11.10 Conclusion


11.10 Conclusion

HJM develop a new methodology for modelling the term structure of interest rates. They make use of a process describing the evolution forward rates to derive a methodology for contingent claim valuation, which is free from arbitrage and independent of the market prices of risk. By modelling forward rates, the stochastic behaviour of the entire term structure, not just the short-term interest rate, is modelled at any point in time. This allows information from the term structure to be used to eliminate the dependence on market prices of risk.

For the single factor case, the HJM formulation does not add much to previously developed models such as the Hull-White extended Vasicek and BDT models. In fact, the complexity of the calibration and contingent claim valuation procedures may act as a deterrent. However, within a multi-factor context the elegance of the HJM framework is undeniable. The methodology provides a coherent framework allowing easy incorporation of additional factors. The resulting increase in computational time tends to be linear (as opposed to exponential increases exhibited by other models). This is because the non-Markovian nature of the model makes Monte Carlo simulation the valuation technique of choice. This allows easy valuation of path -dependent options, but does become problematic for American-style contingent claims.




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