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LIBOR Market Model
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The LMM is an effective framework for the pricing of §interest rate derivatives, not least because it §models observable market quantities. §§There exist three main techniques for incorporating §a volatility smile/skew in any modelling framework: §allowing a local volatility function, stochastic §volatility and jump dynamics. Here various ways to §incorporate smile/skew are studied, loosely based on §the above three approaches.§§Both the CEV and displaced-diffusion processes give §rise to an implied volatility skew. The two §processes produce closely matching prices for §European call options over a variety of strikes and §maturities. Here, this similarity in prices is §analytically quantified using asymptotic expansion §techniques.§§A regime shifting model may be viewed as a reduced §form of a full stochastic volatility model. A two §state, continuous time Markov Chain model, §characterised by a time dependent volatility in each §state is implemented. §§Finally, the Levy LIBOR model is considered as a §generalisation of jump processes.
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