메뉴 건너뛰기




Volumn 33, Issue 2, 2011, Pages 763-785

A contour integral method for the Black-Scholes and Heston equations

Author keywords

Black scholes equation; Financial option pricing; Heston equation; Krylov methods; Laplace transform; Matrix exponential; Numerical contour integration; Parallelism

Indexed keywords

ECONOMICS; FINANCIAL MARKETS; INTEGRAL EQUATIONS; LINEAR SYSTEMS; NUMERICAL METHODS;

EID: 79957621114     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/090776081     Document Type: Article
Times cited : (32)

References (35)
  • 2
    • 85015692260 scopus 로고
    • The pricing of options and corporate liabilities
    • F. BLACK AND M. SCHOLES, The pricing of options and corporate liabilities, J. Polit. Econ., 81 (1973), pp. 637-654.
    • (1973) J. Polit. Econ. , vol.81 , pp. 637-654
    • Black, F.1    Scholes, M.2
  • 3
    • 2942653250 scopus 로고    scopus 로고
    • Algorithm 832: UMFPACK V4.3-an unsymmetric-pattern multifrontal method
    • T. A. DAVIS, Algorithm 832: UMFPACK V4.3-an unsymmetric-pattern multifrontal method, ACM Trans. Math. Software, 30 (2004), pp. 196-199.
    • (2004) ACM Trans. Math. Software , vol.30 , pp. 196-199
    • Davis, T.A.1
  • 4
    • 2942655475 scopus 로고    scopus 로고
    • A column pre-ordering strategy for the unsymmetric-pattern multifrontal method
    • T. A. DAVIS, A column pre-ordering strategy for the unsymmetric-pattern multifrontal method, ACM Trans. Math. Software, 30 (2004), pp. 165-195.
    • (2004) ACM Trans. Math. Software , vol.30 , pp. 165-195
    • Davis, T.A.1
  • 5
    • 0036022621 scopus 로고    scopus 로고
    • H-matrix approximation for the operator exponential with applications
    • DOI 10.1007/s002110100360
    • I. P. GAVRILYUK, W. HACKBUSCH, AND B. N. KHOROMSKIJ, H-matrix approximation for the operator exponential with applications, Numer. Math., 92 (2002), pp. 83-111. (Pubitemid 36161520)
    • (2002) Numerische Mathematik , vol.92 , Issue.1 , pp. 83-111
    • Gavrilyuk, I.P.1    Hackbusch, W.2    Khoromskij, B.N.3
  • 6
    • 14944359407 scopus 로고    scopus 로고
    • Data-sparse approximation to a class of operator-valued functions
    • DOI 10.1090/S0025-5718-04-01703-X, PII S002557180401703X
    • I. P. GAVRILYUK, W. HACKBUSCH, AND B. N. KHOROMSKIJ, Data-sparse approximation to a class of operator-valued functions, Math. Comp., 74 (2005), pp. 681-708. (Pubitemid 40367036)
    • (2005) Mathematics of Computation , vol.74 , Issue.250 , pp. 681-708
    • Gavrilyuk, I.P.1    Hackbusch, W.2    Khoromskij, B.N.3
  • 7
    • 85009773228 scopus 로고    scopus 로고
    • Exponentially convergent parallel discretization methods for the first order evolution equations
    • I. P. GAVRILYUK AND V. L. MAKAROV, Exponentially convergent parallel discretization methods for the first order evolution equations, Comput. Methods Appl. Math., 1 (2001), pp. 333-355.
    • (2001) Comput. Methods Appl. Math. , vol.1 , pp. 333-355
    • Gavrilyuk, I.P.1    Makarov, V.L.2
  • 8
    • 33749034221 scopus 로고    scopus 로고
    • Exponentially convergent algorithms for the operator exponential with applications to inhomogeneous problems in Banach spaces
    • DOI 10.1137/040611045
    • I. P. GAVRILYUK AND V. L. MAKAROV, Exponentially convergent algorithms for the operator exponential with applications to inhomogeneous problems in Banach spaces, SIAM J. Numer. Anal., 43 (2005), pp. 2144-2171. (Pubitemid 44598676)
    • (2005) SIAM Journal on Numerical Analysis , vol.43 , Issue.5 , pp. 2144-2171
    • Gavrilyuk, I.P.1    Makarov, V.L.2
  • 9
    • 0037836721 scopus 로고
    • A closed-form solution for options with stochastic volatility with applications to bond and currency options
