Description
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. Simona has worked in the finacial services industry for a number of years and holds a PhD in Mathematical Finance from the University of Oxford.
