Top

Published in:

2024 | OriginalPaper | Chapter

Theory and Construction of Quasi-Monte Carlo Rules for Asian Option Pricing and Density Estimation

Authors : Alexander D. Gilbert, Frances Y. Kuo, Ian H. Sloan, Abirami Srikumar

Published in: Monte Carlo and Quasi-Monte Carlo Methods

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

In this paper we propose and analyse a method for estimating three quantities related to an Asian option: the fair price, the cumulative distribution function, and the probability density. The method involves preintegration with respect to one well chosen integration variable to obtain a smooth function of the remaining variables, followed by the application of a tailored lattice Quasi-Monte Carlo rule to integrate over the remaining variables.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

previous chapter Unbiased Likelihood Estimation of Wright–Fisher Diffusion Processes

next chapter Application of Dimension Truncation Error Analysis to High-Dimensional Function Approximation in Uncertainty Quantification

Achtsis, N., Cools, R., Nuyens, D.: Conditional sampling for barrier option pricing under the LT method. SIAM J. Financ. Math. 4, 327–352 (2013)MathSciNetCrossRef

Gilbert, A.D., Kuo, F.Y., Sloan, I.H.: Equivalence between Sobolev spaces of first order dominating mixed smoothness and unanchored ANOVA spaces on \({\mathbb{R} }^d\). Math. Comp. 91, 1837–1869 (2022)MathSciNetCrossRef

Gilbert, A.D., Kuo, F.Y., Sloan, I.H.: Analysis of preintegration followed by quasi-Monte Carlo integration for distribution functions and densities. SIAM J. Numer. Anal. 61, 135–166 (2022)MathSciNetCrossRef

Glasserman, P.: Monte Carlo Methods in Financial Engineering. Springer, Berlin (2003)CrossRef

Glasserman, P., Staum, J.: Conditioning on one-step survival for barrier option simulations. Oper. Res. 49, 923–937 (2001)CrossRef

Griebel, M., Kuo, F.Y., Sloan, I.H.: The smoothing effect of the ANOVA decomposition. J. Complexity 26, 523–551 (2010)

Griebel, M., Kuo, F.Y., Sloan, I.H.: Note on “The smoothing effect of integration in \(R^d\) and the ANOVA decomposition’’. Math. Comp. 86, 1847–1854 (2017)MathSciNetCrossRef

Griewank, A., Kuo, F.Y., Leövey, H., Sloan, I.H.: High dimensional integration of kinks and jumps—smoothing by preintegration. J. Comput. Appl. Math. 344, 259–274 (2018)MathSciNetCrossRef

Kuo, F.Y., Sloan, I.H., Schwab, C.: Quasi-Monte Carlo finite element methods for a class of elliptic partial differential equations with random coefficients. SIAM J. Numer. Anal. 50, 3351–3374 (2012)MathSciNetCrossRef

10.

Kuo, F.Y., Sloan, I.H., Wasilkowski, G.W., Waterhouse, B.J.: Randomly shifted lattice rules with the optimal rate of convergence for unbounded integrands. J. Complexity 26, 135–160 (2010)MathSciNetCrossRef

11.

L’Ecuyer, P., Lemieux, C.: Variance reduction via lattice rules. Manag. Sci. 46, 1214–1235 (2000)

12.

L’Ecuyer, P., Puchhammer, F., Ben Abdellah, A.: Monte Carlo and quasi-Monte Carlo density estimation via conditioning. INFORMS J. Comput. 34, 1729–1748 (2022)MathSciNetCrossRef

13.

Liu, S.: Conditional quasi-Monte Carlo with constrained active subspaces (2022). arXiv:2212.13232

14.

Liu, S., Owen, A.B.: Preintegration via active subspaces. SIAM J. Numer. Anal. 61, 495–514 (2023)MathSciNetCrossRef

15.

Nichols, J.A., Kuo, F.Y.: Fast CBC construction of randomly shifted lattice rules achieving \(\cal{O} (n^{-1 + \delta })\) convergence for unbounded integrands over \({\mathbb{R} }^s\) in weighted spaces with POD weights. J. Complexity 30, 444–468 (2014)MathSciNetCrossRef

16.

Weng, C., Wang, X., He, Z.: Efficient computation of option prices and Greeks by quasi-Monte Carlo method with smoothing and dimension reduction. SIAM J. Sci. Comput. 39, B298–B322 (2017)MathSciNetCrossRef

Title: Theory and Construction of Quasi-Monte Carlo Rules for Asian Option Pricing and Density Estimation
Authors: Alexander D. Gilbert
Frances Y. Kuo
Ian H. Sloan
Abirami Srikumar
Publisher: Springer International Publishing
Book: Monte Carlo and Quasi-Monte Carlo Methods
Print ISBN: 978-3-031-59761-9

Electronic ISBN: 978-3-031-59762-6

Copyright Year: 2024
DOI: https://doi.org/10.1007/978-3-031-59762-6_13

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"