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Volumn 43, Issue 4, 2005, Pages 1596-1626

A finite difference scheme for option pricing in jump diffusion and exponential Lévy models

Author keywords

Finite difference methods; Jump diffusion models; L vy process; Option pricing; Parabolic integro differential equations; Viscosity solutions

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; ERROR ANALYSIS; NUMERICAL ANALYSIS; THEOREM PROVING;

EID: 33747178638     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142903436186     Document Type: Review
Times cited : (343)

References (31)
  • 1
    • 0030351484 scopus 로고    scopus 로고
    • Viscosity solutions of nonlinear integro-differential equations
    • O. ALVAREZ AND A. TOURIN, Viscosity solutions of nonlinear integro-differential equations, Ann. Inst. H. Poincaré Anal. Non Linéaire, 13 (1996), pp. 293-317.
    • (1996) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.13 , pp. 293-317
    • Alvarez, O.1    Tourin, A.2
  • 2
    • 0000264693 scopus 로고    scopus 로고
    • Jump-diffusion models: Volatility smile fitting and numerical methods for pricing
    • L. ANDERSEN AND J. ANDREASEN, Jump-diffusion models: Volatility smile fitting and numerical methods for pricing, Rev. Derivatives Research, 4 (2000), pp. 231-262.
    • (2000) Rev. Derivatives Research , vol.4 , pp. 231-262
    • Andersen, L.1    Andreasen, J.2
  • 3
    • 0001737039 scopus 로고
    • Implicit-explicit methods for time-dependent partial differential equations
    • U. M. ASCHER, S. J. RUUTH, AND B. T. R. WETTON, Implicit-explicit methods for time-dependent partial differential equations, SIAM J. Numer. Anal., 32 (1995), pp. 797-823.
    • (1995) SIAM J. Numer. Anal. , vol.32 , pp. 797-823
    • Ascher, U.M.1    Ruuth, S.J.2    Wetton, B.T.R.3
  • 5
    • 0036012033 scopus 로고    scopus 로고
    • On the convergence rate of approximation schemes for Hamilton-Jacobi- Bellman equations
    • G. BARLES AND E. R. JAKOBSEN, On the convergence rate of approximation schemes for Hamilton-Jacobi-Bellman equations, M2AN Math. Model. Numer. Anal., 36 (2002), pp. 33-54.
    • (2002) M2AN Math. Model. Numer. Anal. , vol.36 , pp. 33-54
    • Barles, G.1    Jakobsen, E.R.2
  • 6
    • 84974753170 scopus 로고
    • Convergence of approximation schemes for fully nonlinear second order equations
    • G. BARLES AND P. SOUGANIDIS, Convergence of approximation schemes for fully nonlinear second order equations, Asymptotic Anal., 4 (1991), pp. 271-283.
    • (1991) Asymptotic Anal. , vol.4 , pp. 271-283
    • Barles, G.1    Souganidis, P.2
  • 7
    • 0002443909 scopus 로고    scopus 로고
    • Processes of normal inverse Gaussian type
    • O. BARNDORFF-NIELSEN, Processes of normal inverse Gaussian type, Finance Stoch., 2 (1998), pp. 41-68.
    • (1998) Finance Stoch. , vol.2 , pp. 41-68
    • Barndorff-Nielsen, O.1
  • 9
    • 0002488565 scopus 로고    scopus 로고
    • Option valuation using the fast Fourier transform
    • P. CARR AND D. MADAN, Option valuation using the fast Fourier transform, J. Comput. Finance, 2 (1998), pp. 61-73.
    • (1998) J. Comput. Finance , vol.2 , pp. 61-73
    • Carr, P.1    Madan, D.D.2
  • 10
    • 0142219274 scopus 로고    scopus 로고
    • The finite moment logstable process and option pricing
    • P. CARR AND L. WU, The finite moment logstable process and option pricing, J. Finance, 58 (2003), pp. 753-778.
    • (2003) J. Finance , vol.58 , pp. 753-778
    • Carr, P.1    Wu, L.2
  • 12
    • 21244435312 scopus 로고    scopus 로고
    • Nonparametric calibration of jump-diffusion option pricing models
    • R. CONT AND P. TANKOV, Nonparametric calibration of jump-diffusion option pricing models, J. Comput. Finance, 7 (2004), pp. 1-49.
    • (2004) J. Comput. Finance , vol.7 , pp. 1-49
    • Cont, R.1    Tankov, P.2
  • 13
    • 21244498895 scopus 로고    scopus 로고
    • Integrodifferential equations for option prices in exponential Lévy models
    • R. CONT AND E. VOLTCHKOVA, Integrodifferential equations for option prices in exponential Lévy models, Finance Stoch., 9 (2005), pp. 299-325.
    • (2005) Finance Stoch. , vol.9 , pp. 299-325
    • Cont, R.1    Voltchkova, E.2
  • 14
    • 84967708673 scopus 로고
    • User's guide to viscosity solutions of second order partial differential equations
    • M. G. CRANDALL, H. ISHII, AND P.-L. LIONS, User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. (N.S.), 27 (1992), pp. 1-67.
    • (1992) Bull. Amer. Math. Soc. (N.S.) , vol.27 , pp. 1-67
    • Crandall, M.G.1    Ishii, H.2    Lions, P.-L.3
  • 15
    • 84966245867 scopus 로고
    • Two approximations of solutions of Hamilton-Jacobi equations
    • M. CRANDALL AND P.-L. LIONS, Two approximations of solutions of Hamilton-Jacobi equations, Math. Comp., 43 (1984), pp. 1-19.
