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Pricing European and American bond options under the Hull-White extended Vasicek Model

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dc.contributor.advisor Rapoo, E.M.
dc.contributor.author Mpanda, Marc Mukendi
dc.date.accessioned 2014-04-15T10:47:03Z
dc.date.available 2014-04-15T10:47:03Z
dc.date.issued 2013-01
dc.identifier.citation Mpanda, Marc Mukendi (2013) Pricing European and American bond options under the Hull-White extended Vasicek Model, University of South Africa, Pretoria, <http://hdl.handle.net/10500/13346> en
dc.identifier.uri http://hdl.handle.net/10500/13346
dc.description.abstract In this dissertation, we consider the Hull-White term structure problem with the boundary value condition given as the payoff of a European bond option. We restrict ourselves to the case where the parameters of the Hull-White model are strictly positive constants and from the risk neutral valuation formula, we first derive simple closed–form expression for pricing European bond option in the Hull-White extended Vasicek model framework. As the European option can be exercised only on the maturity date, we then examine the case of early exercise opportunity commonly called American option. With the analytic representation of American bond option being very hard to handle, we are forced to resort to numerical experiments. To do it excellently, we transform the Hull-White term structure equation into the diffusion equation and we first solve it through implicit, explicit and Crank-Nicolson (CN) difference methods. As these standard finite difference methods (FDMs) require truncation of the domain from infinite to finite one, which may deteriorate the computational efficiency for American bond option, we try to build a CN method over an unbounded domain. We introduce an exact artificial boundary condition in the pricing boundary value problem to reduce the original to an initial boundary problem. Then, the CN method is used to solve the reduced problem. We compare our performance with standard FDMs and the results through illustration show that our method is more efficient and accurate than standard FDMs when we price American bond option. en
dc.format.extent 1 online resource (xiii, 120 leaves ) : colored illustrations
dc.language.iso en en
dc.subject Term structure equation en
dc.subject Hull-White extended Vasicek model en
dc.subject European and American bond option en
dc.subject Diffusion equation en
dc.subject Artificial Boundary method en
dc.subject Coupon bearing and zero-coupon bond option
dc.subject Finite Difference Methods and Artificial Boundary method
dc.subject.ddc 332.6323
dc.subject.lcsh Bonds -- Prices -- United States -- Mathematical models en
dc.subject.lcsh Bonds -- Prices -- Europe -- Mathematical models en
dc.title Pricing European and American bond options under the Hull-White extended Vasicek Model en
dc.type Dissertation en
dc.description.department Mathematical Sciences en
dc.description.degree M. Sc. (Mathematics)


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