We now move on to the core part of the Options module. In this brief chapter, we will introduce each of the five Option Greeks, before devoting an entire topic to each one of them following this chapter. Knowing Option Greeks is a very crucialpart of understanding options because each Greek has an impact on option price. Hence, having a thorough understanding of each of them would enable a person to understand option prices better as well as to decidewhat type of option strategies to deploy under the current set of market conditions.
But what does one mean by Option Greeks? Well, put it simply, Option Greeks are factors that measure the sensitivity of an option price to changes in the underlying price, time, volatility, and interest rates. The values for each of the Greeks are derived from various mathematical models, the most eminent of which is the Black-Scholes option pricing model. All these values are then combined to arrive at the theoretical price of an option. A person can then compare this theoretical price with the actual price of an option, to see whether the option is under-priced or over-priced.
It is beneficial to understand how each of the Greeks are calculated - if not mathematically, at least conceptually. Having said that, in today’s world, there are option calculators available everywhere that make our job easier. We just need to feed in values in that calculator. The rest of the job, i.e. finding the value of each of the Greek as well as the theoretical price of an option, would be performed by the option calculator. The values that must be inputted to calculate the output are:
Time to expiration
Dividend, if applicable
Of the six variables mentioned above, only one variable remains constant throughout the life of an option contract - strike price. The rest of the variables fluctuate over the life of the option. Hence, whenever option price changes, it is usually due to a change in the value of one of more of these five variables. Keep in mind that Option Greeks only provide values based on the numbers that we have inputted in the option calculator. Hence, any incorrect value inputted could lead to an incorrect output being generated.
Back when the Black Scholes model was introduced in 1973, it was only used to value European options and that too on stocks that did not pay dividends. Since then however, modifications have been made to the model to include a broader class of underlying assets as well as to include dividend paying stocks. There are quite a few option pricing models in existence today, but Black-Scholes is the most widely used model, despite being nearly half a century old.
So, without any further talk, let us get started with introducing the Option Greeks. There are a total of five Option Greeks, as are mentioned below:
Let us now try to understand, in brief, what each of these Greeks stand for. Keep in mind that in this chapter, we will only introduce you with Option Greeks. We won’t talk in much detail about each Greek, as this would be done over the course of the next five chapters. For now, we will only define each of the Option Greek, so that a reader would have a basic understanding of the Greeks.
The term Delta comes from the Greek symbol ‘Δ’. It measures the rate of change in an option price based on a 1-point change in the price of the underlying.Put it simply, Delta measures the speed at which the price of an option changes for a change in the underlying price.
The term Gamma comes from the Greek symbol ‘Γ’. It measures the rate of change in Delta based on a 1-point change in the price of the underlying. Put it simply, Gamma measures the pace at which the Delta changes for a change in the underlying price.
The term Vega is commonly denoted using the symbol ‘K’. It measures the change in an option price based on a 1-point change in the underlying’s implied volatility (or IV). Put it simply, Vega measures the sensitivity of an option price to changes in volatility of the underlying.
The term Theta comes from the Greek symbol ‘Θ’. It measures the change in option price based on a change in the time to expiration. Put it simply, Theta measures the rate at which the option price loses its value due to the element of time decay.
The term Rho comes from the Greek symbol ‘ρ’. It measures the rate of change in an option price based on a change in the risk-free interest rate. Put it simply, Rho measures the sensitivity of an option price to changes in interest rate.
Now that we have an elementary understanding of what each of the five Greeks represent, it is time to focus on each of the Greek in a much greater detail, something that we would be doing over the course of the next five chapters.
In this chapter, we shall talk in detail about the first of the five Option Greeks: Delta. We shall start right with the basics of Delta and then proceed towards more complex areas such as how option moneyness impacts Delta, how time and volatility impact Delta etc. We will then conclude this chapter by talking about the derivative of Delta: Gamma.
In this chapter, we will study about a derivative of Delta, called Gamma. We will start the chapter by introducing Gamma, including how it impacts the Delta of an option. We will then talk about how Gamma is impacted by option moneyness, time to expiration, and volatility.