Modeling Volatility in the Stocks

Introduction

The study of volatility, the oscillation of the price above and below a constant path, is an important  study in the area of stocks and the price of commodities. As investors, knowing the inherent volatility that might be the stock of interest can give the investor some insight into the future price movement and behavior of the stock. If the stock has a lot of inherent volatility the investor who has a long term stake in the stock will not make irrational decisions based on the stock price movement. Traders, who profit from gyrations in the market, would like to trade in stocks that have high volatility. Traders will not enter a stock for the day if they know that the stock is not capable of much price movement  or volatility. While the study of volatile has many factors that are difficult and even impossible to transform into a value, the main four causes of volatility has been included in this study for simplification. This model is an insight into the simplified version of modeling the behavior of stocks.

Design Rationale

The design was based upon two limiting factors: complexity and validity. The first complexity deals with the fact that all the factors that occur in the market that affects investors and traders cannot be translated into netlogo. The agents in netlogo have simple rules and the interaction of multiple agents brings forth patterns and phenomenon's. The same is try in this model. The turtles of the world have simple rules to determine if they buy or sell. These rules are inherent in them from creation and form from the behavior of other turtles as the model progress. The two basic rules are the price level and price movement. Price level is the price at which a turtle is willing to buy or sell a stock, while the price movement represent the previous turtles decisions and the current turtles interpretation of those decisions. The second factor is validity. The model is as accurate to the behavior of investors and traders as it can be. It is true that investors only buy into a day and that they have a higher tolerance of price gyrations while traders are very "jumpy" and tend to buy in and sell out quickly. This is represented in the model as the turtles decisions. 

How the Model Works

There are four different scenarios preprogrammed into the model for simplifying the interface to the user. Starting from lowest to highest the scenarios represents: stock undervalued, stock overvalued, stock fairly valued, and stock slightly under valued. When the model is running depending on the scenario the investing turtles will either buy or sell if the price of the stock falls into their range or if the price movements is significant for that turtle. The traders if there will do the same but they will only buy into the market and leave right away instead of holding the stock like investors. As the price nears the fair value mark, there is some interaction that causes a slight gyration in both ways before the price is stabilized. Furthermore, there might be additional gyrations and small outbreaks followed by reversals back to the fair market value. 

Behavior of Model

The four factors that affect volatility in this model are price, shares offered, percentage of traders, and the amount of buyers and sellers. The first price is an important aspect in volatility. The present explanation of its interaction with volatility is that the higher the price the more price movements must occur before the price moves considerable percentages. This slows dampens the volatility that is inherent. For example, if the model is set on scenario 1, the stock being undervalued, price set  to 90, and the number of turtles increased to about 650. The volatility of the stock is very small relative to the price. The price almost perfectly lines up with the uniformed increase line, and on the way up the price hardly deviated from the approximate line, which is a visual clue on the dynamic volatility. The volatility  is very small during the first leg of the ascent but gets more shaky near the end. Relatively to other measures of volatility this is a very small shake. Now, decrease the price to 4 and the number of turtles to about 200. Note, decreased the amount of turtles is only done so that the volatile is more easily seen and interpreted. In this model, there is much volatility. The huge spikes up followed by slow decrease down being repeated over and over again in a cyclical fashion shows that the volatility of lesser price stocks is enormous. These gyrations are often 10 % from the fair market value of the stock. 

The next measure shares offered is important as well. This represent the depth of the stock. By depth, it means how much money does it takes to make the stock move. The amount of shares offered is this quantity. The higher means more money has to be pumped in before the stock moves while lower is the opposite. Set the price to 40, shared offered to 8500, and number of turtles to 450, and run the model. Again, the volatility is very small there isn't much fluctuation in any direction. The uniform and approx line are almost matching indication almost a perfect ascent. Now drop the shares offered to 1000 and for now keep the turtle number the same. In this example, the fair market value was reached quickly and then following were numerous gyrations at the  fair market value price. Drop the turtle number to about 65 and keep running the simulation over and over. Here, there is a lot of volatility in the stock not as much as with the price but fair amount. Notice how it crosses over and dashes back down across the approx line. This is the inherent volatility that occurs with stocks that don't require much money to move it. 

The percentage of traders is a little strange because the behaviors are not as apparent as logic dictates. Set traders to a 100 and run the simulation with a 230 turtles and shares offered at 5500, the default. The price moves back and forth over the approx line many times and the climbs are much sharper than before. Decreasing the amount of traders and rerunning the simulation doesn't really improve on the volatility as much as expected. It is only when the amount of traders is very small or zero does that the volatility is much less and dampened

The last is the amount of buyers and sellers in the market. The measure used is how much the price deviates from the fair market value and the volatility of its up trend to the closing price. Set the amount of traders to zero, set turtle number to 250, and percent buy to a 100. In this simulation all the turtles should be buying and note that the turtles decisions are based on other turtles. Notice how the turtles bought up the stock quickly to the fair market value and then the stock price just seems to plateau there. The investors know that the market is up but they are not as jumpy as the traders so no volatility on the way up. Now add some traders, about 50%. The fair market value is about 18 ~ 19, but notice how with traders the price would often go up to about 25 percent or more. This is the traders reaction to the strong draft making g it stronger before they exit at the tend and bring the price closer to the fair market value. Now, set the traders back to zero and set the percent buy to 50 and the scenario to 3, where the stock is fairly valued. Now there is a half-half ratio of investors who want to buoy and those who want to sell. The graph shows the price moving back and forth quickly but tending to be more down than up. 

There are more interesting findings at different scenarios, but the main ones have been discussed. Please feel free to play around with the settings and find situations above that are not ideal and switching something around to make it ideal. Lending to the fact that causes of volatility can be canceled.