While it may be relatively straightforward to understand how stock prices work, options pricing can be a bit more complex. Options pricing is determined by intrinsic and extrinsic values. So, how are options priced? Understanding how to calculate option prices based on the stock price using the Black-Scholes model, for instance, is something an options trader has to do, even as a beginner.
Key takeaways
- Options pricing is determined by intrinsic and extrinsic values.
- To learn how options are priced, you should know that the Black-Scholes model is a widely used formula for calculating option prices.
- Understanding how to calculate option prices can help traders make informed decisions.
How are Options Priced? An Intuitive Approach
The first thing to do when you wonder, “How are options priced?” is to understand that there are two components: intrinsic value and extrinsic value. This section will break down these elements to give you a clear understanding of how to calculate an option price based on the stock price, here’s a quick table to sum it up for you:
How Are Options Priced? Part 1: The Intrinsic Value
Intrinsic value represents the portion of the option cost that comes from the option being “in the money” (ITM). To determine the intrinsic value and understand how options are priced, we need to look at call options and put options separately:
Call Options
For call options, the intrinsic value is the current stock price minus the strike price if the option is in the money. It can be calculated using the following formula:
- Intrinsic Value (Call) = Current Stock Price – Strike Price
For example, if the current stock price is $150 and the strike price is $130, then the intrinsic value is $20. This means the option gives the right to buy the stock at $130, which is $20 less than its current market price.
Put Options
For put options, the intrinsic value is given by the strike price minus the current stock price if the option is in the money. The formula is:
- Intrinsic Value (Put) = Strike Price – Current Stock Price
For example, if the strike price is $150 and the current stock price is $130, then the intrinsic value is $20. This means the option gives the right to sell the stock at $150, which is $20 more than its current market price.
In both cases, if the calculation results in a negative number or zero, the intrinsic value is zero. This scenario occurs when the option is “out of the money” (OTM) or “at the money.” This is a key factor in understanding how options are priced.
How Are Options Priced? Part 2: The Extrinsic Value
Extrinsic value is the part of the option price that exceeds its intrinsic value. It is derived from factors other than the difference between the stock price and the strike price. For any option, the extrinsic value can be calculated as follows:
- Extrinsic Value = Option Premium – Intrinsic Value
Several factors influence extrinsic value, including:
Time Until Expiration
The more time an option has until its expiration date, the greater its extrinsic value. This is because there’s more time for the stock price to move and make the option profitable. As expiration approaches, the extrinsic value decreases, a process known as “time decay.”
Implied Volatility
Implied volatility (IV) measures the market’s forecast of a likely movement in the stock price. Higher IV increases the extrinsic value because higher volatility means a higher probability of significant price movements, making the option more valuable.
For instance, consider an option with a premium (price) of $30, an intrinsic value of $20, and 3 months until expiration. The extrinsic value will be:
- Extrinsic Value = $30 – $20 = $10
Understanding extrinsic value is crucial when deciding whether to buy or sell options, as it helps traders evaluate the potential profitability versus the option cost.
Both intrinsic and extrinsic values play vital roles in determining the overall option price. By breaking down these components, traders can make more informed decisions and better manage their risk in options trading.
Finding the Option Price from a Real-Life Example
As you see above, the formulas to compute the intrinsic and extrinsic values are not too hard. However, a couple of examples will certainly clarify how options are priced.
Calculating the Option Price of a Call Option
Let’s consider Alcoa (AA). Suppose AA is currently trading at $39.78, and you find a call option expiring in 2 weeks with a $39.50 strike price. Here is a look at what you will see from our options screener:
For the scope of this article (remember, we want to answer the question “how are options priced?”), just focus on what matters most to understand the pricing mechanism: the bid-ask prices for the option are $1.36-$1.65, so the mid-price is $1.51.
Step-by-step calculation:
- Intrinsic Value (Call) = Current Stock Price – Strike Price
- Intrinsic Value: $39.78 – $39.50 = $0.28
- Extrinsic Value = Option Premium – Intrinsic Value
- Option Premium (mid-price): $1.51
- Extrinsic Value: $1.51 – $0.28 = $1.23
Therefore, the option cost consists of a $0.28 intrinsic value and a $1.23 extrinsic value. This shows how to calculate an option price based on the stock price and understand its components.
