New methodologies for valuing derivatives

Title:

New methodologies for valuing derivatives

Author(s):

Paskov, Spassimir

Date:

1996

Type:

Technical reports

Department:

Computer Science

Permanent URL:

http://hdl.handle.net/10022/AC:P:29374

Series:

Columbia University Computer Science Technical Reports

Part Number:

CUCS02996

Publisher:

Department of Computer Science, Columbia University

Publisher Location:

New York

Abstract:

Highdimensional 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 costeffective 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.

Subject(s):

Computer science
Finance
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