003) Numerical methods for cliquet options. Working Paper, University of Waterloo.
    • (2003) Working Paper
    • Windcliff, H.A.1    Forsyth, P.A.2    Vetzal, K.R.3
  • 43
    • 0031212664 scopus 로고    scopus 로고
    • Numerical analysis of American option pricing in a jump-diffusion model
    • ZHANG, X. L. (1997) Numerical analysis of American option pricing in a jump-diffusion model. Math. Oper. Res., 22, 668-690.
    • (1997) Math. Oper. Res. , vol.22 , pp. 668-690
    • Zhang, X.L.1


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