Mispricing On Black-Scholes Option Pricing Model: Evidence For BHP Company

This paper studies the reason why the Black-Scholes Option Pricing Model misprices options. The assumption of constant volatility in Black-Scholes Model is the main reason for why the model misprices option contracts. We use the data from BHP company in 1995-2001 and calculate the implied volatility. By comparing the implied volatility calculated from actual option price and the assumed volatility in the model, it is found that Black-Scholes Model does underprice the Out-of-The-Money options and overprice the In-The-Money options because of the wrong assumption on the volatility. This paper further discovers that short-term options are more severely mispriced by the Black-Scholes Model as the magnitude of wrong estimation of volatility decreased with the increase of the time to maturity. It is organized as follows:The first part, including one chapter, presents the academic foundation of this research. First,we presents the three objectives of this paper: 1. how the Black-Scholes model mispriced the option, 2. how the model underpriced the In-The-Money option and overpriced the Out-of-The-Money option, and 3. the relationship between the option price and the maturity of the option. Chapter 1 introduces the definiens .The second part, including three chapters, this part is the keystone of this paper. Our research workflows are: 1. Collect the required data; 2. Filter out the unnecessary data; 3. Calculate the Implied Volatility; 4. Separate the data into different bins; 5. Plot the graph to see the relationship; 6. Verify the Hypotheses. Chapter 2 gives the research hypotheses. Chapter 3 collects the data. Chapter 4 analyze the data and plot the graph.The third part, including chapter 5, giving the conclusions. Three findings can be concluded from this paper: 1. The assumption of constant volatility in Black-Scholes Model is wrong; 2. The model overpriced the ITM call option and underpriced the OTM call option. The only conclusion that can make is that the common sense of the way to misprice by Black-Scholes Model is not suitable for Australian option market, as least for BHP options; 3. The magnitude and way of the option mispricing is related to the term to expiration.