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Volumn 15, Issue 1, 2005, Pages 119-168

A quantization tree method for pricing and hedging multidimensional american options

Author keywords

American option pricing; Local volatility model; Optimal quantization; Optimal stopping; Snell envelope

Indexed keywords


EID: 14544269364     PISSN: 09601627     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.0960-1627.2005.00213.x     Document Type: Article
Times cited : (145)

References (42)
  • 1
    • 1542407760 scopus 로고    scopus 로고
    • The central limit theorem for a nonlinear algorithm based on quantization. Stochastic analysis with applications to mathematical finance
    • BALLY, V. (2004): The Central Limit Theorem for a Nonlinear Algorithm Based on Quantization. Stochastic Analysis with Applications to Mathematical Finance, Proc. R. Soc. Land. 460 (2041), 221-241.
    • (2004) Proc. R. Soc. Land. , vol.460 , Issue.2041 , pp. 221-241
    • Bally, V.1
  • 3
    • 2342581211 scopus 로고    scopus 로고
    • A quantization algorithm for solving discrete time multi-dimensional discrete time optimal stopping problems
    • BALLY, V., and G. PAGÈS (2003): A Quantization Algorithm for Solving Discrete Time Multi-Dimensional Discrete Time Optimal Stopping problems, Bernoulli 9, 1003-1049.
    • (2003) Bernoulli , vol.9 , pp. 1003-1049
    • Bally, V.1    Pagès, G.2
  • 4
    • 0037843726 scopus 로고    scopus 로고
    • Error analysis of a quantization algorithm for obstacle problems
    • BALLY, V., and G. PAGÈS (2003): Error Analysis of a Quantization Algorithm for Obstacle Problems, Stoch. Proc. Appl. 106, 1-40.
    • (2003) Stoch. Proc. Appl. , vol.106 , pp. 1-40
    • Bally, V.1    Pagès, G.2
  • 5
    • 0002262588 scopus 로고    scopus 로고
    • A stochastic quantization method for non linear problems
    • BALLY, V., G. PAGÈS, and J. PRINTEMS (2001): A Stochastic Quantization Method for Non Linear Problems, Monte Carlo Meth. Appl. 7(1-2), 21-34.
    • (2001) Monte Carlo Meth. Appl. , vol.7 , Issue.1-2 , pp. 21-34
    • Bally, V.1    Pagès, G.2    Printems, J.3
  • 6
    • 0141971260 scopus 로고    scopus 로고
    • First order schemes in the numerical quantization method
    • BALLY, V., G. PAGÈS, and J. PRINTEMS (2003): First Order Schemes in the Numerical Quantization Method, Math. Finance 13(1), 1-16.
    • (2003) Math. Finance , vol.13 , Issue.1 , pp. 1-16
    • Bally, V.1    Pagès, G.2    Printems, J.3
  • 7
    • 84974489693 scopus 로고
    • Numerical valuation of high dimensional multivariate American securities
    • BARRAQUAND, J., and D. MARTINEAU (1995): Numerical Valuation of High Dimensional Multivariate American Securities, J. Finance Quant. Anal. 30, 383-405.
    • (1995) J. Finance Quant. Anal. , vol.30 , pp. 383-405
    • Barraquand, J.1    Martineau, D.2
  • 10
    • 2342427092 scopus 로고    scopus 로고
    • Discrete-time approximation and monte carlo simulation of backward stochastic differential equations
    • BOUCHARD, B., and N. TOUZI (2004): Discrete-Time Approximation and Monte Carlo Simulation of Backward Stochastic Differential Equations, Stock. Process. Appl. 111(2), 175-206.
    • (2004) Stock. Process. Appl. , vol.111 , Issue.2 , pp. 175-206
    • Bouchard, B.1    Touzi, N.2
  • 11
    • 38249005144 scopus 로고
    • Residual risks and hedging strategies in markovian markets
    • BOULEAU, N., and D. LAMBERTON (1989): Residual Risks and Hedging Strategies in Markovian Markets, Stock. Process. Appl. 33, 131-150.
    • (1989) Stock. Process. Appl. , vol.33 , pp. 131-150
    • Bouleau, N.1    Lamberton, D.2
  • 12
    • 0030502126 scopus 로고    scopus 로고
    • American option valuation: New bounds, approximations and a comparison with an existing method
