Effects of IMPLIED VOLATILITY (IV) on Option Greek VEGA – With Past DATA and CHARTS

The following is the behavior of Vega in relation to Implied Volatility (IV) changes:

Vega is higher when volatility increases, particularly for ITM and OTM options.

However, Vega is relatively stable / unchanged for ATM option.

We’ll use the same past actual data as shown in the previous post on the behavior of Delta, namely:

Options Chain for Call options of RIMM as at 3 Sep 2010, when the closing price is $44.78 and Implied Volatility (IV) is 54.05, for expiration month of Sep 2010 (10 days to expiration), October 2010 (38 days to expiration) and Dec 2010 (101 days to expiration).

Here is the summary of Vega values for different IV:

 From the table, we can see that for ITM options (e.g. option’s strike price $35 and $37.5) and OTM options (e.g. option’s strike price $55 and $52.5), Vega increases as IV increases , i.e. as it moves from the left (IV = 25, the lowest IV in this example) to the right (IV = 85, the highest IV in this example).

On the other hand, for near ATM options (i.e. the option’s strike price $45.00, because the stock price is $44.78), Vega is relatively unchanged with the change in IV.

Hence, these observations are in line with the statement above.

Now, let’s study the behavior of Vega of different IV at various strike prices (as shown in the chart below).

As can be seen in the chart:

For all the three options with different IV, Vega always behaves the same way, i.e. Vega of ATM options is always higher, and it gets lower as it moves towards deep ITM and deep OTM options.

However, the decrease in Vega as the option moves from ATM towards deep ITM/OTM will be greater for options with lower IV as compared to options with higher IV.

For deep ITM and deep OTM options, Vega is very small (close to zero) when IV is low. 

To view the list of all the series of articles in this topic, please refer to: 

Behaviour of OPTION GREEKS in relation to TIME REMAINING TO EXPIRATION and IMPLIED VOLATILITY (IV) – With Past DATA and CHARTS

Other Learning Resources:

* FREE Trading Educational Videos with Special Feature

* FREE Trading Educational Videos from Trading Experts

Related Topics:

* Understanding Implied Volatility (IV)

* Understanding Option Greek

* Understanding Option’s Time Value

* Learning Candlestick Charts

* Options Trading Basic – Part 1

* Options Trading Basic – Part 2

Read More

Effects of IMPLIED VOLATILITY (IV) on Option Greek THETA – With Past DATA and CHARTS

The following is the behavior of Theta in relation to Implied Volatility (IV) changes:

When Implied Volatility (IV) increases, Theta would be higher.

When IV decreases, Theta will be lower, especially when it is approaching expiration.

We’ll use the same past actual data as shown in the previous post on the behavior of Delta, namely:

Options Chain for Call options of RIMM as at 3 Sep 2010, when the closing price is $44.78 and Implied Volatility (IV) is 54.05, for expiration month of Sep 2010 (10 days to expiration), October 2010 (38 days to expiration) and Dec 2010 (101 days to expiration).

Here is the summary of Theta values for different IV:

From the table, we can observe that:

Regardless of option’s strike prices (ATM/ITM/OTM), Theta always increases as IV increases, i.e. as it moves from the left (IV = 25, the lowest IV in this example) to the right (IV = 85, the highest IV in this example).

Note:

Negative sign (which indicate the losing of time value) is ignored when doing the comparison.

So, these observations verify the statements above.

Now, let’s study the behavior of Theta of different IV at various strike prices (as shown in the chart below).

As can be seen in the chart:

For all the three options with different IV, Theta always behaves the same way, i.e. Theta of ATM options is always higher, and it gets lower as it moves towards deep ITM and deep OTM options.

However, the decrease in Theta as the option moves from ATM towards deep ITM/OTM will be bigger for options with higher IV as compared to options with lower IV.

This is understandable because options with higher IV will contain more time value than options with lower IV (Remember about Options Pricing).