Calculating the Option Price of a Put Option
Now, let’s look at a put option for the same stock, AA. Suppose AA is still trading at $39.78, and you find a put option expiring in 2 weeks with a $40 strike price, just like you can see from the screenshot below:
In this context, once again, the only thing you need to know from the image above is that the bid-ask prices for the option are $1.15-$1.43, so the mid-price is $1.29. So, how are options priced? Let us guide you with a short step-by-step process below.
Step-by-step calculation:
- Intrinsic Value (Put) = Strike Price – Current Stock Price
- Intrinsic Value: $40.00 – $39.78 = $0.22
- Extrinsic Value = Option Premium – Intrinsic Value
- Option Premium (mid-price): $1.29
- Extrinsic Value: $1.29 – $0.22 = $1.07
Thus, the option cost includes a $0.22 intrinsic value and a $1.07 extrinsic value. Both values help explain how to calculate the option price and evaluate the option cost.
Using real-time examples like these helps illustrate how to calculate option prices based on stock prices. It highlights the importance of understanding the option value formula and the role that intrinsic and extrinsic values play in determining the overall option price. This is crucial for comprehending how options are priced.
Option Value Formula – The Black & Scholes Model
The intrinsic and extrinsic value matter is quite intuitive. However, when looking up the “how are options priced?” question, you will often find articles mentioning the Black-Scholes model. This is a rather advanced mathematical model that is frequently used in options pricing. We won’t bore you with the exact equation, as this is a beginner-oriented text, but let us tell you more about each variable. For now, consider this synthetic table that summarizes all you should know about the model:
Stock Price
How to calculate an option price based on the stock price? Well, the stock price, per se, is not sufficient to give you the option price. However, the stock price is still one of the most critical factors in the Black-Scholes model. Here’s how it impacts different participants:
- Call Buyers: The higher the stock price, the higher the option cost because the call buyer has the right to buy the stock at a lower strike price, which can lead to profits.
- Put Buyers: The lower the stock price, the higher the option cost since the put buyer can sell the stock at a higher strike price, leading to potential gains.
- Call Sellers: Higher stock prices increase losses for call sellers because they might have to sell the stock at a lower price than the market rate.
- Put Sellers: Lower stock prices increase losses for put sellers as they might have to buy the stock at a higher price than the market rate.
Strike Price
Strike price significantly affects how options are priced:
- Call Buyers: A lower strike price makes the option more valuable because it allows buying the stock below its market price.
- Put Buyers: A higher strike price makes the option more valuable since it enables selling the stock above its market price.
- Call Sellers: Opposite to call buyers, a higher strike price reduces the loss risk since it is less likely they will need to sell below market price.
- Put Sellers: A lower strike price reduces the loss risk as it is less likely they will need to buy above market price.
Time to Expiration
Time to expiration impacts the option value through time decay:
- Call Buyers: Longer times until expiration increase the option price because there’s more opportunity for the stock price to move favorably.
- Put Buyers: Similarly, more time until expiration increases the option price for puts as well.
- Call Sellers: Shorter times until expiration reduce the loss risk since the likelihood of significant price movement decreases.
- Put Sellers: The same applies to put sellers, as shorter durations mean less the loss risk of adverse price movements.
Implied Volatility
Implied volatility reflects market expectations of future stock price fluctuations:
- Call Buyers: Higher implied volatility increases option prices as it suggests a greater chance of the stock price rising above the strike price.
- Put Buyers: Likewise, higher implied volatility raises put option prices due to increased likelihood of the stock price dropping below the strike price.
- Call Sellers: Lower implied volatility decreases losses as it indicates less potential for significant upward price movements.
- Put Sellers: Similarly, lower implied volatility means lower losses.
Risk-Free Interest Rate
The risk-free interest rate is also a factor in the Black-Scholes model:
- Call Buyers: Higher risk-free rates increase call option prices because holding cash becomes more expensive, making the option more attractive.
- Put Buyers: Conversely, higher rates decrease put option prices as they make holding cash less costly.
- Call Sellers: Lower risk-free rates reduce call option prices, benefiting sellers by decreasing the likelihood of adverse price movements.
- Put Sellers: Similarly, lower rates increase put option prices, creating more favorable conditions for put sellers.
Understanding these variables in the option value formula helps you better understand how to calculate option prices based on the stock price and other factors using the Black-Scholes model, and learn how options are priced.
