The Cost of Options
December 20, 2024·7 min read
The Cost of Options
Before we dive in, let's establish some terminology.
Key Terminology
- Underlying asset — The asset that the option is based on.
- Call option — An option that gives the holder the right to buy the underlying asset at a specified price. Think of it as a ceiling.
- Put option — An option that gives the holder the right to sell the underlying asset at a specified price. Think of it as a floor.
- Strike price — The price at which the underlying asset can be bought or sold. If a call option has a strike price of 100, it means that the buyer of the call option has the right to buy at 100. If a put option has a strike price of 100, it means that the buyer of the put option has the right to sell at 100.
- Expiration date — The date on which the option expires.
- Volatility — The degree of variation in the price of the underlying asset.
- In the money — An option is in the money when its strike price is in favor of the holder. For holders of call options, this means the strike price is below the current price of the underlying asset. For holders of put options, this means the strike price is above the current price of the underlying asset. If, at expiration date, the option is in the money, the holder of the option will receive the difference between the current price of the underlying asset and the strike price. This portion is called the intrinsic value. The holder receives the intrinsic value. The seller of the option will pay the intrinsic value.
- Out of the money — An option is out of the money when its strike price is not in favor of the holder. For holders of call options, this means the strike price is above the current price of the underlying asset. For holders of put options, this means the strike price is below the current price of the underlying asset. If, at expiration date, the option is out of the money, the holder of the option will receive nothing. The seller of the option will pay nothing. The option has no intrinsic value.
- At the money — An option is at the money when its strike price is equal to the current price of the underlying asset. Unfortunately for the holder, if an option expires at the money, the holder receives nothing. For example, if the strike price is 100.00 and, at expiration date, the underlying asset closes at 100.00, the intrinsic value is zero.
- Premium — The premium is the price (cost) of the option. It is the amount that the holder of the option pays to the seller of the option. This is why options are often compared to "insurance" - you pay a premium to protect yourself from potential losses. This assumes you start losing money if the underlying asset moves against your position, and the farther it goes in the money, the more you would be losing had you not purchased the option. Buyers of calls seek protection from rising prices (consumers/buyers of the underlying asset). Buyers of puts seek protection against falling prices (producers/sellers of the underlying asset).
The estimation of the premium is the focus of this article, and the premium is what reflects the cost of the option.
There is a multidimensional aspect to the price of options. The option premium depends on:
Strike Price
Level of the strike price relative to the current price of the underlying asset.
Generalizations
- The further the strike price is from the current price of the underlying asset, the less expensive the option will be.
- The closer the strike price is from the price of the underlying asset, the more expensive it will be.
In the case of call options with strike of 100.00:
As the underlying falls in price and gets farther away from 100.00, the call will decay in price. The call is further and further out of the money. All of its value is time value, this time value is the cost of the option. In this case, premium = time value = cost of the option.
As the underlying rises and approaches, but does not cross 100.00, the call will increase in price. The call is getting closer to at the money. All of its value is time value, this time value is the cost of the option. Also, in this case, premium = time value = cost of the option.
Once the underlying crosses and trades above 100.00, a portion becomes in the money, creating some intrinsic value. This intrinsic value is part of the premium, but not part of the cost. The premium will have an intrinsic value component and a time value component. In this case, the premium = intrinsic value + time value, but cost = time value.
The bottom line
The cost is the cost of optionality, and optionality focuses on what could happen, not what has already happened.
Need proof?
Under IFRS and US GAAP, the intrinsic value of an option is amortized over the life of the option, and the time value is marked to market. Amortization of intrinsic value affects net income, while time value marking to market affects OCI (Other Comprehensive Income).
As you explore options, you'll come to realize that in the money options, those with intrinsic value, start to experience a decaying time value component. The deeper in the money, the less time value component there is in their premium. This is why we dared to make the above generalizations.
Time to Expiration
The longer the time to expiration, the higher the cost of the option. This makes intuitive sense, right? We will not explore it in detail because it is very obvious. The more time you have to exercise an option, the more it should cost because the probability of the underlying asset price moving into the in the money zone increases.
Volatility of the Underlying Asset
The higher the volatility of the underlying asset, the higher the cost of the option. This is also intuitive. If the underlying asset is very volatile, there is a higher probability that it will move into the in the money zone, and therefore, the option should cost more.
Two types of volatility
- Historical volatility — The realized volatility of the underlying asset over a past period. It is a backward-looking measure.
- Implied volatility — The market's expectation of future volatility, as implied by the current price of the option. It is a forward-looking measure.
So, why does implied volatility exist? Because even though anyone can calculate historical volatility, it doesn't tell us what the market expects future volatility to be. Implied volatility is the market's expectation of future volatility, as implied by the current price of the option.
Other factors affecting pricing
- Cash flows expected from the underlying asset:
- Dividends
- Interest payments
- Time value of money:
- Risk-free interest rate
These other factors are less impactful than the ones discussed above but affect in some degree, so be mindful of them and experiment with them.
The interaction between these factors is complex and non-linear. The Black-Scholes model provides a framework for understanding how they interact. Even though it is not a perfect model, it is the tool that has been used for decades to price options and understand their behavior. You can read more about it in What Is the Black-Scholes Model? (Plain English).
If you want to discuss more about options pricing, reach out any time. In the meantime, if you want to play around with the Black-Scholes model, check out our options calculator.