Options are financial derivatives that grant the holder the right, but not the obligation, to buy or sell an underlying asset at a predetermined price before or on a specific expiration date.
While seemingly straightforward, the pricing of options involves a variety of variable factors. There are many formulas that one may apply.
How Options are Priced: The Basics
The most widely used framework for pricing options is the Black-Scholes-Merton (BSM) model. Developed in the early 1970s, this mathematical model incorporates several variables to determine the "fair" price of an option:
S: The current stock price of the underlying asset
K: The strike price at which the option can be exercised
T: Time to expiration
r: The risk-free interest rate
σ: The volatility of the underlying asset
Black-Scholes-Merton (BSM) Model: The Mathematical Foundation
The BSM model is the cornerstone for options pricing and has won its creators the Nobel Prize in Economics. It provides a theoretical value for European-style options, which can only be exercised at expiration.
The formula for calculating the price (C) of a European call option using the BSM model is:
The model assumes a constant risk-free interest rate (r) and volatility (σ), and it doesn't account for dividends. Despite these simplifications, the model is widely used due to its computational efficiency and reasonable accuracy.
The Role of Volatility
Volatility is a measure of the asset's price variation over time. It has a direct impact on option pricing: higher volatility generally leads to higher option premiums, and vice versa.
The rationale is that a volatile market increases the likelihood of the option ending in-the-money (ITM), making it more valuable.
Implied vs. Historical Volatility
Two types of volatility are often discussed in the context of options:
Historical Volatility: Based on the past price movements of the underlying asset.
Implied Volatility: Derived from the current market price of the option.
Implied volatility is particularly intriguing because it reflects market sentiment about future volatility. Traders often use it to assess whether an option is underpriced or overpriced.
Understanding Gamma and Dealer Exposure
Gamma is the rate of change of an option's delta with respect to the underlying asset's price. In simpler terms, it measures how sensitive the option's price is to changes in the price of the underlying asset.
Why Gamma Matters
For options traders, particularly market makers or dealers, gamma is a crucial risk management tool. A high gamma level means that the option's price will be highly sensitive to even small movements in the underlying asset.
Understanding gamma is also essential for investors who use options to hedge other investments. A well-managed gamma position can help mitigate risk and optimize returns.
Selling Options: Often More Profitable Than Buying
Many new traders are drawn to the idea of buying options because of the prospect of high returns. However, the reality is that the majority of options expire worthless, making selling covered options often more profitable in the long run.
For example, having 100 shares of a stock and selling an out of the money call against it to collect premium or to sell seemingly expensive volatility.
Time Decay and Premium Collection
One reason why selling options can be profitable is "theta," or time decay. Options lose value over time, all else being equal.
When you sell an option, you collect the premium upfront, and as time passes, the option you sold loses value, increasing your chances of keeping the entire premium.
Selling Volatility
Another strategy involves selling options when implied volatility is high, thereby collecting a higher premium. If the actual future volatility turns out to be lower, the option's price will decrease, allowing the option seller to buy it back at a lower price or let it expire worthless.
In Closing
Options are an important vehicle for both traders and investors to consider for a variety of use cases, from selling premium and volatility to speculating on future price movements. While this article provides a surface-level view, there's plenty more to consider. I will plan to write more content regarding options and I am happy to hear your questions and suggestions for future content on this subject in the comments below.