Since Theta is the decrease of time value due to the passage of time, Theta will naturally be higher for options with higher IV as it has more time value to lose, as compared to options with lower IV.

To view the list of all the series on this topic, please refer to:

Behaviour of OPTION GREEKS in relation to TIME REMAINING TO EXPIRATION and IMPLIED VOLATILITY (IV) – With Past DATA and CHARTS.

Other Learning Resources:

* FREE Trading Educational Videos with Special Feature

* FREE Trading Educational Videos from Trading Experts

Related Topics:

* Understanding Implied Volatility (IV)

* Understanding Option Greek

* Understanding Option’s Time Value

* Learning Candlestick Charts

* Options Trading Basic – Part 1

* Options Trading Basic – Part 2

Read More

Effects of IMPLIED VOLATILITY (IV) on Option Greek GAMMA – With Past DATA and CHARTS

Impact of Implied Volatility (IV) on Gamma

When the Implied Volatility increases, the Gamma of ATM options decreases, whereas the Gamma for deep ITM or OTM options increases.

When the Implied Volatility is very low, the Gamma of ATM options is relatively high, while the Gamma for deep ITM / OTM options is relatively low (close to 0).

This is because when the volatility is low, the time value portion of an option is low. However, time value of ATM option is still higher relative to ITM & OTM options, hence the Gamma of ATM option is higher as compared to ITM & OTM options.

On the other hand, when IV is high, Gamma tends to be stable for ATM option as well as ITM and OTM options. This is because when volatility is high, the time value of deep ITM / OTM options are already quite substantial. As a result, the increase in the time value of deep ITM / OTM options as they go nearer the money will be less dramatic. Therefore, Gamma tends to be more stable across all strike prices in this case.

We’ll use the same past actual data as shown in the previous post on the behavior of Delta, namely:

Options Chain for Call options of RIMM as at 3 Sep 2010, when the closing price is $44.78 and Implied Volatility (IV) is 54.05, for expiration month of Sep 2010 (10 days to expiration), October 2010 (38 days to expiration) and Dec 2010 (101 days to expiration).

Here is the summary of Gamma values for different IV:

From the table, we can observe that for near ATM options (i.e. the option’s strike price $45.00, because the stock price is $44.78), Gamma decreases as IV increases, i.e. as it moves from the left (IV = 25, the lowest IV in this example) to the right (IV = 85, the highest IV in this example).

Whereas for deep ITM options (e.g. option’s strike price $35 and $37.5) and deep OTM options (e.g. option’s strike price $55 and $52.5), Gamma increase when IV increases.

Hence, these observations show evidence to the first statement above.

Now, let’s observe the behavior of Gamma of different IV at various strike prices (as shown in the chart below) to verify the next statements.

As can be seen in the chart:

For all the three options with different IV, Gamma always behaves the same way, i.e. Gamma of ATM options is always higher, and it gets lower as it moves towards deep ITM and deep OTM options.

That means:

Regardless of IV levels, the delta of ATM option is most sensitive to changes in stock price (i.e. gamma is the highest for ATM option), as compared to ITM and OTM options.

The chart also shows that when the IV is very low (i.e. IV = 25 in this example), the Gamma of ATM options is relatively high, while the Gamma for deep ITM / OTM options is relatively low (close to 0).

When IV is high (i.e. IV = 85 in this example), Gamma values do not change so drastically (i.e. tend to be more stable) as the price moves across different level of option moneyness / strike prices.

Conclusion:

Given the same IV, Gamma of ATM option will always be higher than that of deeper ITM and OTM options.

However, when IV is very low, Gamma of ATM options is relatively high, while the Gamma for deep ITM / OTM options is relatively low (close to 0).

And when IV is very high, Gamma values do not change so drastically (i.e. tend to be more stable) as the price moves from deeper ITM/OTM towards ATM.

Given an ATM option, the option with higher IV will have lower Gamma.