    • S. L. HESTON, A closed-form solution for options with stochastic volatility with applications to bond and currency options, Rev. Finan. Stud., 6 (1993), pp. 327-343.
    • (1993) Rev. Finan. Stud. , vol.6 , pp. 327-343
    • Heston, S.L.1
  • 11
    • 70350310997 scopus 로고    scopus 로고
    • ADI finite difference schemes for option pricing in the Heston model with correlation
    • 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. Model., 7 (2010), pp. 303-320.
    • (2010) Int. J. Numer. Anal. Model. , vol.7 , pp. 303-320
    • In't Hout, K.J.1    Foulon, S.2
  • 12
    • 33750505893 scopus 로고    scopus 로고
    • Stability of ADI schemes applied to convection-diffusion equations with mixed derivative terms
    • DOI 10.1016/j.apnum.2005.11.011, PII S0168927405002230
    • 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 (2007), pp. 19-35. (Pubitemid 44667065)
    • (2007) Applied Numerical Mathematics , vol.57 , Issue.1 , pp. 19-35
    • T Hout, K.J.1    Welfert, B.D.2
  • 13
    • 70350278572 scopus 로고    scopus 로고
    • Laplace transformation method for the Black-Scholes equation
    • S. LEE AND D. SHEEN, Laplace transformation method for the Black-Scholes equation, Int. J. Numer. Anal. Model., 6 (2009), pp. 642-658.
    • (2009) Int. J. Numer. Anal. Model. , vol.6 , pp. 642-658
    • Lee, S.1    Sheen, D.2
  • 14
    • 5144231600 scopus 로고    scopus 로고
    • On the numerical inversion of the Laplace transform of certain holomorphic mappings
    • M. LÓPEZ-FERNÁNDEZ AND C. PALENCIA, On the numerical inversion of the Laplace transform of certain holomorphic mappings, Appl. Numer. Math., 51 (2004), pp. 289-303.
    • (2004) Appl. Numer. Math. , vol.51 , pp. 289-303
    • López-Fernández, M.1    Palencia, C.2
  • 15
    • 33749020865 scopus 로고    scopus 로고
    • A spectral order method for inverting sectorial laplace transforms
    • DOI 10.1137/050629653
    • M. LÓPEZ-FERNÁNDEZ, C. PALENCIA, AND A. SCHÄDLE, A spectral order method for inverting sectorial Laplace transforms, SIAM J. Numer. Anal., 44 (2006), pp. 1332-1350. (Pubitemid 47135926)
    • (2006) SIAM Journal on Numerical Analysis , vol.44 , Issue.3 , pp. 1332-1350
    • Lopez-Fernandez, M.1    Palencia, C.2    Schadle, A.3
  • 16
    • 43049125305 scopus 로고
    • Zur numerischen Auswertung uneigentlicher Integrale
    • E. MARTENSEN, Zur numerischen Auswertung uneigentlicher Integrale, ZAMM Z. Angew. Math. Mech., 48 (1968), pp. T83-T85.
    • (1968) ZAMM Z. Angew. Math. Mech. , vol.48
    • Martensen, E.1
  • 17
    • 84968505392 scopus 로고
    • Error-bounds for the evaluation of integrals by the Euler-Maclaurin formula and by Gauss-type formulae
    • J. MCNAMEE, Error-bounds for the evaluation of integrals by the Euler-Maclaurin formula and by Gauss-type formulae, Math. Comp., 18 (1964), pp. 368-381.
    • (1964) Math. Comp. , vol.18 , pp. 368-381
    • McNamee, J.1
  • 18
    • 0142188202 scopus 로고    scopus 로고
    • The solution of parametrized symmetric linear systems
    • DOI 10.1137/S0895479800380386, PII S0895479800380386
    • K. MEERBERGEN, The solution of parametrized symmetric linear systems, SIAM J. Matrix Anal. Appl., 24 (2003), pp. 1038-1059. (Pubitemid 37311573)
    • (2003) SIAM Journal on Matrix Analysis and Applications , vol.24 , Issue.4 , pp. 1038-1059
    • Meerbergen, K.1
  • 19
    • 0037354371 scopus 로고    scopus 로고
    • Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later
    • C. MOLER AND C. VAN LOAN, Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later, SIAM Rev., 45 (2003), pp. 3-49.
