The Black Model for Interest Rate Derivatives Essay

The Black Model for Interest Rate Derivatives - Essay Example Over the last two and half decades, finance has experienced tremendous and exciting developments especially with reference to derivatives markets. One of the reasons explaining the idea of tremendous and exciting developments within financial sector is the fact that both hedger and speculators within financial markets find it attractive to trade derivate specifically assets rather than trading on the assets themselves (Gupta and Subrahmanyam. 2005). Development of derivatives is considered as one of the most successful upcoming within capital markets (Brigo and Mercurio 2001). Within derivatives, there are three main traders; hedger, speculators, and arbitrageurs. Application of derivatives within financial markets helps in eliminating or reducing risk associated with the fluctuations in the prices of assets. Overview and Development of Black Model Financial markets have experienced an increase in the interest-rate contingent claims that include amongst others caps, swaptions, bond o ptions, mortgage-backed securities, as well as captions. The main problem however that is currently experienced is the development of effective and efficient instruments for valuing such contingent claims. Different models have been developed and used in an attempt to find the best and most effective one. Nonetheless, there has been indifference amongst traders on the model effective and efficient enough to help in measuring, controlling, and supervision of interest-rate risks. Hull (234) identifies Black-Scholes Model as a major innovation is pricing of various stock options. During the early 1970s, Fischer Black, Myron Scholes, and Robert Merton developed a model that can be used effectively and efficiently in pricing stock options (Hull p234). In addition, Clewlow and Strickland (2000) confirm that Black Model has been frequently used in valuing bond options due to its effectiveness and efficiency. Black Model borrows extensively from the Black-Scholes Model (Black, 1976). Actual ly the former is an extension and modification of the latter. Black Model for pricing stock options assumes that the value of an interest rate, bond price, or other variables at a given time is future follows a lognormal distribution. One of the reasons that necessitated the extension and modification of the Black-Scholes Model to Black Model is the difficulty experienced in valuing interest rate derivatives as opposed to valuing foreign exchange derivative (Hull p508). The difficulty is experienced due to a number of reasons such as complications within the behavior of individual interest rate as compared to stock prices of exchange rates (Hull p508). In addition, there has been the need to develop a model that will help in evaluating the behavior of the entire derivate including the zero-coupon yield rate. Consequently, Black Model was developed, which derives most of its assumptions from the Black-Scholes-Merton differential equation that represents the model. For instance, the m odel assumes that there are no transactional costs of taxes involved in applying the model to value stock options (Black, 1976). What’s more, the model assumes that there are no dividends obtained during the derivatives’ life coupled with facts that arbitrate opportunities are termed as riskless. In this model, another important assumption is that the rate of risk-free interest is constant and equals