Basics of Option "Greeks"

Once the basic concepts of options trading are understood - Call and Put options, strike and expiration, and how to evaluate the benefit of holding an option at expiration (https://apptrade.ffin.am/faq/17851), it is useful to delve into the following concepts for a deeper understanding of the nature of options. Mastering these concepts will enable better selection of options for different situations.

In this article, we will discuss the important concept of implied volatility, provide an overview of option "Greeks," and explain the concepts of theoretical price and implied probability.

Implied Volatility (IV%)

This is the market's estimate of the future volatility of the underlying asset's price. This value can be calculated based on market prices of options. To be able to compare volatilities from different expirations, values are presented in an annualized form. Below are some examples to clarify the concept. It should be noted that the examples provide simplified calculations for initial acquaintance with the concept (specifically, assuming normal distribution of market returns; for more in-depth information see here - https://apptrade.ffin.am/faq/17852)

Example 1:

Expiration in: 1 week
IV = 70% (annualized value)
Current price of the underlying asset: $100

Example 2:

Expiration in: 1 month
IV = 45% (annualized value)
Current price of the underlying asset: $100

Example 3:

Expiration in: 1 year
IV = 19% (annualized value)
Current price of the underlying asset: $100

Note on IV:

The actual calculation of ranges is somewhat more complex and is discussed in more detail in the article (https://apptrade.ffin.am/faq/17852). The current calculation is indicative and simplified, and in cases of large implied volatility values and time to expiration, it will provide incorrect results.
The higher the IV, the higher the option prices.

Implied Probability (IP%)

The probability that the price of the underlying asset will be above the strike (in the case of Call options) or below the strike (in the case of Put options) at expiration. The value is estimated based on market option prices.

Example 1:

Consider a Call option with a strike of $110 and expiration in 3 months and IP% equal to 23%.

This means that the market estimates the probability of the underlying asset's price exceeding $110 at expiration at 23%. It is important to emphasize that this is the probability at expiration, not the probability that the asset's price will be above $110 at some point before expiration.

Example 2:

A Put option with a strike of $90 and expiration in 3 days, IP% is 7%.

This means that the market estimates the probability of the underlying asset's price falling below $90 at 7%.

Theoretical Price

The theoretical price of an option is an indicative price calculated taking into account the prices of all options for a given expiration (in some situations also other expirations). Theoretical price is useful as a reference price in situations of wide spreads and when bid and ask prices are absent.

Delta - ∆

Sensitivity of the option price to changes in the price of the underlying asset. The value ranges between -1 and 1 and can be approximately interpreted as follows: a $1.00 change in the price of the underlying asset will result in a change of *$1.00 in the price of the option. Since the price of a Put option increases when the price of the underlying asset falls, the ∆ of Put options will be negative, and the ∆ of Call options will be positive.

Example 1:

Call option with ∆ = 0.5.

If the price of the underlying asset increases by $1.00, the option price will change by 0.5*$1.00 = $0.50 (increase)
If the price of the underlying asset falls by $1.00 (i.e., -$1.00), the option price will change by 0.5* -$1.00 = -$0.50 (decrease)
If the price of the underlying asset increases by $0.35, the option price will change by 0.5*$0.35 = $0.175 (increase)
If the price of the underlying asset falls by $0.2, the option price will change by 0.5* -$0.2 = -$0.1 (decrease)

Example 2:

Put option with ∆ = -0.4.

If the price of the underlying asset increases by $1.00, the option price will change by -0.4*$1.00 = -$0.40 (decrease)
If the price of the underlying asset falls by $1.00 (i.e., -$1.00), the option price will change by -0.4* -$1.00 = $0.40 (increase)
If the price of the underlying asset increases by $0.35, the option price will change by -0.4* $0.35 = -$0.14 (decrease)
If the price of the underlying asset falls by $0.2, the option price will change by -0.4* -$0.2 = $0.08 (increase)

Note:

The price of options depends non-linearly (i.e., not proportionally) on the price of the underlying asset. ∆ shows the "linear part of the change," so this approximation is good for small changes in the asset's price. The quality of the approximation depends on the value of another "Greek" - Gamma. As an empirical rule - up to a 1% change in the asset's price, ∆ can relatively accurately estimate the change in the option price. If a 10% change in the asset's price is considered, the accuracy of this approach strongly depends on Gamma.

Theta - Θ

Θ indicates approximately how much the option price falls per day, all else being equal (the price of the underlying asset and implied volatility remain unchanged). For example, Θ equal to -0.13 means the option price will fall by $0.13 per day. Θ is always negative, indicating the nature of option decay.

Note:

Like with ∆, this is a linear approximation intended to give an indicative estimate of the option price change over one day.

Vega - V

Vega indicates how much the option price will change if the implied volatility (IV%) changes by 1%. Vega is always positive, which makes sense because the higher the uncertainty, the higher the option prices.

Example:

Vega is 0.14

Current IV% - 23%

If IV% increases to 24%, the option price will change by 0.14 * (24 - 23) = $0.14 (increase)
If IV% increases to 27%, the option price will change by 0.14 * (27 - 23) = $0.56 (increase)
If IV% decreases to 22%, the option price will change by 0.14 * (22 - 23) = -$0.14 (decrease)
If IV% decreases to 18%, the option price will change by 0.14 * (18 - 23) = -$0.7 (decrease)

Gamma - Γ

Γ determines how much Δ changes with small changes in the underlying asset's price. As stated earlier, Δ does not fully determine the change in the option price with a change in the underlying asset's price; it is itself subject to change (for example, the more in-the-money an option is, the greater its absolute Δ). Γ of any option is always positive.

Example 1:

If the considered option has Γ equal to 0.04 and the price of the underlying asset increases by $1.00, then the option's Δ will change by 0.04 * 1.00 = $0.04 (increase)

Example 2:

If the considered option has Γ equal to 0.07 and the price of the underlying asset falls by $0.50, then the option's Δ will change by 0.07 * -0.50 = -$0.035 (decrease).

Rho - ρ

Sensitivity of the option price to changes in the risk-free interest rate. For Call options, this is a positive number, for Put options - negative. The assessment is made following the same principle as for previous "Greeks."

Example:

If the rho of an option is equal to 4.16, and the risk-free interest rate increases by 0.25%, then the option price will change by 4.16 * 0.0025 = $0.0104 (increase)

Print out, sign and upload the scanned copy of the signed document to the website

Please carefully check all your details