Closing Remarks


Initial attempts to model the term structure of interest rates developed along the same lines as stock price models. These term structure models are based within an economic setting where Brownian motions give rise to random shocks. Most models make the assumption that the entire term structure is driven by the short-term interest rate of interest. Some models allow this short-term interest rate to be driven by underlying economic variables , hence introducing multiple factors. Other models introduce a second factor such a long interest rate or short-term interest rate volatility, modelling these two factors as mutually dependent processes.

The early models are concerned with determining an appropriate level of the term structure in such a way that it is consistent with the underlying economic model. This makes it difficult to incorporate information from an initial observed term structure and hence to reproduce the market prices of securities.

A change of perspective introduced the need for a model to perfectly fit an initial term structure and reproduce market-observed prices of vanilla instruments. The focus shifted to calibrating model parameters in such a way as to account for, rather than explain, the shape of the yield curve. This has remained the driving force behind current research into term structure modelling. Given the market-observed prices of vanilla securities, practitioners need to price more exotic instruments in a consistent manner.

Models allowing the instantaneous short-term interest rate to be the single driving factor of the entire yield curve are quite restrictive , in part because returns on bonds of all maturities are instantaneously perfectly correlated. This is unrealistic and imposes restrictions on the resulting yield curve which makes many market-observed term structures difficult, if not impossible , to replicate.

The HJM framework introduces a new perspective to term structure modelling. By allowing the instantaneous forward rate to be the fundamental variable, they are able to specify the entire term structure at any one time. This is in contrast to models where the instantaneous short-term interest rate, a single point on the yield curve, is the fundamental variable.

However, the HJM approach still shares a fundamental problem with all its predecessors. The state variables are in fact unobservable: instantaneous short and/or forward interest rates do not trade in the market. Hence to calibrate these models one must perform a translation of unobservable model variables to appropriately selected market proxies. Among others, this is one of the landmark features of the approach taken by BGM, who develop a model which determines the stochastic process followed by a market traded rate of interest: the discretely compounded LIBOR. This introduces yet another dimension to term structure models since a trader may directly express her/his views on movements in market traded quantities . The BGM model becomes a tool whereby a trader's views are directly translated into option prices.

The older more traditional models such as Vasicek and CIR still have a place in the financial markets. Movements in market variables, that cannot be replicated within the model, will show up as anomalies and mispricing. This may lead users to perform a more detailed analysis of the causes of such anomalies. Therefore, the qualitative insight they provide about the dynamics of the yield curve can be beneficial for the understanding of more advanced models.




Interest Rate Modelling
Interest Rate Modelling (Finance and Capital Markets Series)
ISBN: 1403934703
EAN: 2147483647
Year: 2004
Pages: 132

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