Multifactor implied volatility functions for HJM models

Abstract

This study evaluates two one-factor, two two-factor, and two three-factor implied volatility functions in the HJM class, with the use of eurodollar futures options across both strike prices and maturities. The primary contributions of this article are (a) to propose and test three implied volatility multifactor functions not considered by K. I. Amin and A. J. Morton (1994), (b) to evaluate models using the AIC criteria as well as other standard criteria neglected by S. Y. M. Zeto (2002), and (c) to find that multifactor models incorporating the exponential decaying implied volatility functions generally outperform other models in fitting and prediction, in sharp contrast to K. I. Amin and A. J. Morton, who find the constantvolatility model superior. Correctly specified and calibrated simple constant and square-root factor models may be superior to inappropriate multifactor models in option trading and hedging strategies.

Implied deterministic volatility functions: An empirical test for Euribor options

“…Generally, all models show various magnitudes of prediction error across moneyness so that the moneyness bias appears across all IDVF models. The moneyness bias is also found by Kuo and Paxson (2006), who conducted HJM models using Eurodollar options.…”

“…The HJM model encompasses the Libor market models proposed by Brace, Gatarek, and Musiela (1997), Jamshidian (1997), and Miltersen, Sandmann, and Sondermann (1997) and the discrete tenor string models of Longstaff, Santa-Clara, and Schwartz (2001). Early empirical tests for HJM models generally focus on IDVFs of one-factor models (such as Amin & Morton, 1994;Flesaker, 1993), but more recent empirical findings show that one-factor models are outperformed by multifactor models (see Driessen, Klaassen, & Melenberg, 2003;Gupta & Subrahmanyam, 2005;Kuo & Paxson, 2006;Zeto, 2002). For this reason, this study also considers two-and threefactor models.…”

“…Amin and Morton (1994) and Zeto (2002) reported that the volatility of out-of-the-money (OTM) options is greater than at-the-money (ATM) and in-the-money (ITM) options, indicating a pattern of volatility skew or smile. Kuo and Paxson (2006) documented that this pattern depends upon the models used. The findings of Amin and Morton (1994) and Kuo and Paxson (2006) also displayed the volatility function differing across time-to-maturity of options.…”

“…Kuo and Paxson (2006) documented that this pattern depends upon the models used. The findings of Amin and Morton (1994) and Kuo and Paxson (2006) also displayed the volatility function differing across time-to-maturity of options.…”

“…Black's implied volatility in the final column shows that volatility smile and volatility term structure are observed in the Euribor options. Zeto (2002), Kuo and Paxson (2006), and Kuo and Lin (2007) test several IVDFs based on their choices with selected data. However, none of their tests consider the relationship between option volatility and its underlying price, shown in Figures 1 and 2.…”