Implied adjusted voladility functions : empirical evidence using Australian index options

Abstract

Volatility implied by an option pricing model is seen as the market participants’ assessment of volatility. With the implied volatility as a significant aspect particularly in option valuation, this study examines the implied volatility smiles and term structures in the Australian Standard and Poor/Australian Stock Exchange (S&P/ASX) 200 index options over the course of 2001-2010, including the global financial crisis in the mid-2007 until the end of 2008. This study utilised the models of Leland (1985) and Leland (2007).The results show that the implied volatility rises significantly during the crisis period, which is more than the rate found before the crisis. Given the fact that the pricing biases of Leland option pricing models and the implied volatility structure of the option are related, secondly, this research adapts and modifies the models in Peña, Rubio and Serna (1999) and Engström (2002), in order to analyse whether the use of the implied adjusted volatility functions delivers an improvement in the option valuation accuracy of the index options. Both in- and out-of-sample resulted in approximately similar pricing error along the different Leland’s models. This study employs 2-step process. Results indicate that different implied adjusted volatility functions best explain the index options in different period of intervals (pre-, during and post-crisis). This shows that it is tremendously important to identify the intervals beforehand in investigating the implied adjusted volatility function.