    • BROADIE, M., and J. DETEMPLE (1996): American Option Valuation: New Bounds, Approximations and a Comparison with an Existing Method, Rev. Financial Stud. 9(4), 1211-1250.
    • (1996) Rev. Financial Stud. , vol.9 , Issue.4 , pp. 1211-1250
    • Broadie, M.1    Detemple, J.2
  • 13
    • 0031590025 scopus 로고    scopus 로고
    • Pricing American-style securities using simulation
    • BROADIE, M., and P. GLASSERMAN (1997): Pricing American-Style Securities Using Simulation, J. Econ. Dynam. Control 21(8-9), 1323-1352.
    • (1997) J. Econ. Dynam. Control , vol.21 , Issue.8-9 , pp. 1323-1352
    • Broadie, M.1    Glasserman, P.2
  • 15
    • 0011463188 scopus 로고
    • American options: Theory and numerical analysis
    • Manchester, UK: Manchester University Press
    • CAVERHILL, A. P., and N. WEBBER (1990): American Options: Theory and Numerical Analysis; in Options: Recent Advances in Theory and Practice. Manchester, UK: Manchester University Press.
    • (1990) Options: Recent Advances in Theory and Practice
    • Caverhill, A.P.1    Webber, N.2
  • 16
    • 0038056397 scopus 로고    scopus 로고
    • An analysis of a least squares regression method for American option pricing
    • CLÉMENT, É., P. PROTTER, and D. LAMBERTON (2002): An Analysis of a Least Squares Regression Method for American Option Pricing, Finance & Stochastics 6(2), 449-471.
    • (2002) Finance & Stochastics , vol.6 , Issue.2 , pp. 449-471
    • Clément, É.1    Protter, P.2    Lamberton, D.3
  • 17
    • 14544300483 scopus 로고    scopus 로고
    • Limit theorems for the random normalized distortion
    • COHORT, P. (2004): Limit Theorems for the Random Normalized Distortion, Ann. Appl. Prob. 14(1), 118-143.
    • (2004) Ann. Appl. Prob. , vol.14 , Issue.1 , pp. 118-143
    • Cohort, P.1
  • 19
    • 0031483012 scopus 로고    scopus 로고
    • Reflected solutions of backward stochastic differential equations and related obstacle problems for PDE's
    • EL KAROUI, N., C. KAPOUDJAN, É. PARDOUX, S. PENG, and M. C. QUENEZ (1997): Reflected Solutions of Backward Stochastic Differential Equations and Related Obstacle Problems for PDE's, Ann. Probab. 25(2), 702-737.
    • (1997) Ann. Probab. , vol.25 , Issue.2 , pp. 702-737
    • El Karoui, N.1    Kapoudjan, C.2    Pardoux, É.3    Peng, S.4    Quenez, M.C.5
  • 20
    • 0002289762 scopus 로고
    • Hedging of non redundant contingent claims
    • W. Hildebrand and A. Mas-Coffel (eds.) Amsterdam: North-Holland
    • FÖLLMER, H., and D. SONDERMANN (1986): Hedging of Non Redundant Contingent Claims; in Contributions to Mathematical Economics, W. Hildebrand and A. Mas-Coffel (eds.) Amsterdam: North-Holland, 205-223.
    • (1986) Contributions to Mathematical Economics , pp. 205-223
    • Föllmer, H.1    Sondermann, D.2
  • 21
    • 0000039677 scopus 로고    scopus 로고
    • Applications of malliavin calculus to monte carlo methods in finance II
    • FOURNIÉ, É., J. M. LASRY, J. LEBOUCHOUX, and P. L. LIONS (2001): Applications of Malliavin calculus to Monte Carlo Methods in Finance II, Finance Stock. 5, 201-236.
    • (2001) Finance Stock , vol.5 , pp. 201-236
    • Fournié, É.1    Lasry, J.M.2    Lebouchoux, J.3    Lions, P.L.4
  • 22
    • 0001488061 scopus 로고    scopus 로고
    • Applications of malliavin calculus to monte carlo methods in finance
    • FOURNIÉ, É., J. M. LASRY, J. LEBOUCHOUX, P. L. LIONS, and N. TOUZI (1999): Applications of Malliavin Calculus to Monte Carlo Methods in Finance, Finance Stock. 3, 391-412.
    • (1999) Finance Stock , vol.3 , pp. 391-412
    • Fournié, É.1    Lasry, J.M.2    Lebouchoux, J.3    Lions, P.L.4    Touzi, N.5
  • 27
    • 0038355030 scopus 로고    scopus 로고
