Probablity and Statistics (7)

Probability and Statistics (Part 7)

By Madison Nef

The Stock Market

Probability and statistics play a large role in the stock market, and in predicting what the price of a stock will be on any given day. The stock market is constantly changing, and since the price of stocks are determined by humans, the price of a stock is very unpredictable. Louis Bachelier developed one of the first methods for figuring out where a stock’s price would end up using a random walk- starting the walk at the stock’s current price and then letting it go. This technique was logical, but it lacked any underlying global trend… so it didn’t work.

When you try to figure out the price of a stock, expected value is a key component in figuring out how much the stock will rise or fall. Naturally we don’t know for sure how much it will, but we make and apply estimates that rely on underlying trends. Since Bachelier’s model lacked that, it was unreliable.  

What is an option?

An option is a form of contract used in stock trading. Once bought, it gives it’s buyer a certain set of rights. The rights given are to buy a security, commodity, or a stock at a specified price and at a specified future date. This can go two ways, because after buying an option, it means that no matter what price the stock is trading at at the specified date, you have to pay the given amount for it. It can be good, because you could be getting an $100 stock for $10… but it could also go against you and force you to pay $10 for a $2 stock.

Options can also be used as insurance, of sorts. If copper is trading at 100 per share today, but you are worried about it going up within the time you need it, you can buy an option allowing you to purchase it in 3 months time at the same price that it currently is. 

How much should you pay for an option?
The price you pay for an option depends on the probability of it reaching it's target price.  Usually with options, there is an agreement that for every certain amount the stock makes, you (the option-holder) give the seller a fraction of money. Let's say that for every $100, you owe the seller $1. If there is a 9/10 chance that it will reach 100, or a 90% chance of you getting $1. Since this is the case, .90 is a good price to charge for the option.

 However, the buyer will have a different view of the probability. The buyer will see it as a 50% chance of having to pay the dollar… but also a 50% chance of never having to pay the dollar. Therefore, the stock's expected value to the buyer is .50.

 So what can we do to get rid of the risk of paying $1?

 If you buy 1/100 of a share of the stock today, then you OWN 1/100 of a share of that stock.  If the share goes up to 100, then you automatically have enough money to pay off the dollar.

Maddie