    • (2003) SIAM Rev. , vol.45 , pp. 3-49
    • Moler, C.1    Van Loan, C.2
  • 20
    • 0028695631 scopus 로고
    • Pseudospectra of the convection-diffusion operator
    • S. C. REDDY AND L. N. TREFETHEN, Pseudospectra of the convection-diffusion operator, SIAM J. Appl. Math., 54 (1994), pp. 1634-1649.
    • (1994) SIAM J. Appl. Math. , vol.54 , pp. 1634-1649
    • Reddy, S.C.1    Trefethen, L.N.2
  • 22
    • 0034407089 scopus 로고    scopus 로고
    • A parallel method for time-discretization of parabolic problems based on contour integral representation and quadrature
    • D. SHEEN, I. H. SLOAN, AND V. THOMÉE, A parallel method for time-discretization of parabolic problems based on contour integral representation and quadrature, Math. Comp., 69 (2000), pp. 177-195.
    • (2000) Math. Comp. , vol.69 , pp. 177-195
    • Sheen, D.1    Sloan, I.H.2    Thomée, V.3
  • 23
    • 0345016412 scopus 로고    scopus 로고
    • A parallel method for time discretization of parabolic equations based on Laplace transformation and quadrature
    • DOI 10.1093/imanum/23.2.269
    • D. SHEEN, I. H. SLOAN, AND V. THOMÉE, A parallel method for time discretization of parabolic equations based on Laplace transformation and quadrature, IMA J. Numer. Anal., 23 (2003), pp. 269-299. (Pubitemid 37445949)
    • (2003) IMA Journal of Numerical Analysis , vol.23 , Issue.2 , pp. 269-299
    • Sheen, D.1    Sloan, I.H.2    Thomee, V.3
  • 25
    • 33846787171 scopus 로고    scopus 로고
    • Recent computational developments in Krylov subspace methods for linear systems
    • V. SIMONCINI AND D. B. SZYLD, Recent computational developments in Krylov subspace methods for linear systems, Numer. Linear Algebra Appl., 14 (2007), pp. 1-59.
    • (2007) Numer. Linear Algebra Appl. , vol.14 , pp. 1-59
    • Simoncini, V.1    Szyld, D.B.2
  • 27
    • 0002152334 scopus 로고
    • The accurate numerical inversion of Laplace transforms
    • A. TALBOT, The accurate numerical inversion of Laplace transforms, J. Inst. Math. Appl., 23 (1979).
    • (1979) J. Inst. Math. Appl. , vol.23
    • Talbot, A.1
  • 30
    • 84972047930 scopus 로고
    • Linear stability analysis in the numerical solution of initial value problems
    • J. L. M. VAN DORSSELAER, J. F. B. M. KRAAIJEVANGER, AND M. N. SPIJKER, Linear stability analysis in the numerical solution of initial value problems, Acta Numer., 2 (1993), pp. 199-237.
    • (1993) Acta Numer. , vol.2 , pp. 199-237
    • Van Dorsselaer, J.L.M.1    Kraaijevanger, J.F.B.M.2    Spijker, M.N.3
  • 31
    • 76549125164 scopus 로고    scopus 로고
    • Improved contour integral methods for parabolic PDEs
    • J. A. C. WEIDEMAN, Improved contour integral methods for parabolic PDEs, IMA J. Numer. Anal., 30 (2010), pp. 334-350.
    • (2010) IMA J. Numer. Anal. , vol.30 , pp. 334-350
    • Weideman, J.A.C.1
  • 32
    • 34548162562 scopus 로고    scopus 로고
    • Parabolic and hyperbolic contours for computing the Bromwich integral
    • J. A. C. WEIDEMAN AND L. N. TREFETHEN, Parabolic and hyperbolic contours for computing the Bromwich integral, Math. Comp., 76 (2007), pp. 1341-1356.
    • (2007) Math. Comp. , vol.76 , pp. 1341-1356
    • Weideman, J.A.C.1    Trefethen, L.N.2
  • 33
    • 0003931587 scopus 로고    scopus 로고
    • reprinted edition, Wiley, Chichester, England
    • P. WILMOTT, Derivatives, reprinted edition, Wiley, Chichester, England, 1999.
    • (1999) Derivatives
    • Wilmott, P.1
  • 35
    • 24644475497 scopus 로고    scopus 로고
    • T. G. WRIGHT, Eig Tool, http://www.comlab.ox.ac.uk/pseudospectra/eigtool, 2002.
    • (2002) Eig Tool
    • Wright, T.G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.