    • Variance reduction methods for simulation of densities on wiener space
    • KOHATSU-HIGA, A., and R. PETTERSSON (2002): Variance Reduction Methods for Simulation of Densities on Wiener Space, SIAM J. Numer. Anal. 40(2), 431-450.
    • (2002) SIAM J. Numer. Anal. , vol.40 , Issue.2 , pp. 431-450
    • Kohatsu-Higa, A.1    Pettersson, R.2
  • 29
    • 0003924011 scopus 로고    scopus 로고
    • Applications of Mathematics 24, Stochastic Modeling and Applied Probability. New York: Springer-Verlag
    • nd edition, Applications of Mathematics 24, Stochastic Modeling and Applied Probability. New York: Springer-Verlag, p. 475.
    • (2001) nd Edition , pp. 475
    • Kushner, H.J.1    Dupuis, P.2
  • 32
    • 0037718695 scopus 로고    scopus 로고
    • Brownian optimal stopping and random walks
    • LAMBERTON, D. (2002): Brownian Optimal Stopping and Random Walks, Appl. Math. Optim. 45, 283-324.
    • (2002) Appl. Math. Optim. , vol.45 , pp. 283-324
    • Lamberton, D.1
  • 33
    • 0000828528 scopus 로고
    • Sur l'Approximation des réduites
    • LAMBERTON, D., and G. PAGÈS (1990): Sur l'Approximation des réduites, Ann. Inst. H. Poincaré 26(2), 331-355.
    • (1990) Ann. Inst. H. Poincaré , vol.26 , Issue.2 , pp. 331-355
    • Lamberton, D.1    Pagès, G.2
  • 35
    • 84860096823 scopus 로고    scopus 로고
    • Calcul des Prix et des Sensibilités d'une Option Américaine par une Méthode de Monte Carlo
    • LIONS, P. L., and H. RÉGNIER (2001): Calcul des Prix et des Sensibilités d'une Option Américaine par une Méthode de Monte Carlo. Working paper coc ixis.
    • (2001) Working Paper Coc Ixis
    • Lions, P.L.1    Régnier, H.2
  • 36
    • 0035578679 scopus 로고    scopus 로고
    • Valuing American options by simulation: A simple least-squares approach
    • LONGSTAFF, F. A., and E. S. SCHWARTZ (2001): Valuing American Options by Simulation: A Simple Least-Squares Approach, Rev. Financial Stud. 14, 113-148.
    • (2001) Rev. Financial Stud. , vol.14 , pp. 113-148
    • Longstaff, F.A.1    Schwartz, E.S.2
  • 38
    • 0032498777 scopus 로고    scopus 로고
    • A space vector quantization method for numerical integration
    • PAGÈS, G. (1997): A space vector quantization method for numerical integration, J. Comput. Appl. Math. 89, 1-38.
    • (1997) J. Comput. Appl. Math. , vol.89 , pp. 1-38
    • Pagès, G.1
  • 39
    • 2342563487 scopus 로고    scopus 로고
    • Optimal quadratic quantization for numerics: The gaussian case
    • PAGÈS, G., and J. PRINTEMS (2003): Optimal Quadratic Quantization for Numerics: The Gaussian Case, Monte Carlo Meth. Appl. 9(2), 135-168.
    • (2003) Monte Carlo Meth. Appl. , vol.9 , Issue.2 , pp. 135-168
    • Pagès, G.1    Printems, J.2
  • 41
    • 0033351917 scopus 로고    scopus 로고
    • Optimal stopping of markov processes: Hilbert space theory, approximation algorithms, and an application to pricing high-dimensional financial derivatives
    • TSITSIKLIS, J. N., and B. VAN ROY (1999): Optimal Stopping of Markov Processes: Hilbert Space Theory, Approximation Algorithms, and an Application to Pricing High-Dimensional Financial Derivatives, IEEE Trans. Automat. Cont. 44(10), 1840-1851.
    • (1999) IEEE Trans. Automat. Cont. , vol.44 , Issue.10 , pp. 1840-1851
    • Tsitsiklis, J.N.1    Van Roy, B.2
  • 42
    • 0036474580 scopus 로고    scopus 로고
    • Parabolic A.D.I. methods for pricing American option on two stocks
    • VILLENEUVE, S., and A. ZANETTE (2002): Parabolic A.D.I. Methods for Pricing American Option on Two Stocks, Math. Oper. Res. 27(1), 121-149.
    • (2002) Math. Oper. Res. , vol.27 , Issue.1 , pp. 121-149
    • Villeneuve, S.1    Zanette, A.2


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