Option Greeks are a set of elements that help us understand the different risks involved in trading options. They are named after Greek symbols and are important for option traders. The Greeks, like Delta, Vega, and Theta, are used to figure out how risky a portfolio is. They help traders calculate the potential profit or loss of a trade when the price of the underlying asset changes, which helps them manage risk.
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| OPTION GREEKS |
The Greeks measure how sensitive the price of an option is to different factors that affect its value. The Black Scholes Model is a popular mathematical model used to price options.
There are five main Option Greeks: Delta, Gamma, Vega,
Theta, and Rho. Each Greek is sensitive to different parameters and helps
calculate the price of an option. In the upcoming parts of this book, we will
learn more about each of these Greeks and how they work.
Delta:
Among all the Greeks used by options traders, Delta is the
most common one. Delta measures how quickly the price of an option changes when
the price of the underlying asset moves. It tells us how sensitive the option
price is to changes in the stock price.
If the market goes up or down by 1 point, Delta measures how
much the option premium will change. For both call and put options with the
same strike price, we calculate Delta separately. Call options have a positive
Delta value, while put options have a negative Delta value. The value of Delta
for call options ranges from 0 to 1, while the value for put options ranges
from -1 to 0.
Let's use an example to better understand the Greek Delta.
Assume that the current market price of a stock, let's say XYZ, is ₹100. The
table below shows the various Delta values for call options. The values in the
table are speculative. It is prepared purely as an example.
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| Call Option |
The values of Delta for call
options are higher for in-the-money (ITM) strikes than out-of-the-money (OTM)
strikes, according to the above table.
Consider an ITM option with a strike price of 90. The delta
is worth 0.70 rupees, and the premium is 15. In other words, if the price of
the underlying, XYZ, goes to ₹101, the new premium of the 90 strike will
increase to ₹15.70 (₹15.00 + 0.70), taking other aspects into consideration. On
the contrary, the option price will instead drop to ₹14.30 if the stock price
drops to ₹99. (₹15.00 – 0.70).
Take yet another put option example for the same stock. At
various strike prices, the accompanying table includes possible values for the
option price and delta. In this case, the ITM put option's Delta value bears
move values, but it does so negatively. It indicates the Delta has a negative
co-relation with option premium for put options. It is evident from the table
that option prices are more sensitive to price at ITM strikes than at OTM
strikes.
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| Put Option |
For demonstration purposes, we'll
use the same strike price, 90, which is now an OTM option. It states that the
premium is ₹3.00 and that the Delta is just ₹0.30. According to the definition
of Delta, if the stock price rises to ₹101, the price of the ₹90 strike will
reduce by ₹0.30 and the new price will be ₹2.70. (₹3.00 – 0.30). But, if the
underlying price drops to ₹99, the option price will rise by ₹0.30.
Also, it can be seen from the aforementioned table that the
value of Delta for a call option is almost 0.50 for at-the-money (ATM) options,
less than 0.50 for out-of-the-money (OTM) options, and greater than 0.50 for
in-the-
money (ITM) options. The value of a put option, on the other
hand, is - 0.50 for ATM strikes, larger than - 0.50 for ITM strikes, and less
than - 0.50 for OTM strikes. The graph below will give you an idea of how the
Delta values for call and put options change depending on the spot price.
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| Gamma |
Gamma:
The option Greek gamma is the rate of change of Greek Delta.
A call option's gamma, which is always reported in percentage terms, shows how
the delta changes as the underlying asset moves by one point. Its basic
definition is the rate of change of Delta. Gamma can be thought of as
acceleration if Delta is speed at which the option premium
changes. It serves as a gauge for the stability of Delta.