    • (1984) Math. Comp. , vol.43 , pp. 1-19
    • Crandall, M.1    Lions, P.-L.2
  • 16
    • 2442536011 scopus 로고    scopus 로고
    • A penalty method for American options with jump diffusion processes
    • Y. D'HALLUIN, P. A. FORSYTH, AND G. LABAHN, A penalty method for American options with jump diffusion processes, Numer. Math., 97 (2004), pp. 321-352.
    • (2004) Numer. Math. , vol.97 , pp. 321-352
    • D'Halluin, Y.1    Forsyth, P.A.2    Labahn, G.3
  • 17
    • 0005787419 scopus 로고    scopus 로고
    • Application of generalized hyperbolic Lévy motions to finance
    • O. Barndorff-Nielsen, T. Mikosch, and S. Resnick, eds., Birkhäuser Boston, Boston
    • E. EBERLEIN, Application of generalized hyperbolic Lévy motions to finance, in Lévy Processes - Theory and Applications, O. Barndorff-Nielsen, T. Mikosch, and S. Resnick, eds., Birkhäuser Boston, Boston, 2001, pp. 319-336.
    • (2001) Lévy Processes - Theory and Applications , pp. 319-336
    • Eberlein, E.1
  • 20
    • 21244438823 scopus 로고    scopus 로고
    • A maximum principle for semicontinuous functions applicable to integra-partial differential equations
    • University of Oslo, Oslo, Norway
    • E. JAKOBSEN AND K. KARLSEN, A Maximum Principle for Semicontinuous Functions Applicable to Integra-Partial Differential Equations, working paper, University of Oslo, Oslo, Norway, 2004.
    • (2004) Working Paper
    • Jakobsen, E.1    Karlsen, K.2
  • 21
    • 0007455893 scopus 로고    scopus 로고
    • On the rate of convergence of finite difference approximations for Bellman's equations
    • N. KRYLOV, On the rate of convergence of finite difference approximations for Bellman's equations, St. Petersburg Math. J., 9 (1997), pp. 245-256.
    • (1997) St. Petersburg Math. J. , vol.9 , pp. 245-256
    • Krylov, N.1
  • 22
    • 0034384390 scopus 로고    scopus 로고
    • On the rate of convergence of finite difference approximations for Bellman's equations with variable coefficients
    • N. KRYLOV, On the rate of convergence of finite difference approximations for Bellman's equations with variable coefficients, Probab. Theory Related Fields, 117 (1997), pp. 1-16.
    • (1997) Probab. Theory Related Fields , vol.117 , pp. 1-16
    • Krylov, N.1
  • 23
    • 84986841347 scopus 로고
    • Option pricing with variance gamma martingale components
    • D. MADAN AND F. MILNE, Option pricing with variance gamma martingale components, Math. Finance, 1 (1991), pp. 39-55.
    • (1991) Math. Finance , vol.1 , pp. 39-55
    • Madan, D.1    Milne, F.2
  • 24
    • 33747192640 scopus 로고    scopus 로고
    • Purely discontinuous asset price processes
    • J. Cvitanic, E. Jouini, and M. Musiela, eds., Cambridge University Press, Cambridge, UK
    • D. MADAN, Purely discontinuous asset price processes, in Option Pricing, Interest Rates and Risk Management, J. Cvitanic, E. Jouini, and M. Musiela, eds., Cambridge University Press, Cambridge, UK, 2001, pp. 105-153.
    • (2001) Option Pricing, Interest Rates and Risk Management , pp. 105-153
    • Madan, D.1
  • 26
    • 0031677847 scopus 로고    scopus 로고
    • Optimal stopping of controlled jump-diffusion processes: A viscosity solution approach
    • H. PHAM, Optimal stopping of controlled jump-diffusion processes: A viscosity solution approach, J. Math. Systems Estim. Control, 8 (1998), pp. 1-27.
    • (1998) J. Math. Systems Estim. Control , vol.8 , pp. 1-27
    • Pham, H.1
  • 28
    • 0011991991 scopus 로고
    • Equations d'Hamilton Jacobi du premier ordre avec termes integro-differentiels
    • A. SAYAH, Equations d'Hamilton Jacobi du premier ordre avec termes integro-differentiels, Comm. Partial Differential Equations, 16 (1991), pp. 1057-1093.
    • (1991) Comm. Partial Differential Equations , vol.16 , pp. 1057-1093
    • Sayah, A.1
  • 29
    • 11544313334 scopus 로고
    • Optimal control of jump-Markov processes and viscosity solutions
    • Stochastic Differential Systems, Stochastic Control Theory and Applications, IMA Vol. Springer-Verlag, New York
    • H. SONER, Optimal control of jump-Markov processes and viscosity solutions, in Stochastic Differential Systems, Stochastic Control Theory and Applications, IMA Vol. Math. Appl. 10, Springer-Verlag, New York, 1988, pp. 501-511.
    • (1988) Math. Appl. , vol.10 , pp. 501-511
    • Soner, H.1
  • 31
    • 0141646779 scopus 로고    scopus 로고
    • Valuation of American options in a jump-diffusion model
    • Cambridge University Press, Cambridge, UK
    • X. ZHANG, Valuation of American options in a jump-diffusion model, in Numerical Methods in Finance, Cambridge University Press, Cambridge, UK, 1997, pp. 93-114.
    • (1997) Numerical Methods in Finance , pp. 93-114
    • Zhang, X.1


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