Interpolation of Forward Rates in the LIBOR Market Model

Since its development in 1997, the LIBOR market model has gained widespread use in interest rate modelling, largely owing to its consistency with the Black futures formula for pricing interest rate caps and floors. From its original construction(s), the LIBOR market model specifies a discrete set of forward rates that correspond to a fixed tenor structure, e.g. market tenors. This implies the pricing of interest rate contingent claims is restricted to claims with cashflow dates that coincide with the fixed tenor structure. In this light, several interpolation schemes have been suggested to handle the pricing restrictions, however at the cost of introducing possible arbitrage opportunities. The present dissertation studies four such interpolation schemes, paying particular attention to arbitrage-free interpolation schemes: Piterbarg deterministic interpolation, Schlogl deterministic interpolation, Schlogl stochastic interpolation, and Beveridge-Joshi stochastic interpolation.

Grantor

African Institute of Financial Markets and Risk Management

Year dc:date.issued

2020

Author dc:creator

• Mbele, Buhlebezwe Bandile Sthombe

Advisor dc:contributor.advisor

• McWalter, Thomas

• Mathematical Finance

Handle dc:identifier.uri

http://hdl.handle.net/11427/32836

OAI identifier oai:identifier

oai:open.uct.ac.za:11427/32836