Least-squares polynomial quasi-Monte Carlo for short-term generation unit asset valuation

Valuation of American options is a difficult and challenging problem encountered in financial engineering. Longstaff and Schwartz [Longstaff, FA and ES Schwartz (2001). Valuing American Options by Simulation: A Simple Least-squares Approach, Review of Financial Studies, 14(1), 113–147.] Proposed the least-squares Monte Carlo (LSM) method for valuing American options. As this approach is intuitive and easy to apply, it has received much attention in the finance literature. However, a drawback of the LSM method is the low efficiency. In order to overcome this problem, we propose the least-squares randomized quasi-Monte Carlo (LSRQM) methods which can be viewed as a use low-discrepancy sequences as a variance reduction technique in the LSM method for valuing American options in this paper. Numerical results demonstrate that our proposed LSRQM methods are more efficient than the LSM method in terms of the valuation accuracy, the computation time and the convergence rate.

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Zastosowanie modeli wyceny aktywów CAPM, market timing i DLM do oceny inwestycji w spółki innowacyjne

Ekonomia ◽

10.19195/2658-1310.26.1.7 ◽

2020 ◽

Vol 26 (1) ◽

pp. 109-124

Author(s):

Agnieszka Panek

Keyword(s):

Least Squares ◽

Dynamic Models ◽

Market Timing ◽

Distributed Delays ◽

Asset Valuation ◽

Short Term ◽

Rates Of Return ◽

Timing Model ◽

The Impact

The aim of this article is to verify whether investment innovation managers, due to their specificity, should in particular have the ability to sense short-term trends and how this affects the effectiveness and risk of such investments.Empirical research was based on the use of asset valuation models of the classic CAPM, MT (market timing) model, and DLM (dynamic models with distributed delays), the parameters of which were estimated using the Classical Least Squares Methods, based on logarithmic rates of return of companies listed on the WSE in the period from 1st February 2015 to 2nd February 2020.The significantly negative value of the MNK — the estimator of parameter of the MT model, means that managers do not have the ability to sense short-term changes in the market regardless of the sector in which they operate. Furthermore, the impact of delays on market rates of return has been observed. The presented results may constitute recommendations for managers in terms of valuation of MT’s assets and skills and their impact on the effectiveness and risk of innovative investments.

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A New Quasi-Monte Carlo Technique Based on Nonnegative Least Squares and Approximate Fekete Points

Numerical Mathematics Theory Methods and Applications ◽

10.4208/nmtma.2016.m1516 ◽

2016 ◽

Vol 9 (4) ◽

pp. 640-663 ◽

Cited By ~ 3

Author(s):

Claudia Bittante ◽

Stefano De Marchi ◽

Giacomo Elefante

Keyword(s):

Monte Carlo ◽

Monte Carlo Method ◽

Least Squares ◽

Space Dimension ◽

Main Idea ◽

Approximation Order ◽

Nonnegative Least Squares ◽

Fekete Points ◽

3 Dimensional ◽

Quasi Monte Carlo

AbstractThe computation of integrals in higher dimensions and on general domains, when no explicit cubature rules are known, can be ”easily” addressed by means of the quasi-Monte Carlo method. The method, simple in its formulation, becomes computationally inefficient when the space dimension is growing and the integration domain is particularly complex. In this paper we present two new approaches to the quasi-Monte Carlo method for cubature based onnonnegative least squaresandapproximate Fekete points. The main idea is to use less points and especiallygood pointsfor solving the system of the moments.Good pointsare here intended as points with good interpolation properties, due to the strict connection between interpolation and cubature. Numerical experiments show that, in average, just a tenth of the points should be used mantaining the same approximation order of the quasi-Monte Carlo method. The method has been satisfactory applied to 2 and 3-dimensional problems on quite complex domains.

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