Given a deeper ITM or OTM option, the option with higher IV will have higher Gamma.

To view the list of all the series on this topic, please refer to:
“Behaviour of OPTION GREEKS in relation to TIME REMAINING TO EXPIRATION and IMPLIED VOLATILITY (IV) – With Past DATA and CHARTS.”

Other Learning Resources:

* FREE Trading Educational Videos with Special Feature

* FREE Trading Educational Videos from Trading Experts

Related Topics:

* Understanding Implied Volatility (IV)

* Understanding Option Greek

* Understanding Option’s Time Value

* Learning Candlestick Charts

* Options Trading Basic – Part 1

* Options Trading Basic – Part 2

Read More

Behaviour of VEGA in relation to TIME REMAINING TO EXPIRATION – With Past DATA and CHARTS

The following is the behavior of Vega in relation to Time to Expiration:

Assuming all other things unchanged, Vega decreases as the option gets nearer to expiration.

We’ll use the same past actual data as shown in the previous post on the behavior of Delta, namely:
Options Chain for Call options of RIMM as at 3 Sep 2010, when the closing price is $44.78 and Implied Volatility (IV) is 54.05, for expiration month of Sep 2010 (10 days to expiration), October 2010 (38 days to expiration) and Dec 2010 (101 days to expiration).

The summary of Vega values for different Time to Expiration:


As can be seen from the table, for all level of moneyness (ITM, ATM, OTM), Vega values are always lower for the options with expiration month “Sep-10” (nearer to expiration), followed by “Oct-10”, and then “Dec-10” (further to expiration).
This proves the statement above.

Now, let’s move on to compare Vega of different time to expiration at various strike prices.



As can be seen in the chart:

For all the three options with different time to expiration, Vega always behaves the same way, i.e. Vega of ATM options is always higher than deeper ITM and OTM options.

Comparing the Vega values between deeper ITM and OTM options given the same time to expiration, OTM option seem to have higher Vega than ITM option.

This makes sense because ATM options have the highest time value component, and changes in Implied Volatility (IV) would only affect the time value portion of an option’s price.Comparing between ITM & OTM options, volatility changes would have greater effect for OTM options than for ITM options. This because OTM options comprise merely of time value, while ITM options comprise of intrinsic value plus time value. The deeper the ITM options, the smaller the portion of time value the ITM option would have.

To view the list of all the series on the this topic, please refer to:
“Behaviour of OPTION GREEKS in relation to TIME REMAINING TO EXPIRATION and IMPLIED VOLATILITY (IV) – With Past DATA and CHARTS.”

Other Learning Resources:
* FREE Trading Educational Videos with Special Feature
* FREE Trading Educational Videos from Trading Experts

Related Topics:
* Understanding Implied Volatility (IV)
* Understanding Option Greek
* Understanding Option’s Time Value
* Learning Candlestick Charts
* Options Trading Basic – Part 1
* Options Trading Basic – Part 2

Read More

Behaviour of THETA in relation to TIME REMAINING TO EXPIRATION – With Past DATA and CHARTS

The following is the behavior of Theta in relation to Time to Expiration:

For ATM option, Theta increases as an option gets closer to the expiration date.
On the other hand, for ITM & OTM options, Theta decreases as an option is approaching expiration.
The above effects are particularly observed in the last few weeks (about 30 days) before expiration.

Using the same past actual data as shown in the previous post on the behavior of Delta, namely:
Options Chain for Call options of RIMM as at 3 Sep 2010, when the closing price is $44.78 and Implied Volatility (IV) is 54.05, for expiration month of Sep 2010 (10 days to expiration), October 2010 (38 days to expiration) and Dec 2010 (101 days to expiration).

