Implied deterministic volatility functions: An empirical test for Euribor options

Abstract

This study proposes the implied deterministic volatility function (IDVF) for the volatility as the function of moneyness and time in the Heath, Jarrow, and Morton (1992) model to price and hedge Euribor options across moneyness and maturities from 1 January 2003 to 31 December 2005. The IDVF models are extended to two-and three-factor models, indicating that they are potential candidates for interest rate risk management. Based on the criteria of in-sample fitting, prediction, and hedging, it is found that two-factor IDVF models provide the best in-sample and prediction performance, whereas three-factor IDVF models yield the best results for hedging. Correctly specified multifactor models with the volatility as the function of moneyness and time can replace inappropriate onefactor models.

Survey sentiment and interest rate option smile

“…9 The mathematical expressions of model-free skewness and their computation procedure can be found in Bakshi et al (2003) and Han (2008) so they are not shown here. 10 Recent literature shows that multifactor models outperform single-factor models (See Driessen, Klaassen, & Melenberg, 2003;Gupta and Subrahmanyam, 2005;Kuo and Wang, 2009;Zeto, 2002. 11 For the specification of volatility function, we use models 1, 5, and 7 from Kuo and Wang (2009) to represent one-, two-, and three-factor models, respectively.…”

“…10 Recent literature shows that multifactor models outperform single-factor models (See Driessen, Klaassen, & Melenberg, 2003;Gupta and Subrahmanyam, 2005;Kuo and Wang, 2009;Zeto, 2002. 11 For the specification of volatility function, we use models 1, 5, and 7 from Kuo and Wang (2009) to represent one-, two-, and three-factor models, respectively. 12 Across the sample period, the mean, median, and standard deviation of μ is −0.00016, −0.00042, and 0.00152.…”

Pricing and hedging volatility smile under multifactor interest rate models

“…Kuo and Paxson (2006) and Kuo and Lin (2007) found similar results using multifactor models in Eurodollar and Euribor options markets. Kuo and Wang (2009) found a downward shape of implicit volatilities in the Euribor options market between January 1 2003 and December 31 2005, with a tendency of higher implicit volatility for OTM options than at-the-money (ATM) and ITM options. But this tendency was asymmetric around zero moneyness, indicating that volatility is not constant, as the model assumed.…”

“…In recent studies, Kuo and Paxson (2006), Kuo and Lin (2007), and Kuo and Wang (2009) focused on Gaussian interest rate models and found mispricing for options across strikes. Under the Gaussian assumption, the implied volatilities across strikes are skewed.…”

“…Dumas et al (1998) reject all models due to instability of deterministic volatility functions. Similarly, all deterministic volatility functions are rejected by Kuo and Wang (2009) using single and multifactor HJM models for interest rate options. Dumas et al (1998) and Kuo and Wang (2009) indicate that although models with deterministic volatility may entirely capture the reported structure of option prices, they are unstable between in-sample and out-of-sample estimates.…”