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dc.contributor.advisorPatidar, Kailash C.
dc.contributor.advisorGhomrasni, Raouf
dc.contributor.authorKazeem, Funmilayo Eniola
dc.date.accessioned2015-07-30T11:22:14Z
dc.date.available2015-07-30T11:22:14Z
dc.date.issued2014
dc.identifier.urihttp://hdl.handle.net/11394/4349
dc.description>Magister Scientiae - MScen_US
dc.description.abstractIn Monte Carlo path simulations, which are used extensively in computational -finance, one is interested in the expected value of a quantity which is a functional of the solution to a stochastic differential equation [M.B. Giles, Multilevel Monte Carlo Path Simulation: Operations Research, 56(3) (2008) 607-617] where we have a scalar function with a uniform Lipschitz bound. Normally, we discretise the stochastic differential equation numerically. The simplest estimate for this expected value is the mean of the payoff (the value of an option at the terminal period) values from N independent path simulations. The multilevel Monte Carlo path simulation method recently introduced by Giles exploits strong convergence properties to improve the computational complexity by combining simulations with different levels of resolution. This new method improves on the computational complexity of the standard Monte Carlo approach by considering Monte Carlo simulations with a geometric sequence of different time steps following the approach of Kebaier [A. Kebaier, Statistical Romberg extrapolation: A new variance reduction method and applications to options pricing. Annals of Applied Probability 14(4) (2005) 2681- 2705]. The multilevel method makes computation easy as it estimates each of the terms of the estimate independently (as opposed to the Monte Carlo method) such that the computational complexity of Monte Carlo path simulations is minimised. In this thesis, we investigate this method in pricing path-dependent options and the computation of option price sensitivities also known as Greeks.en_US
dc.language.isoenen_US
dc.publisherUniversity of the Western Capeen_US
dc.subjectMonte Carlo simulationen_US
dc.subjectComputational costen_US
dc.subjectRisk-neutral measureen_US
dc.titleMultilevel Monte Carlo simulation in options pricingen_US
dc.rights.holderUniversity of the Western Capeen_US


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