An analysis of the Libor and Swap market models for pricing interest-rate derivatives

Mutengwa, Tafadzwa Isaac (2011) An analysis of the Libor and Swap market models for pricing interest-rate derivatives. Masters thesis, Rhodes University.

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Abstract

This thesis focuses on the non-arbitrage (fair) pricing of interest rate derivatives, in particular caplets and swaptions using the LIBOR market model (LMM) developed by Brace, Gatarek, and Musiela (1997) and Swap market model (SMM) developed Jamshidan (1997), respectively. Today, in most financial markets, interest rate derivatives are priced using the renowned Black-Scholes formula developed by Black and Scholes (1973). We present new pricing models for caplets and swaptions, which can be implemented in the financial market other than the Black-Scholes model. We theoretically construct these "new market models" and then test their practical aspects. We show that the dynamics of the LMM imply a pricing formula for caplets that has the same structure as the Black-Scholes pricing formula for a caplet that is used by market practitioners. For the SMM we also theoretically construct an arbitrage-free interest rate model that implies a pricing formula for swaptions that has the same structure as the Black-Scholes pricing formula for swaptions. We empirically compare the pricing performance of the LMM against the Black-Scholes for pricing caplets using Monte Carlo methods.

Item Type:Thesis (Masters)
Uncontrolled Keywords:LIBOR market model, Monte Carlo method, Interest rates, Derivative securities
Subjects:Q Science > QA Mathematics > QA273 Probabilities. Mathematical statistics
Divisions:Faculty > Faculty of Commerce > Statistics
Faculty > Faculty of Science > Statistics
Supervisors:Szyszkowski, Irek
ID Code:2969
Deposited By: Ms Chantel Clack
Deposited On:11 Jun 2012 07:12
Last Modified:11 Jun 2012 07:12
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