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Volumn 58, Issue 11, 2008, Pages 1687-1703

Efficient solution of a partial integro-differential equation in finance

Author keywords

Conjugate Gradient method; L vy process; Partial integro differential equations; Toeplitz matrices

Indexed keywords

CONJUGATE GRADIENT METHOD; DIFFERENTIAL EQUATIONS; DIFFERENTIATION (CALCULUS); FINITE DIFFERENCE METHOD; GRADIENT METHODS; INTEGRAL EQUATIONS; INTEGRODIFFERENTIAL EQUATIONS; LINEAR SYSTEMS; NUMERICAL ANALYSIS; PARTIAL DIFFERENTIAL EQUATIONS;

EID: 52149111671     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2007.11.002     Document Type: Article
Times cited : (84)

References (36)
  • 1
    • 13644258481 scopus 로고    scopus 로고
    • Numerical valuation of options with jumps in the underlying
    • Almendral A., and Oosterlee C. Numerical valuation of options with jumps in the underlying. Appl. Numer. Math. 53 (2005) 1-18
    • (2005) Appl. Numer. Math. , vol.53 , pp. 1-18
    • Almendral, A.1    Oosterlee, C.2
  • 2
    • 0000264693 scopus 로고    scopus 로고
    • Jump-diffusion processes: Volatility smile fitting and numerical methods for option pricing
    • Andersen L., and Andreasen J. Jump-diffusion processes: Volatility smile fitting and numerical methods for option pricing. Rev. Derivatives Res. 4 (2000) 231-262
    • (2000) Rev. Derivatives Res. , vol.4 , pp. 231-262
    • Andersen, L.1    Andreasen, J.2
  • 3
    • 0030534228 scopus 로고    scopus 로고
    • Jumps and stochastic volatility: Exchange rate processes implicit in Deutsche Mark options
    • Bates D. Jumps and stochastic volatility: Exchange rate processes implicit in Deutsche Mark options. Rev. Financial Studies 9 (1996) 69-107
    • (1996) Rev. Financial Studies , vol.9 , pp. 69-107
    • Bates, D.1
  • 4
    • 85015692260 scopus 로고
    • The pricing of options and corporate liabilities
    • Black F., and Scholes M. The pricing of options and corporate liabilities. J. Political Economy 81 3 (1973) 637-654
    • (1973) J. Political Economy , vol.81 , Issue.3 , pp. 637-654
    • Black, F.1    Scholes, M.2
  • 5
    • 52149085127 scopus 로고    scopus 로고
    • M. Briani, Numerical methods for option pricing in jump-diffusion markets, PhD thesis, Università degli Studi di Roma "La Sapienza", 2003
    • M. Briani, Numerical methods for option pricing in jump-diffusion markets, PhD thesis, Università degli Studi di Roma "La Sapienza", 2003
  • 6
    • 52149117299 scopus 로고    scopus 로고
    • M. Briani, R. Natalini, G. Russo, Implicit-explicit numerical schemes for jump-diffusion processes. Technical Report 38 (4/2004), IAC Report, 2004
    • M. Briani, R. Natalini, G. Russo, Implicit-explicit numerical schemes for jump-diffusion processes. Technical Report 38 (4/2004), IAC Report, 2004
  • 7
    • 0001403957 scopus 로고
    • Circulant preconditioners for Hermitian Toeplitz systems
    • Chan R. Circulant preconditioners for Hermitian Toeplitz systems. SIAM J. Matrix Anal. Appl. 10 (1989) 542-550
    • (1989) SIAM J. Matrix Anal. Appl. , vol.10 , pp. 542-550
    • Chan, R.1
  • 8
    • 0011667587 scopus 로고
    • The spectrum of a family of circulant preconditioned Toeplitz systems
    • Chan R. The spectrum of a family of circulant preconditioned Toeplitz systems. SIAM J. Numer. Anal. 26 (1989) 503-506
    • (1989) SIAM J. Numer. Anal. , vol.26 , pp. 503-506
    • Chan, R.1
  • 9
    • 0002520370 scopus 로고
    • The circulant operator in the Banach algebra of matrices
    • Chan R., Jin X., and Yeung M. The circulant operator in the Banach algebra of matrices. Linear Algebra Appl. 149 (1991) 41-53
    • (1991) Linear Algebra Appl. , vol.149 , pp. 41-53
