What Are Derivative Greeks?
Derivative greeks are fundamental in the options market. Each of "the Greeks" are greek symbols that serve to identify different types of risks when it comes to trading options. The risk generated from imperfect pricing relationships between the underlying asset that the option is trading and assumptions made when pricing options are represented by each greek symbol. The derivative greeks are used mainly by portfolio managers and options traders as workers in these fields need to have a deep understanding in how price movements will affect their options investments, and learn to hedge the risk of their positions accordingly.
A Crash Course On Options
Because derivative greeks are built upon the ideas of options, you need to have a good idea about what options are, how they function, and how they are traded. This section will give a quick overview of the basics!
What are options?: Options are contracts that can be traded by investors and are used to have the right (but not the liability) to buy or sell an asset at a specified price for a period of time. Options are a type of derivative, since their value comes from another asset. Options are used to hedge risk against stock market volatility. However, options trading can become very complex and is not for everyone.
What are call options?: A contract that gives you the right (but not the liability) to buy the underlying asset of the option at a given price (i.e. strike price). If the current market price is greater than the strike price, then the option is in the money and has positive returns.
What are put options?: A contract that gives you the right (but not the liability) to sell the underlying asset of the option at a given price (i.e. strike price). If the current market price is less than the strike price, then the option is in the money and has positive returns.
What Does Each Greek Symbol Represent?
Delta (Δ): The MOST IMPORTANT greek in option investments. Delta will tell you how much the price of the option changes for every $1 change in the price of the underlying asset. The higher the delta, the more sensitive an option's price will be to the underlying asset's price. A option in defined to be in the money (ITM) when exercising the option will lead to a profit as the market price of a call option (current market price of the underlying asset) is above the strike price (price you buy the underlying asset at) of the option or the market price of a put option (current market price of the underlying asset) is below the strike price (price you sell the underlying asset at) of the option. A lot of the time, traders use the value of delta in order to predict whether an option will be ITM at expiration. For example, if delta equals 0.40, then the option has approximately a 40% chance of expiring ITM. However, note that larger premiums (price of an option) detract from the profitability of an option.
Range: 0.00 to 1.00 for call options and 0.00 to -1.00 for put options
Gamma(Øܬ): Gamma is the rate of change of an option's Delta for every $1 change in the price of the underlying asset. It can also be thought of as the derivative of Delta. Thus, you can think of Delta as speed and Gamma as acceleration. Since Delta cannot exceed 1, the closer Delta gets to 1, the smaller Gamma becomes. Following the analogy, the closer we get to top speed, the smaller our acceleration becomes.
Theta(╬ÿ): Assuming all outside factors remain constant, theta tells you how much an option price will decrease by each day. The price of an option decreases each day due to time decay. Time decay occurs because as time goes on and the option's expiration date approaches, the chance that the price of the underlying asset's price will change decreases. Note that this time decay is not linear, and as the expiration date gets closer, the price of the option will decrease at a faster rate. This is because the option's value deteriorates as you get closer to its expiration day since there is no option to exercise after it expires and thus, it will have no value.
Vega(V): Vega is the rate of change of an option's price for every 1% change in the volatility of the underlying asset. Since volatility in the market is what gives options their value, an increase in vega will increase the value of options.
Rho(Ôì┤): Rho is the expected change of an option's price for every 1% change in risk-free interest rates. Rho is positive for call options and negative for put options because interest rates and call options have a direct relationship while interest rates and put options have an inverse relationship. This is because the value of buying a call option instead of directly buying the underlying asset increases as interest rates increase and stocks become less attractive. The opposite can be said for put options. Rho plays a small role in option pricing, but is still an important consideration, especially when risk-free interest rates are expected to change.
And there you have it! The derivative greeks. If you find this interesting and would like to learn more, consider taking FNCE 2170: Financial Derivatives.
Sources:
https://www.investopedia.com/terms/g/greeks.asp
https://www.investopedia.com/terms/i/inthemoney.asp#:~:text=A%20call%20option%20is%20in,options%20that%20are%20not%20ITM
https://learn.robinhood.com/articles/3oJP2aXJ9HDFNf1E8y0qls/what-are-options-greeks/
https://www.schwab.com/learn/story/get-to-know-option-greeks
https://www.forbes.com/advisor/investing/options-trading/