# Black-Scholes Option Pricing Model

In this video I discuss the famous equation from Black-Scholes…

VIDEO SUMMARY

In this video we are going to discuss the Black-Scholes pricing model. This is a mathematical formula first published in 1973 by Fischer Black and Myron Scholes. And they received the Nobel Prize in 1997 for their work.

What this equation does is explains mathematically how you value the option to purchase something. Not the purchasing value, but the option to purchase something. I’m going to put up the equation. Now this gets into some complicated math, but you don’t have to understand advanced mathematics to understand this equation. Because there is some simple main concepts in this equation that you can use. What this formula is describing is a fairly simple idea. The value of an option is based on the riskiness of the payout. So you look at the expected payout, and you apply some discount for risk. So the more unlikely something is, the bigger the discount, and the cheaper the option compared to the payout.

So let’s look at an option to purchase a stock. If it is likely the option is going to payout, it will be a fairly expensive option, because you won’t get much of a discount for risk. If it is less likely the option is going to payout, it will be a fairly cheap option, because of the much bigger discount for risk.

The way the Black-Scholes model calculates this, is it looks at the value of options based on five major variables: volatility, time to maturity, current price, exercise price, risk free rate. So we have these variables, and we are trying to determine the likely state at a specific point in the future. Considering time, a longer time span will be more uncertain than a shorter time span. What you will notice, is that as the time span shrinks to zero, the option price gets closer and closer to the expected payout. One millisecond before the exercise date, the prices will be virtually the same. Then we look at the difference between the current stock price and the option strike price, or the price where you can exercise the option. Let’s assume you can only exercise the option if the price is \$110, and the current price is \$90. The closer the price gets to \$110, the more valuable the option becomes.

So let’s use some actual numbers. You can find calculators for the equation online. Let’s assume both the Stock asset price and the option strike price are the same at \$100. Let’s say the maturity is one year, the risk-free rate is 5% and the volatility is 20%. A European Call Option would be worth \$10.45. So we are at \$100 right now, and the value of being able to purchase \$100 one year from now would be roughly \$10.

Let’s look at this another way. You can look at a table of call pricing for different stock prices.

• The table uses the same assumptions as the previous example
• If the stock value is \$50, it is unlikely you will make the exercise price of \$100, so the option is worthless
• If the stock is \$100, the value is 10.45 as we said. But notice that the price at expiration would be zero. Because you would buy the stock at \$100 and be able to sell at \$100 so you make no profit. That is why midway through the year, the price would be less.
• However, as the price increases you make more money at expiration. So at \$125 you would make \$25, by buying at \$100 and selling at \$125. So the option 1 year out is worth more money.
• In the same way when the stock price is at \$150, you would make \$50 at expiration and the option 1 year out is worth even more.

Now in a practical sense, you won’t often find someone willing to sell you an option with a strike price at \$100 when the stock price is already at \$150, but this is just an example to show you the concept.

So the main concept is this: You assess the situation for risk. The more unlikely a payout, the less value you would be willing to pay for it. It’s very easy to use these Black-Scholes calculators, which enables you to use advanced mathematics to guide your financial decisions.