    • Chan, R.1    Jin, X.2    Yeung, M.3
  • 10
    • 0026172324 scopus 로고
    • The spectra of super-optimal circulant preconditioned Toeplitz systems
    • Chan R., Jin X., and Yeung M. The spectra of super-optimal circulant preconditioned Toeplitz systems. SIAM J. Numer. Anal. 28 (1991) 871-879
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 871-879
    • Chan, R.1    Jin, X.2    Yeung, M.3
  • 11
    • 84968515314 scopus 로고
    • Circulant preconditioners for Toeplitz matrices with positive continuous generating functions
    • Chan R., and Yeung M. Circulant preconditioners for Toeplitz matrices with positive continuous generating functions. Math. Comp. 58 (1992) 233-240
    • (1992) Math. Comp. , vol.58 , pp. 233-240
    • Chan, R.1    Yeung, M.2
  • 12
    • 0033457596 scopus 로고    scopus 로고
    • Pricing contingent claims on stocks driven by Lévy processes
    • Chan T. Pricing contingent claims on stocks driven by Lévy processes. Ann. Appl. Probab. 9 2 (1999) 504-528
    • (1999) Ann. Appl. Probab. , vol.9 , Issue.2 , pp. 504-528
    • Chan, T.1
  • 13
    • 0000853646 scopus 로고
    • An optimal circulant preconditioner for Toeplitz systems
    • Chan T. An optimal circulant preconditioner for Toeplitz systems. SIAM J. Sci. Stat. Comput. 9 (1988) 766-771
    • (1988) SIAM J. Sci. Stat. Comput. , vol.9 , pp. 766-771
    • Chan, T.1
  • 14
    • 33747178638 scopus 로고    scopus 로고
    • A finite difference scheme for option pricing in jump diffusion and exponential Lévy models
    • Cont R., and Voltchkova E. A finite difference scheme for option pricing in jump diffusion and exponential Lévy models. SIAM J. Numer. Anal. 43 4 (2005) 1596-1626
    • (2005) SIAM J. Numer. Anal. , vol.43 , Issue.4 , pp. 1596-1626
    • Cont, R.1    Voltchkova, E.2
  • 16
    • 2442536011 scopus 로고    scopus 로고
    • A penalty method for American options with jump diffusion processes
    • d'Halluin Y., Forsyth P., and Labahn G. A penalty method for American options with jump diffusion processes. Numer. Math. 97 (2004) 321-352
    • (2004) Numer. Math. , vol.97 , pp. 321-352
    • d'Halluin, Y.1    Forsyth, P.2    Labahn, G.3
  • 17
    • 11444268256 scopus 로고    scopus 로고
    • Robust numerical methods for contingent claims under jump diffusion processes
    • d'Halluin Y., Forsyth P., and Vetzal K. Robust numerical methods for contingent claims under jump diffusion processes. IMA J. Numer. Anal. 25 (2005) 87-112
    • (2005) IMA J. Numer. Anal. , vol.25 , pp. 87-112
    • d'Halluin, Y.1    Forsyth, P.2    Vetzal, K.3
  • 20
    • 0037836721 scopus 로고
    • A closed-form solution for options with stochastic volatility with applications to bond and currency options
    • Heston S. A closed-form solution for options with stochastic volatility with applications to bond and currency options. Rev. Financial Studies 6 2 (1993) 327-343
    • (1993) Rev. Financial Studies , vol.6 , Issue.2 , pp. 327-343
    • Heston, S.1
  • 21
    • 0000859514 scopus 로고
    • Some aspects of circulant preconditioners
    • Huckle T. Some aspects of circulant preconditioners. SIAM J. Sci. Comput. 14 3 (1993) 531-541
    • (1993) SIAM J. Sci. Comput. , vol.14 , Issue.3 , pp. 531-541
    • Huckle, T.1
  • 22
    • 52149108394 scopus 로고    scopus 로고
    • T. Huckle, Iterative methods for Toeplitz-like matrices, Technical Report SCCM 94-5, Stanford Scientific Computing/Computational Mathematics, 1994
    • T. Huckle, Iterative methods for Toeplitz-like matrices, Technical Report SCCM 94-5, Stanford Scientific Computing/Computational Mathematics, 1994
  • 23
    • 84977709229 scopus 로고
    • The pricing of options on assets with stochastic volatilities
