Dissertation writing help - A Two-Regime Markov-Chain Model for the Swaption Matrix

Custom Dissertation Writing Service on models for pricing complex interest rate

The most commonly used models for pricing complex interest rate products are LIBOR Market Models. These models describe the evolution of a set of forward LIBOR rates. For a given set of LIBOR rates such a model is defined by the term structures of their volatilities and the correlations among these rates. It is therefore of vital importance to use a parameterization for these quantities that is able to capture the important features of the market the model is calibrated to. Since this is usually the swap market a good parameterization of the LIBOR Market Model should also be a good model for the volatility term structure of forward rates, i.e. the swaption matrix which contains all available information about the volatility term structure in the swap market.

It is a well known feature of the interest rate markets that in times of market turmoil the volatility term structure undergoes sudden changes in shape when the market enters these excited regimes. After a short period the market is normal again which also switches the shape of the volatility term structure back to normal. Kainth and Rebonato proposed an approach to capture this market feature in a LIBOR Market Model. They use the most common parameterization of the volatility term structure to explain the normal market situation and the excited regime each with one set of stochastic parameters. In the current work a more simplistic approach is taken by keeping the parameters constant. The model captures the switches between the two regimes by transition probabilities.

After introducing the setup of a LIBOR Market Model the parameterization of the forward rate volatility term structure is presented and it is shown how this relates to swap rates. The algorithms for calibrating to caplets as well as swaptions are discussed. The sensitivities of the model parameters are systematically analyzed. By allowing the fit to vary several settings of parameters the quality of the calibration to swaption data is assessed. Finally, a very promising and simple parameterization of the model that captures the regime switches is fitted with four parameters to a series of monthly market data spanning a period of four years that adds major financial events. This model yields a dramatic improvement over the model without regime switches in the description of the swaption matrix without increasing the number of fitting parameters. While the latter approach yields an average deviation of 76 basis points in implied volatility the new model obtains 63. Dramatic improvements are obtained during and after periods of market turbulence. In addition the fit parameters are a lot more stable over time which implies lower re-hedging costs when using this model.