The following is the summary of Theta values for different Time to Expiration:



For easier analysis, we can plot the Theta values of different Degree of Moneyness across various Time to Expiration, as follows:




As can be seen from the table and the chart above:
For (near) ATM options (i.e. strike price $45.00, because the stock price is $44.78), Theta (in absolute value) is the higher for the options with expiration month “Sep-10” (nearer to expiration), as compared to “Oct-10” and “Dec-10”.
In other words, Theta (in absolute value) increases as time to expiration gets nearer.

Whereas for both deep ITM (strike price $35.00 & $37.50) and deep OTM options (strike price $52.50 & $55.00), Theta (in absolute value) is the lower for the options with expiration month “Sep-10” (nearer to expiration), as compared to “Oct-10” and “Dec-10”.
In other words, Theta (in absolute value) decreases as time to expiration gets nearer.

Note:
For Theta, we’re always comparing Theta here (whether it’s high or low) in terms of the absolute value, because the negative sign only represents the decaying effect.

Likewise, we’ll also compare Theta of different time to expiration at various strike prices, as shown in the chart below.



As can be seen in the chart:
For all the three options with different time to expiration, Theta always behaves the same way, i.e. given the same time to expiration, Theta of ATM options is higher, and it gets lower as it moves towards deep ITM and deep OTM options.

That means:
Given the same time to expiration, ATM options will always decay faster as time goes by, as compared to deeper ITM and OTM options would.

However, the blue line (i.e. options with expiration month “Sep-10”) is much steeper than the red line (i.e. options with expiration month “Oct-10”) and green line (i.e. options with expiration month “Dec-10”).
This means:

Theta values for options with nearer time to expiration differ more significantly along various strike prices, as compared to those with further time to expiration.
The further the time to expiration is, the smaller the difference in the Theta values across different strike prices will be.

Conclusion:
Given the same time to expiration, ATM options will always decay faster as time goes by (i.e. have higher Theta) than the deeper ITM and OTM options would.

Given an ATM option, the option with nearer time to expiration will have the highest Theta (will decay the fastest), as compared to that with longer time to expiration.

Given a deeper ITM / OTM option, the option with nearer time to expiration will have the lowest Theta (will decay the slowest), as compared to that with longer time to expiration.


To view the list of all the series on the this topic, please refer to:
“Behaviour of OPTION GREEKS in relation to TIME REMAINING TO EXPIRATION and IMPLIED VOLATILITY (IV) – With Past DATA and CHARTS.”

Other Learning Resources:
* FREE Trading Educational Videos with Special Feature
* FREE Trading Educational Videos from Trading Experts

Related Topics:
* Understanding Implied Volatility (IV)
* Understanding Option Greek
* Understanding Option’s Time Value
* Learning Candlestick Charts
* Options Trading Basic – Part 1
* Options Trading Basic – Part 2

Read More

Behaviour of GAMMA in relation to TIME REMAINING TO EXPIRATION – With Past DATA and CHARTS

As discussed previously in the earlier post, here is the behavior of Gamma in relation to
Time to Expiration:

Assume all other factors unchanged:
For ATM options, Gamma increases (is higher) as time to expiration is nearing.
In contrast, for both deep ITM and deep OTM options, Gamma normally decreases (is lower) as time to expiration is nearing.

We will use the same past actual data as shown in the previous post on the behavior of Delta, namely:
Options Chain for Call options of RIMM as at 3 Sep 2010, when the closing price is $44.78 and Implied Volatility (IV) is 54.05, for expiration month of Sep 2010 (10 days to expiration), October 2010 (38 days to expiration) and Dec 2010 (101 days to expiration).

Similarly, here is the summary of Gamma values for different Time to Expiration:



As can be seen from the table, for both deep ITM (strike price $35.00 & $37.50) and deep OTM options (strike price $52.50 & $55.00), the Gamma values are the lowest for the options with expiration month “Sep-10” (nearer to expiration), followed by “Oct-10”, and then “Dec-10” (further to expiration).

