Two-Factor Model for Low Interest Rate Regimes

Shane Miller and Eckhard Platen ()

No 130, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

Abstract: 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 yield 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 squared Bessel process of dimension four. Although this setup can be applied to any interest rate environment, this study focuses on 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 niether possible 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, the model replicates the key features of the interest rate cap market for economies with low interest 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.

Keywords: interest rate term structure; growth optimal portfolio; fair pricing; total market price for risk; interest rate caps (search for similar items in EconPapers)
JEL-codes: G10 G13 (search for similar items in EconPapers)
Pages: 28 pages
Date: 2004-08-01
New Economics Papers: this item is included in nep-fin and nep-fmk
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

Published as: Miller, S. and Platen, E., 2004, "A Two-Factor Model for Low Interest Rate Regime", Asia-Pacific Financial Markets, 11(1), 107-133.

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Journal Article: A Two-Factor Model for Low Interest Rate Regimes (2004)
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