    • Hull J., and White A. The pricing of options on assets with stochastic volatilities. J. Finance 42 2 (1987) 281-300
    • (1987) J. Finance , vol.42 , Issue.2 , pp. 281-300
    • Hull, J.1    White, A.2
  • 24
    • 52149094461 scopus 로고    scopus 로고
    • S. Ikonen, J. Toivanen, Numerical valuation of European and American options with Kou's jump-diffusion model, in: Amamef Conference on Numerical Methods in Finance, INRIA-Rocquencourt, France, February 2006
    • S. Ikonen, J. Toivanen, Numerical valuation of European and American options with Kou's jump-diffusion model, in: Amamef Conference on Numerical Methods in Finance, INRIA-Rocquencourt, France, February 2006
  • 25
    • 0036698288 scopus 로고    scopus 로고
    • A jump-diffusion model for option pricing
    • Kou S. A jump-diffusion model for option pricing. Management Science 48 8 (August 2002) 1086-1101
    • (2002) Management Science , vol.48 , Issue.8 , pp. 1086-1101
    • Kou, S.1
  • 26
    • 26644461683 scopus 로고    scopus 로고
    • Wavelet Galerkin pricing of American options on Lévy driven assets
    • Matache A.-M., Nitsche P.-A., and Schwab C. Wavelet Galerkin pricing of American options on Lévy driven assets. Quantitative Finance 5 4 (2005) 403-424
    • (2005) Quantitative Finance , vol.5 , Issue.4 , pp. 403-424
    • Matache, A.-M.1    Nitsche, P.-A.2    Schwab, C.3
  • 27
    • 33644953246 scopus 로고    scopus 로고
    • Fast numerical solution of parabolic integrodifferential equations with applications in finance
    • Matache A.-M., Schwab C., and Wihler T. Fast numerical solution of parabolic integrodifferential equations with applications in finance. SIAM J. Sci. Comput. 27 (2005) 369-393
    • (2005) SIAM J. Sci. Comput. , vol.27 , pp. 369-393
    • Matache, A.-M.1    Schwab, C.2    Wihler, T.3
  • 29
    • 34248474317 scopus 로고
    • Option pricing when underlying stock returns are discontinuous
    • Merton R. Option pricing when underlying stock returns are discontinuous. J. Financial Economics 3 (1976) 125-144
    • (1976) J. Financial Economics , vol.3 , pp. 125-144
    • Merton, R.1
  • 31
    • 5744238206 scopus 로고
    • On the algebraic structure of the spaces of Toeplitz and Hankel matrices
    • Pustyl'nikov L. On the algebraic structure of the spaces of Toeplitz and Hankel matrices. Soviet Math. Dokl. 21 (1980) 141-144
    • (1980) Soviet Math. Dokl. , vol.21 , pp. 141-144
    • Pustyl'nikov, L.1
  • 32
    • 52149101330 scopus 로고    scopus 로고
    • S. Raible, Lévy processes in finance: Theory, numerics, and empirical facts, PhD thesis, Albert-Ludwigs-Universität Freiburg i. Br., 2000
    • S. Raible, Lévy processes in finance: Theory, numerics, and empirical facts, PhD thesis, Albert-Ludwigs-Universität Freiburg i. Br., 2000
  • 33
    • 0022694911 scopus 로고
    • A proposal for Toeplitz matrix calculations
    • Strang G. A proposal for Toeplitz matrix calculations. Stud. Appl. Math. 74 (1986) 171-176
    • (1986) Stud. Appl. Math. , vol.74 , pp. 171-176
    • Strang, G.1
  • 34
    • 0040072382 scopus 로고
    • A decomposition of Toeplitz matrices and optimal circulant preconditioner
    • Tismenetsky M. A decomposition of Toeplitz matrices and optimal circulant preconditioner. Linear Algebra Appl. 156 (1991) 105-121
    • (1991) Linear Algebra Appl. , vol.156 , pp. 105-121
    • Tismenetsky, M.1
  • 35
    • 0000415943 scopus 로고
    • Optimal and superoptimal circulant preconditioners
    • Tyrtyshnikov E. Optimal and superoptimal circulant preconditioners. SIAM J. Matrix Anal. Appl. 13 2 (1992) 459-473
    • (1992) SIAM J. Matrix Anal. Appl. , vol.13 , Issue.2 , pp. 459-473
    • Tyrtyshnikov, E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.