Option volatility study from a data analysis perspective

In this research, we will investigate both financial option pricing models and link the theory to real market performance studies. By combining traditional option pricing theory and real market data analysis, we propose that, in the real world, some behaviour of the financial option price is strongly associated with the local maximum or minimum of asset price. Firstly, we analyse some mathematical formulas and theorems to understand how to simulate the random process of asset price movement. Based on these foundations we discuss Black-Scholes option pricing model, stochastic volatility models and numerical methods to price options. Secondly, we utilise Monte-Carlo simulation to learn about the mechanisms of European option pricing with different models. Subsequently, regression analysis is presented in preparation for studying real market data analysis. Thirdly, we use nine years of real market data to reveal the relationship among variables involved in pricing European options. It will be concluded that the implied Black-Scholes risk calculated using real world call options and put options correlates with asset prices in opposing ways. For call options: with dominant probability, the instantaneous implied option risk and the asset price have a negative correlation; whereas with dominant probability, one-day earlier implied option risk and the asset price have a positive correlation. Put options are the exact opposite. Finally, we conclude that when the real market option prices are undervalued, they have the ability to catch local extreme values of asset prices statistically.