LIBOR Market Model

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.

Autorentext

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.

Klappentext

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.