dc.contributor.advisor Witbooi, Peter dc.contributor.author Don, Marlon Junaide dc.date.accessioned 2020-02-17T10:47:49Z dc.date.available 2020-02-17T10:47:49Z dc.date.issued 2019 dc.identifier.uri http://hdl.handle.net/11394/7113 dc.description >Magister Scientiae - MSc en_US dc.description.abstract The risk associated with currency exposure is one of the main sources of risk in terms of internationally en_US diversi ed portfolios. Controlling the risk is important for improving the performance of international investments. One approach to hedging against exchange rate exposure is by employing financial derivatives, particularly, foreign currency options. Currency options provide insurance against unfavorable exchange rate fluctuation, but also make provision to lock in a pro t when the exchange rate fluctuation are favorable. However, these instruments cannot be traded or managed without the relevant valuation techniques. In this dissertation we discuss one of the approaches to cover the risk associated with currency exposure. In particular, we focus on the partial differential equation (PDE) valuation of currency options by employing various finite difference schemes. We commence by introducing the mathematical tools required for the valuation of financial derivatives. Thereafter we study the valuation of European options. This involves deriving the famous Black-Scholes PDE for pricing options on stocks that do not yield dividends. Using the Black-Scholes PDE we derive the Black-Scholes formula for pricing European options. This derivation involves transforming the Black-Scholes PDE into the heat equation and by solving the heat equation we obtain the Black-Scholes formula. After completing the pricing of European options we now move to the pricing of American options. The early exercise facility associated with American options, leads to a free boundary problem which makes the pricing process of American options a challenging task. As in the case of the European options, we first derive the Black-Scholes inequality for American options and then transform this inequality for application to the heat equation to value American options. In the absence of an explicit formula for pricing American options we use numerical methods. Thus, we discuss the finite difference methods quite extensively with a focus on the implicit and Crank-Nicholson finite difference methods. dc.language.iso en en_US dc.publisher University of the Western Cape en_US dc.subject Heat diffusion equation en_US dc.subject Early exercise boundary en_US dc.subject Black-Scholes model en_US dc.subject Free boundary problem en_US dc.subject Explicit difference method en_US dc.title Valuation of options for hedging against exchange rate exposure en_US dc.rights.holder University of the Western Cape en_US
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