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Multilevel monte carlo method for Asian options under the square root process Azra May B. Kabiri

By:

Kabiri, Azra May B

Material type: Text

TextPublication details: Diliman, Quezon City : University of the Philippines Diliman ,2018. Description: vii, 64 pages 29 cmSubject(s):

Finance -- Options (specifically Asian options) -- Computational methods

LOC classification:

LG 996 2018 C6 K33

Summary: Asian options are path dependent options whose payoff depends on the average price of an asset. The price of these options are not available in closed form. The multilevel Monte Carlo method is a method for discretization with application of the standard Monte Carlo. This method is easy to implement and has less computational cost than the standard Monte Carlo method. The application of this method in pricing Asian options under geometric Brownian motion has already been studied. However, this has not been applied in pricing Asian options under the square root process. In this study, we use multilevel Monte Carlo method to price Asian options under the square root process. We use the Riemman scheme to discretize the temporal integral of the square root process and a simulation algorithm based on the transition density of the square root process to determine the values of the process at a specified time, as needed for the use of the Riemann scheme. We also determine an upper bound of the rate of mean square convergence of the Riemann sum in approximating the temporal integral of the square root process as it is significant in the analysis of the use of multilevel Monte Carlo method. The results are compared with those obtained using standard Monte Carlo in terms of computational cost.

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Holdings
Item type	Current library	Collection	Call number	Copy number	Status	Date due	Barcode
CHED Funded Research	Commission on Higher Education Thesis	Thesis and Dissertation	LG 996 2018 C6 K33 (Browse shelf(Opens below))	1	Staff collection (Restricted Access)		CHEDFR-000291
CHED Funded Research	Commission on Higher Education Digital Thesis and Dissertation	Digital Thesis and Dissertation	LG 996 2018 C6 K33 (Browse shelf(Opens below))	1	Storage Area (Restricted Access)		DCHEDFR-000040

Thesis (Master of Science in Applied Mathematics of Finance) -- University of the Philippines Diliman, May 2018.

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Asian options are path dependent options whose payoff depends on the average price of an asset. The price of these options are not available in closed form. The multilevel Monte Carlo method is a method for discretization with application of the standard Monte Carlo. This method is easy to implement and has less computational cost than the standard Monte Carlo method. The application of this method in pricing Asian options under geometric Brownian motion has already been studied.

However, this has not been applied in pricing Asian options under the square root process. In this study, we use multilevel Monte Carlo method to price Asian options under the square root process. We use the Riemman scheme to discretize the temporal integral of the square root process and a simulation algorithm based on the transition density of the square root process to determine the values of the process at a specified time, as needed for the use of the Riemann scheme. We also determine an upper bound of the rate of mean square convergence of the Riemann sum in approximating the temporal integral of the square root process as it is significant in the analysis of the use of multilevel Monte Carlo method. The results are compared with those obtained using standard Monte Carlo in terms of computational cost.

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