Let's use an illustration;
Suppose that ABC Company's stock is currently trading at
₹100. Assume the following hypothetical values for the various variables for
the ₹100 call option:
|
Stock price |
Delta |
Gamma |
Option premium |
|
100 |
0.50 |
0.1 |
0.60 |
|
Stock price |
Delta |
Gamma |
Option premium |
|
101 |
0.60 (0.50 + 0.10) |
0.09 (say) |
10.60 (10 + 0.60) |
The gamma values are influenced by the proximity of the
strike prices and the expiration time. When comparing at-the-money options to
out-of the-money and in-the-money options, the value is significant for at-the
money options and gradually declines. In addition, gamma value is greater for
contracts with near term expiration and decreases for those with far term
expiration. The accompanying graph demonstrates the relation
among the gamma value, strike price and time to expiry.
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| Vega |
Vega:
Vega is the change in option price for every 1% change in
implied volatility (IV). And implied volatility is the market's prediction of a
potential movement in the price of an asset. Vega affects time value but not
the intrinsic value of the option. Implied volatility and it are positively
correlated. This implies that Vega rises in parallel with an increase in the
expected volatility of a security. Also, whereas the value of Vega is negative
for short option positions, it is positive for long option positions. The table
that follows demonstrates how implied volatility and consequently the option
price affect Vega value.
Moreover, unlike Gamma, the Greek Vega option's value peaks for at the-money options while steadily decreasing for both in-the-money and out of-the-money options. However, the value of Vega is also influenced by the period of expiration. The Vega has more value for long-term expiry than for short-term expiry. To better understand their relationship, look at the chart below.
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| Theta |
Theta:
Even while all other factors remain constant until the
contract's maturity, the price of an option depreciates. Theta is the measure
of how much an option's value declines. Hence, the Greek Theta is the amount of
decline in call and put option prices for a change of one day in the maturity
time. It is also known as time decay and is expressed as a negative number. Due
to its negative value, theta, also known as time decay, is the number one enemy
of option buyers. Instead, it is the best buddy of option writers.
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| Days Expiry |
An at-the-money option premium decay is displayed in the graph above with more than three months to maturity. When ₹4 declined for the
following 30 days while other factors remained constant, the
option value only depreciated by ₹3 from 90 to 60 days. The value of the
premium decline rate for the final 30 days before expiration drops to zero from
₹11. As the time value nears its expiration, it falls off more quickly. This
sensation is comparable to the hot summer sun on an ice cube. The temporal
value of an option diminishes with each passing second. Moreover, the loss of
time value happens more quickly close to maturation.
The value of Theta also relies on the strike price. Theta
has a high time value for at-the-money strikes, but it has a lower value for
in-the-money and out-of-the-money strike prices. This indicates that OTM
options are least sensitive to Theta value while ATM options are more sensitive
to time value decay than ITM options. However, keep in mind that Theta's value
is always negative.
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| Rho |
Rho:
Rho is an option Greek that measures how an option's price
changes when there are changes in interest rates. It tells us the expected
price change of an option for a 1% increase in interest rates. Rho is usually
positive for call options, which means the price of the option will go up when
interest rates rise. On the other hand, Rho is often negative for put options,
indicating that the price of the option will decrease when interest rates go
up.
This relationship exists because interest rates affect the
cost of carrying an asset over time. The cost of carry includes things like
interest rates, storage costs, and insurance fees. When interest rates go up,
the cost of carrying an asset also increases, which can lead to higher prices
for the underlying asset. As a result, call options on the underlying asset may
become more expensive.
It's important to note that Rho is usually only meaningful
for longer-term options because short-term interest rate changes don't have a significant
impact on option prices. Longer-term options that are "in the money"
are more sensitive to changes in interest rates. Short-term options are less
affected because interest rates don't fluctuate frequently.
However, for long term options, the cost of carrying can have a big impact on
their value. It's worth mentioning that Rho is not always a major factor in
option pricing, especially for options on stocks. This is because interest
rates often have a smaller effect on stock prices compared to other factors
like company earnings, market sentiment, and overall economic conditions.
However, Rho can be more important for options on assets that are sensitive to
interest rates, such as bonds or currencies.