An Examination Of The Value-At-Risk Volatility Relationship In The Options Market: New Evidence On Mispricing In The Black-Scholes Model

Given the price of a call or put option, the Black-Scholes (1973) implied volatility is the unique volatility parameter to be put into the Black-Scholes formula to give the same price as the option price. A prediction of the Black-Scholes formula is that all option prices on the same underlying stock with different exercise prices should have the same implied volatility. But in practice, as our results demonstrated, when the Black-Scholes formula is inverted to imply volatilities from reported option prices, the volatility estimates seem to be different across exercise prices. Furthermore, this article is concerned with the link between the implied volatility and the actual volatility of the underlying stock. In deriving this link, Value at Risk (VaR) was proposed to examine underlying stock volatilities and their forecasts. In the forecasting of volatility, the Value at Risk (VaR) approach was found to be a significant forecasting tool of future underlying stocks' volatility; and therefore the significance could be confirmed for the implied volatility forecasting.