Pricing of a European Call Option Under a Local Volatility Interbank Offered Rate Model

Abstract

Financial derivatives offer a great investment opportunity when accurately priced. Developing countries such as Kenya are yet to establish the mechanisms of trading in derivatives. This research seeks to demonstrate how advances in developed money markets can be reflected towards the establishment of derivatives markets in developing countries. To achieve this, the dynamics of the inter bank offered interest rates in developing markets and developed markets are compared. The two interbank offered rates are found to be similar under an appropriate martingale measure. A European caplet for the developed money market is priced using the local volatility interbank offered rate model. The accuracy of the local volatility interbank offered rate is found to be better when benchmarked against the industry accepted Black’s model. The local volatility model is used as it captures the volatility smiles more efficiently in one sweep.