In: Applied mathematical finance, 2011, vol. 18, no. 4, p. 277-289
Over the years a number of two-factor interest rate models have been proposed that have formed the basis for the valuation of interest rate contingent claims. This valuation equation often takes the form of a partial differential equation, that is solved using the finite difference approach. In the case of two factor models this has resulted in solving two second order partial derivatives...
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The CKLS (1992) short-term risk-free interest rate process leads to valuation model for both default free bonds and contingent claims that can only be solved numerically for the general case. Valuation equations of this nature in the past have been solved using the Crank Nicholson scheme. In this paper, we introduce a new numerical scheme – the Box method, and compare it with the traditional...
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The application of Green’s theorem to free boundary problems in option pricing leads to a new metric to measure numerical errors. Free boundaries for a variety of interest rate models are computed more accurately through minimization of our metric.
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Less expensive than standard options, barrier options have become very popular in recent years as useful hedging instruments for risk management strategies. Thus far valuation approaches have largely focused on equity barrier options, where in certain instances analytical expressions may be available. In this paper we use Monte Carlo procedure to value barrier options based on the Chan, Karolyi,...
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