Accounting for roll-over risk in the pricing of caps and floors

Master Thesis

2022

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The peak of the global financial crisis necessitated practitioners to rethink the single curve approach to pricing interest-rate derivatives. This was as a result of a violation in spot-forward parity relationships thereby prompting markets to realise the presence of a new type of risk and subsequently the need for a multi-curve pricing framework. The roll-over risk framework is one that accounts for liquidity constraints and default risk thereby providing a cogent explanation for the spotforward parity violation that led to the need for multiple curves. The primary objective of this work is to price XIBOR-based caps and floors under a framework which accounts for roll-over risk. This reformulation of interest-rate derivatives is achieved using Fourier Transform methods as well as Monte Carlo simulations for comparison. We found that the results obtained using the two approaches were comparable even though the two methods are different in nature. This agreement in prices is compelling evidence that the computations are correct.
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