On the other hand, for near ATM options (i.e. strike price $45.00, because the stock price is $44.78), the Gammas are the highest for the options with expiration month “Sep-10” (nearer to expiration), followed by “Oct-10”, and then “Dec-10” (further to expiration).

These prove the statement above.

Now, let’s compare Gamma of different time to expiration at various strike prices, as shown in the chart below.



As can be seen in the chart:

For all the three options with different time to expiration, Gamma always behaves the same way, i.e. Gamma of ATM options is always higher, and it gets lower as it moves towards deep ITM and deep OTM options.

That means:
Given the same time to expiration, the Delta of ATM options changes the most when the stock price moves up or down, as compared to deeper ITM and OTM options.

However, the blue line (i.e. options with expiration month “Sep-10”) is much steeper than the red line (i.e. options with expiration month “Oct-10”) and green line (i.e. options with expiration month “Dec-10”).
This shows that:

Gamma values for options with nearer time to expiration differ more significantly along various strike prices, as compared to those with further time to expiration.
The further the time to expiration is, the smaller the difference in the Gamma values across different strike prices will be.

Conclusion:
Given the same time to expiration, Gamma of ATM option will always be higher than Gamma of deeper ITM and OTM options.

Given an ATM option, the option with nearer time to expiration will have the highest Gamma, as compared to the option with longer time to expiration.

Given a deeper ITM or OTM option, the option with nearer time to expiration will have the lowest Gamma, as compared to the option with longer time to expiration.

To view the list of all the series on the this topic, please refer to:
“Behaviour of OPTION GREEKS in relation to TIME REMAINING TO EXPIRATION and IMPLIED VOLATILITY (IV) – With Past DATA and CHARTS.”

Other Learning Resources:
* FREE Trading Educational Videos with Special Feature
* FREE Trading Educational Videos from Trading Experts

Related Topics:
* Understanding Implied Volatility (IV)
* Understanding Option Greek
* Understanding Option’s Time Value
* Learning Candlestick Charts
* Options Trading Basic – Part 1
* Options Trading Basic – Part 2

Read More

Behaviour of DELTA in relation to TIME REMAINING TO EXPIRATION – With Past DATA and CHARTS

The following is the behavior of Delta in relation to Time to Expiration:

Assume all other factors unchanged:
As the time to expiration is nearing, the Delta of ITM options increases (i.e. ITM option’s Delta gets closer to 1 for Calls or to -1 for Puts) and the Delta of OTM options decreases (i.e. OTM option’s Delta gets closer to 0).

Now, let’s observe using the past real data.
The following is the Options Chain for Call options of RIMM as at 3 Sep 2010, when the closing price is $44.78 and Implied Volatility (IV) is 54.05, for expiration month of Sep 2010 (10 days to expiration), October 2010 (38 days to expiration) and Dec 2010 (101 days to expiration).
(The rows highlighted in yellow are ITM options, while those in white are OTM).



For easier reading and comparison, I summarize the Delta for different time to expiration as follow:



As can be seen from the table, for ITM options (highlighted in yellow), the Deltas are the highest for the expiration month “Sep-10” (nearer to expiration), followed by “Oct-10”, and then “Dec-10” (further to expiration).

On the other hand, for OTM options, the Deltas are the lowest for the expiration month “Sep-10” (nearer to expiration), followed by “Oct-10”, and then “Dec-10” (further to expiration).

For near ATM options (i.e. the option’s strike price $45.00, because the stock price is $44.78), the Delta is about the same, i.e. close to 0.5.

These observations are in line with the statement above.

In addition, we can also look from different point of view, i.e. by comparing Delta at various strike prices at different time to expiration, as shown in the chart below.



From the chart, we can see that:

The effect of stock price changes on the option price (i.e. Delta) are more “extreme“ for ITM and OTM options with nearer time to expiration, as compared to those with further time to expiration.
Nearer time to expiration will push the Deltas of ITM Calls closer to 1 (-1 for Puts) and the OTM option’s Delta closer to 0.

