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Bergische Universität Wuppertal
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Bergische Universität Wuppertal
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Bilateral German-South African Project
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The popular Black-Scholes model for option pricing has been criticized over the years owing to the fact that the constant interest rate, one of the market's assumptions, has to be modelled as a function of time. The emergence of certain derivative securities or interest rate contingent claims like caps, swaps, bond options, etc, whose payoffs fully depend on interest rates posed the need for interest rate modelling. Financial analysis such as the quantification of interest rate risks and the valuation of interest rate contingent claims need to be considered using the term structure model. These contingent claims have been identified by market participants as essential risk management tools. Interest rate swaps for instance, have been considered as useful liquid derivatives that are found in the fixed-income markets, which have helped investors and market practitioners to hedge and speculate interest rate. They have also provided access to cheap funds through the concept of comparative advantage and thus, their valuations are of paramount importance.
In the pricing of these securities, certain models have been employed to capture the stochastic nature and impact of interest rate. These stochastic short interest rate models such as Hull-White, Cox-Ingersoll-Ross (CIR), Dothan, Vasicek, etc, have been used to obtain the dynamics of interest rates under the risk-neutral pricing measure. They have been used to price bonds, bond options, barrier options, European options, Treasury bond options. In the valuation of foreign exchange options, Ahlip & Rutkowski (2003) employed the Heston stochastic volatility model, together with the CIR model. In this research project however, we aim at using the CIR model to value the barrier options and interest rate swaption prices.
Furthermore, from a partial differential perspective, the resulting partial differential equations arising from the conventional problems of these derivative pricing will be discretised and solved using higher order numerical methods. We propose to use higher order numerical methods to evaluate the corresponding initial value problems, in conjunction with the boundary and terminal conditions. The significance of this work will aim at obtaining the values of swaptions and barrier options, defined on a stochastic interest rate from higher order numerical perspective.
German team:
South African team: German institution:
South African Institution:
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