Through this project, we will predict the price of an option on a security for N days in the future according to the current set of observed features derived from the time of expiration, the price of the security, and volatility. The question would be: what model should we use for such an option pricing model? The answer is that there are actually many; Black-Scholes stochastic partial differential equations (PDE) is one of the most recognized.
Where V is the price of the option as a function of stock price S and time t, r is the risk-free interest rate, and σ σ (displaystyle sigma) is the volatility of the stock. One of the key financial insights behind the equation is that anyone can perfectly hedge the option by buying and selling the underlying asset in just the right way without any risk. This hedge implies that there is only one right price for the option, as returned by the Black-Scholes formula.
Consider a January maturity call option on an IBM with an exercise price of $95. You write a January IBM put option with an exercise price of $85. Let us consider and focus on the call options of a given security, IBM. The following chart plots the daily price of the IBM stock and its derivative call option for May 2014, with a strike price of $190:
Now, what will be the profit and loss be for this position if IBM is selling at $87 on the option maturity date? Alternatively, what if IBM is selling at $100? Well, it is not easy to compute or predict the answer. However, in options trading, the price of an option depends on a few parameters, such as time decay, price, and volatility:
- Time to expiration of the option (time decay)
- The price of the underlying security
- The volatility of returns of the underlying asset
A pricing model usually does not consider the variation in trading volume in terms of the underlying security. Therefore, some researchers have included it in the option trading model. As we have described, any RL-based algorithm should have an explicit state (or states), so let us define the state of an option using the following four normalized features:
- Time decay (timeToExp): This is the time to expiration once normalized in the range of (0, 1).
- Relative volatility (volatility): within a trading session, this is the relative variation of the price of the underlying security. It is different than the more complex volatility of returns defined in the Black-Scholes model, for example.
- Volatility relative to volume (vltyByVol): This is the relative volatility of the price of the security adjusted for its trading volume.
- Relative difference between the current price and the strike price (priceToStrike): This measures the ratio of the difference between the price and the strike price to the strike price.
The following graph shows the four normalized features that can be used for the IBM option strategy:
Now let us look at the stock and the option price dataset. There are two files IBM.csv and IBM_O.csv contain the IBM stock prices and option prices, respectively. The stock price dataset has the date, the opening price, the high and low price, the closing price, the trade volume, and the adjusted closing price. A shot of the dataset is given in the following diagram:
On the other hand, IBM_O.csv has 127 option prices for IBM Call 190 Oct 18, 2014. A few values are 1.41, 2.24, 2.42, 2.78, 3.46, 4.11, 4.51, 4.92, 5.41, 6.01, and so on. Up to this point, can we develop a predictive model using a QLearning, algorithm that can help us answer the previously mentioned question: Can it tell us the how IBM can make maximum profit by utilizing all the available features?
Well, we know how to implement the QLearning, and we know what option trading is. Another good thing is that the technologies that will be used for this project such as Scala, Akka, Scala Play Framework, and RESTful services are already discussed in Chapter 3, High-Frequency Bitcoin Price Prediction from Historical Data. Therefore, it may be possible. Then we try it to develop a Scala web project that helps us maximize the profit.