Analyzing the effects of Bollinger bands on the probability of stock options using support vector machines

The purpose of this research is to efficiently analyze certain data provided and to see if a useful trend can be observed as a result. This trend can be used to analyze certain probabilities. There are three main pieces of data which are being analyzed in this research: The value for δ of the call and put option, the %B value of the stock, and the amount of time until expiration of the stock option. The %B value is the most important. The purpose of analyzing the data is to see the relationship between the variables and, given certain values, what is the probability the trade makes money. This result will be used in finding the probability certain trades make money over a period of time.

Since options are so dependent on probability, this research specifically analyzes stock options rather than stocks themselves. Stock options have value like stocks except options are leveraged. The most common model used to calculate the value of an option is the Black-Scholes Model [1]. There are five main variables the Black-Scholes Model uses to calculate the overall value of an option. These variables are θ, δ, γ, v, and ρ. The variable, θ is the rate of change in price of the option due to time decay, δ is the rate of change of the option’s price due to the stock’s changing value, γ is the rate of change of δ, v represents the rate of change of the value of the option in relation to the stock’s volatility, and ρ represents the rate of change in value of the option in relation to the interest rate [2]. In this research, the %B value of the stock is analyzed along with the time until expiration of the option. All options have the same δ. This is due to the fact that all the options analyzed in this experiment are less than two months from expiration and the value of δ reveals how far in or out of the money an option is.

The machine learning technique used to analyze the data and the probability



is support vector machines. Support vector machines analyze data that can be classified in one of two or more groups and attempts to find a pattern in the data to develop a model, which reliably classifies similar, future data into the correct group. This is used to analyze the outcome of stock options.