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Academic Commons Search Resultsen-usNew Results on Deterministic Pricing of Financial Derivatives
http://academiccommons.columbia.edu/catalog/ac:110273
Papageorgiou, Anargyros; Traub, Joseph F.http://hdl.handle.net/10022/AC:P:29373Mon, 25 Apr 2011 00:00:00 +0000Computer science, Financeap206, jft2Computer ScienceTechnical reportsNew methodologies for valuing derivatives
http://academiccommons.columbia.edu/catalog/ac:110276
Paskov, Spassimirhttp://hdl.handle.net/10022/AC:P:29374Mon, 25 Apr 2011 00:00:00 +0000High-dimensional integrals are usually solved with Monte Carlo algorithms although theory suggests that low discrepancy algorithms are sometimes superior. We report on numerical testing which compares low discrepancy and Monte Carlo algorithms on the evaluation of financial derivatives. The testing is performed on a Collateralized Mortgage Obligation (CMO) which is formulated as the computation of ten integrals of dimension up to 360. We tested two low discrepancy algorithms (Sobol and Halton) and two randomized algorithms (classical Monte Carlo and Monte Carlo combined with antithetic variables). We conclude that for this CMO the Sobol algorithm is always superior to the other algorithms. We believe that it will be advantageous to use the Sobol algorithm for many other types of financial derivatives. Our conclusion regarding the superiority of the Sobol algorithm also holds when a rather small number of sample points are used, an important case in practice. We have built a software system called FINDER for computing high dimensional integrals. Routines for computing Sobol points have been published. However, we incorporated major improvements in FINDER and we stress that the results reported here were obtained using this software. The software system FINDER runs on a network of heterogeneous workstations under PVM 3.2 (Parallel Virtual Machine). Since workstations are ubiquitous, this is a cost-effective way to do very large computations fast. The measured speedup is at least $.9N$ for$N$ workstations, $N \leq 25$. The software can also be used to compute high dimensional integrals on a single workstation.Computer science, FinanceComputer ScienceTechnical reportsFaster valuation of financial derivatives
http://academiccommons.columbia.edu/catalog/ac:110279
Paskov, Spassimir; Traub, Joseph F.http://hdl.handle.net/10022/AC:P:29375Mon, 25 Apr 2011 00:00:00 +0000Monte Carlo simulation is widely used to value complex financial instruments. An alternative to Monte Carlo is to use "low discrepancy" methods. Theory suggests that low discrepancy methods might be superior to the Monte Carlo method. We compared the performance of low discrepancy methods with Monte Carlo on a Collateralized Mortgage Obligation (CMO) with ten tranches. We found that a particular low discrepancy method based on Sobol points consistently outperforms Monte Carlo. Although our tests were for a CMO, we believe it will be advantageous to use the Sobol method for many other types of instruments. We have made major improvements in published routines for generating Sobol points which we have embedded in a software system called FINDER.Computer science, Financejft2Computer ScienceTechnical reports