Option Pricing Model: Understanding the Black – Scholes Model

Option Pricing Model

Written by Aryan Agarwal

December 1, 2020

Understanding option pricing is the key to success in this business; if you understand the effects of implied volatility and time decay on option prices, you’ll understand our edge in trading. In this article, we’ll discuss option pricing using the Black-Scholes model, explaining how it can be simplified into two concepts: intrinsic and extrinsic value.

Intrinsic Value and Extrinsic Value

Put simply, stock prices are based on company profit and the cash they generate for their shareholders. If a company produces good earnings and attracts investors, its stock price increases. If a company loses money or goes into bankruptcy, its stock price decreases.

Option pricing, however, is more complicated and depends on more than one factor. Option prices are determined using a mathematical model called the Black-Scholes model.

This model takes into account five different inputs, all of which can change the price of the option. Often, multiple factors shift simultaneously to produce changes in the option price.

We don’t need to calculate the option price using a complex formula to make money. We just need to understand the five inputs into the formula and how each factor can affect the price of an options.

These are the five inputs into the Black-Scholes model:

 Stock Price
● Strike Price
● Time to Expiration
● Volatility
● Interest Rates

Stock price and strike price work together to calculate intrinsic value. Time to expiration, volatility, and interest rates form extrinsic value. The option price, or premium, is the sum of intrinsic and extrinsic value.

Option premium = Intrinsic value + extrinsic value

Intrinsic Value

The intrinsic value of an option is calculated by comparing the stock price to the strike price.

For example, a call option with a strike price of $50 and a stock price of $55 then the intrinsic value is $5. This is because you could use the call contract to buy stock at $50 and subsequently sell the shares in the open market for $55, producing an instant payoff of $5.

If instead the stock price was $40, the call option with a strike price of $50 would have a $0 intrinsic value. There is no reason to use the call contract to buy shares at $50 when you could buy it for $40 in the open market, so the call option itself has no intrinsic value.

The same rule, but in reverse, is true of put contracts. A put contract with a strike price of $50 and stock price trading at $40 has an intrinsic value of $10.

You could buy shares in the open market for $40, then subsequently sell the shares using the put contract at a higher price of $50, producing a $10 payoff.

However, if the stock price was $55, there would be $0 of intrinsic value because it would be preferable to sell stock in the open market for $55 instead of using the put contract.

As option sellers, we don’t want the options that we sell to have intrinsic value. We want the option contracts that we sell to eventually expire worthless, and this only occurs if the option does not have intrinsic value.

Stock Price

The stock price of the underlying asset is the first input into the model. A stock with a higher price ($200) will have a higher option premium relative to a lower price stock ($50).

If we think of options as insurance contracts, a more expensive stock requires a greater insurance premium to cover larger damages.

Stock price fluctuations also affect option premiums. For call options, as the stock price goes up, call premiums go up. As the stock price goes down, call premiums also go down. For put options, however, as the stock price goes up, put premiums go down. Lastly, as the stock price goes down, put premiums go up.

Stock price direction is random, so this input into the model is the least predictable. We do not try to predict stock direction because we do not have an edge here.

As we continue through the other inputs into the model, we will see how we can use options to our advantage.

Strike Price

The strike price is the price at which the option buyer and seller agree to buy or sell stock. For example, you can buy a call option that gives you the right to buy 100 shares of stock at $50. In this case, $50 is the strike price.

The strike price in relation to the stock price determine intrinsic value, as described earlier.

Extrinsic Value

Time to expiration, volatility, and interest rates make up the extrinsic value of an option. As options sellers, extrinsic value is where we put our focus.

Extrinsic value is the “extra” value of the price of an option above the intrinsic value. An option without any intrinsic value can still have value because of the extrinsic portion of the option price.

Options without any intrinsic value can still have value because of the chance that it will gain intrinsic value in the future.

Time to Expiration

Time to expiration is the third factor for option pricing. Time to expiration is how many days that remain in the life of the contract.

An option contract with more days until expiration will have a higher premium, all else being equal. If we think of options contracts like insurance policies, the more time there is until the policy expires, the greater the chance that an accident will occur.

Similarly, more time until expiration equals a greater chance the option seller will have to make good on the contract. An option seller, like an insurance seller, will require a higher option premium to be fairly compensated for the added risk of duration.

option pricing time to expiration

When buying options, time works against you. With every day that ticks by, the option contract loses value. This is one of the reasons we at Financetasy choose to be option sellers.

As option sellers, we let time work in our favor. Each day that goes and the option contract that we sold loses value, we can eventually buy it back at a lower price for a profit.

Volatility

Volatility is how much movement a stock price has during a certain timeframe. For an options seller, volatility is the most important factor to consider, and it is where we gain an edge in the market.

A stock that moves wildly from $50 to $100 over a year has a higher volatility than a stock that moves from $50 to $55 over the same timeframe.

All else being equal, a stock with high volatility will have a higher option premium. Volatility plays a factor in the price of an option because of the more volatile the stock, the greater the chance that the option contract will become valuable to the option buyer.

The option buyer must pay for this advantage.

At Financetasy, we sell options in order to take advantage of a few characteristics of volatility. When volatility is high, option prices will also be high because there is greater uncertainty.

In this type of environment, we can sell more expensive options. As option sellers, we want to sell what is more expensive. Volatility tends to revert to the mean or average; high volatility tends to fall back to the mean. When this occurs, options prices subsequently decrease, which is good for options sellers because we can later close our position for a profit.

Interest Rates

Interest rates are the last input into the option pricing model, but rarely make a difference for short-term trades. Increasing interest rates increase the price of call options, but lower the price of put options.

Interest rates affect the price of options because they simulate leverage and borrowing. Option contracts represent ownership of 100 shares of stock.

However, when you purchase an options contract, you don’t have to pay the full price of 100 shares. Typically, you only pay around 20% of the full value of 100 shares when purchasing an option contract.

Because you don’t pay the full amount upfront, you are levered.

Because interest rates play such a small role in the type of trades we make (which are <60 days), interest rates do not come into our decision-making process.

Conclusion

The main five factors which factor into option pricing all boil down to intrinsic and extrinsic value. Intrinsic value is determined by the stock price and the strike price.

As options sellers, we want our option premiums to become worthless, so we do not want intrinsic value.

On the other hand, extrinsic value, determined by time to expiration, volatility, and interest rates, is what keeps options sellers in business through time decay and volatility.

Understanding option pricing is a key aspect of successful options trading.

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