A two-factor model for low interest rate regimes

Publication Type:
Journal Article
Asia-Pacific Financial Markets, 2005, 11 (1), pp. 107 - 133
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This paper derives a two-factor model for the term structure of interest rates that segments the yield curve in a natural way. The first factor involves modelling a non-negative short rate process that primarily determines the early part of the yielf curve and is obtained as a truncated Gaussian short rate. The second factor mainly influences the later part of the yield curve via the market index. The market index proxies the growth optimal portfolio (GOP and is modelled as a aquared Bessel process of dimension four. Although this setup can be applied to any interest rate environment, thsi study focusses in the difficult but important case where the short rate stays close to zero for a prolonged period of time. FOr the proposed model, an equivalent risk neutral martingale measure is neither possile nor required. Hence we use the benchmark approach where the GOP is chosen as numeraire. Fair derivative prices are then calculated via conditional expectations under the real world probability measure. Using this methodology we derive pricing functions for zero coupon bonds and options on zero coupon bonds. The proposed model naturally generates yield curve shapes commonly observed in the market. More importantly, themodel replicates the ket features of the inetrest rate cap market for economies with low inetrest rate regimes. In particular, the implied volatility term structure displays a consistent downward slope from extremely high levels of volatility together with a distinct negative skew.
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