Real estate market

The HJM framework has the advantage that it allows seamless extension from one to several sources of uncertainty. The choice of number of volatility factors to use is driven by a number of often conflicting considerations. Additional sources of uncertainty introduce additional degrees of freedom to the evolution of the term structure which allows decorrelation [...]

Principal component analysis (PCA) may be performed on a time series of historical term structure data in an attempt to identify the dominant factors driving its evolution. PCA produces factors maximising successive contributions to overall variance. Hence these factors attempt to explain the diagonal of the covariance matrix. The resulting factors are surrogate volatility factors [...]

Calibration to historical data could be performed in a manner similar to that described for implied volatility data. First a specific formulation of the HJM model is chosen, that is a specific volatility structure is imposed by specifying the number of volatility factors and their specific functional form. Time series of historical term structure data [...]