Implied volatility functions of BS versus Leland: empirical evidence from Australian index option market

• Main Authors: Harun, Hanani Farhah, Abdullah, Mimi Hafizah
• Format: Conference or Workshop Item
• Language: English
• Published: 2022
• Subjects: QA Mathematics
• Online Access: http://irep.iium.edu.my/102453/18/102453_%20Implied%20volatility%20functions%20of%20BS%20versus%20Leland.pdf; http://irep.iium.edu.my/102453/
• Institution: Universiti Islam Antarabangsa Malaysia

The Black-Scholes-Merton (BSM) model is a fundamental model in pricing option. The implied volatility for the option’s returns on the same underlying asset is assumed to be constant or invariant of the strike price or time to maturity of the options in this model. However, the implication of this assumption in real option market is misleading. The volatility surface is not flat. This study aims to investigate the accuracy valuation of implied volatility derived from the BSM option pricing model than of the Leland models. The investigation is conducted based on smile pattern and respective pricing performance of the model functions. The implied volatility is examined in the context of Standard and Poor/Australian Stock Exchange (S&P/ASX) 200 index call and put options over the course of 2001-2010, which covers the global financial crisis in the mid-2007 until the end of 2008. The congruent visual 3-dimensional plot indicates that the BSM implied volatility and Leland implied adjusted volatility for both call and put options are consistent with each other. Yet, the Leland option pricing models resulted in better pricing performance than the BSM model based on the RMSE value. The in-sample test indicates the model which includes the blended effect of both option moneyness and time-to-maturity explain the data better, whereas parsimonious model shows the least estimation error in out-of-sample test.