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Numerical Valuation of High Dimensional Multivariate American Securities

Jerome Barraquand, Didier Martineau
1995 Journal of Financial and Quantitative Analysis  
However, these methods cannot be used for high-dimensional problems, since their memory requirement is exponential in the number of risk sources.  ...  Our numerical experiments show that the method is practical for pricing American claims depending on up to 400 risk sources.  ...  We wish to thank Thierry Pudet for reviewing an earlier draft.  ... 
doi:10.2307/2331347 fatcat:lj2qarsd5fcttot67mwbit6cuy

Page 829 of Mathematical Reviews Vol. , Issue 2000a [page]

2000 Mathematical Reviews  
Analysis of the SSAP method for the numerical valuation of high-dimensional multivariate American securities. (English summary) Algorithmica 25 (1999), no. 1, 75-98.  ...  Summary: “We consider a new numerical method developed by Barraquand and Martineau for the pricing of American securities For the web version of Mathematical Reviews, see http: //www.ams.org/mathscinet  ... 

Implied Stopping Rules for American Basket Options from Markovian Projection [article]

Christian Bayer, Juho Häppölä, Raúl Tempone
2017 arXiv   pre-print
In high dimensions, nonlinear partial differential equation methods for solving the problem become prohibitively costly due to the curse of dimensionality.  ...  The resulting near-optimal early-exercise boundary is used to produce an exercise strategy for the high-dimensional option, thereby providing a lower bound for the price of the American basket option.  ...  We thank Professors Ernesto Mordecki and Fabián Crocce for their feedback which significantly improved this manuscript. Gillis Danielsen provided much-valued practitioner's views.  ... 
arXiv:1705.00558v4 fatcat:ompm6zsu2jdbvnjacjb5eswuru

Implied stopping rules for American basket options from Markovian projection

Christian Bayer, Juho Häppölä, Raúl Tempone
2018 Quantitative finance (Print)  
In high dimensions, nonlinear partial differential equation methods for solving the problem become prohibitively costly due to the curse of dimensionality.  ...  The resulting near-optimal early-exercise boundary is used to produce an exercise strategy for the high-dimensional option, thereby providing a lower bound for the price of the American basket option.  ...  We thank Professors Ernesto Mordecki and Fabián Crocce for their feedback which significantly improved this manuscript. Gillis Danielsen provided much-valued practitioner's views.  ... 
doi:10.1080/14697688.2018.1481290 fatcat:3ox4yognrnbshnntpzcgizjl3a

Pricing high-dimensional Bermudan options using the stochastic grid method

Shashi Jain, Cornelis W. Oosterlee
2012 International Journal of Computer Mathematics  
Finance 7 (2004), pp. 35-72], and stratified state aggregation along the pay-off method of Barraquand and Martineau [Numerical valuation of high-dimensional multivariate American securities, J.  ...  We focus on the numerical results for high-dimensional problems such as max option and arithmetic basket option on several assets, with basic error analysis for a general one-dimensional problem. 1187  ...  Mapping high-dimensional state to single-dimensional g(·)-space In an approach similar to Barraquand and Martineau's SSAP method [3] , we reduce the dimensions of the problem by using g(S t i+1 ) rather  ... 
doi:10.1080/00207160.2012.690035 fatcat:4smszcq675bonlz57yx3czzmmq

Page 2539 of Mathematical Reviews Vol. 32, Issue Index [page]

Mathematical Reviews  
Analysis of the SSAP method for the numerical valuation of high-dimensional multivariate American securities.  ...  (English summary) 2000d:91064 Buff, Robert Worst-case scenarios for American options.  ... 

Page 2117 of Mathematical Reviews Vol. 32, Issue Index [page]

Mathematical Reviews  
Analysis of the SSAP method for the numerical valuation of high-dimensional multivariate American securities. (English summary) Algorithmica 25 (1999), no. 1, 75-98.  ...  Numer. Methods Fluids 31 (1999), no. 4, 747-765. (Summary) 2000f:76085 76M20 — (with Lee, Shyi-Shiun; Lee, Shih-Tuen) Numerical solution of the system of Vlasov-Poisson equations.  ... 

Efficient Numerical Methods for Stochastic Differential Equations in Computational Finance

Juho Happola
2017
In this dissertation, we present novel effective methods for evaluating Quantities of Interest relevant to computational finance when the state of the system is described by an SDE.  ...  Numerical approximation methods are typically needed in evaluating relevant Quantities of Interest arising from such models.  ...  The authors would like to thank Arturo Kohatsu-Higa for his helpful suggestions for improvements in the proof of Theorem 6.2.1.  ... 
doi:10.25781/kaust-71t82 fatcat:dgrmduu3azegpp7wx2w43tlkya