In contrast, for ATM options, the Delta is relatively unaffected to changes in time to expiration, i.e. all will have Deltas close to 0.5.

Implication
So, what’s the implication?
We can use this knowledge to help us consider and choose which options to use for trading, given the trading opportunities, expectation of whether the price movement is big or small, expected time frame, and options strategies.

For instance:
If you’re playing a swing trading and expect a stock’s price will change moderately within a short period, and you want to buy a straight Long Call to take advantage of this opportunity. In this case, you could consider using ITM options from a nearer time to expiration, as this option has higher Delta. Hence, when the stock price indeed increases as expected, you can gain more (in terms of dollar) from the increase in the option’s price.

However, given the scenario, suppose due to capital constraint, you would like to use OTM options, then choosing OTM options from a longer time to expiration should be better to take advantage from the stock price movement (in terms of dollar), as this option has higher Delta.
(Note: This is just a simple example about how to make use of the knowledge on Delta behavior in your trading. Actually, using OTM options in such case would have lower chance to be profitable, as an OTM option would require a very big increase in the stock price for the option to be profitable.)

The bottom line:
Whatever strategy you use, do consider the behaviors of the Option Greeks to help you choose which options to use (ITM, ATM, or OTM) to enhance the probability to make money.

Next, we’ll discuss about the behavior of the rest of the Options Greek.

To view the list of all the series on the this topic, please refer to:
“Behaviour of OPTION GREEKS in relation to TIME REMAINING TO EXPIRATION and IMPLIED VOLATILITY (IV) – With Past DATA and CHARTS.”

Other Learning Resources:
* FREE Trading Educational Videos with Special Feature
* FREE Trading Educational Videos from Trading Experts

Related Topics:
* Understanding Implied Volatility (IV)
* Understanding Option Greek
* Understanding Option’s Time Value
* Learning Candlestick Charts
* Options Trading Basic – Part 1
* Options Trading Basic – Part 2

Read More

Behaviour of OPTION GREEKS in relation to TIME REMAINING TO EXPIRATION and IMPLIED VOLATILITY (IV) – With Past DATA and CHARTS

The past articles in this blog have discussed many times about the effect of time remaining to expiration and IV on Options Greeks.
In fact, not only this blog, many other websites have done the same too.
Nevertheless, generally these topics are only discussed qualitatively, as it is quite tedious and time consuming to show these using real data.

While there is an adage “A picture speaks a thousand words”, I am trying to show how Options Greeks behave in relation to the changes in time remaining to expiration or Implied Volatility (IV) by using the past real data and showing the relevant charts.

The following is the list of articles in this series:

Behaviour of Option Greeks in relation to TIME REMAINING TO EXPIRATION:
1. Delta
2. Gamma
3. Theta
4. Vega

Behaviour of Option Greeks in relation to IMPLIED VOLATILITY:
1. Delta
2. Gamma
3. Theta
4. Vega

By knowing better how Options Greeks behave in relation to the change in time remaining to expiration or Implied Volatility (IV), I hope this info can help you in your trading to enhance the probability to make money using whatever strategies that suit you.

We'll start with the first article soon.

Other Learning Resources:
* FREE Trading Educational Videos with Special Feature
* FREE Trading Educational Videos from Trading Experts

Related Topics:
* Understanding Implied Volatility (IV)
* Understanding Option Greek
* Understanding Option’s Time Value
* Learning Candlestick Charts
* Options Trading Basic – Part 1
* Options Trading Basic – Part 2

Read More

Relationship between OPTION GREEK with DEGREE of MONEYNESS, IMPLIED VOLATILITY and TIME TO EXPIRATION: Summary – Part 2

Go back to Part 1.

THETA
Theta is an options greeks that measures of the rate of decline of option’s time-value resulting from the passage of time (time decay).
Theta provides an estimate of the dollar amount that an option price would lose due to 1 day decrease in the time remaining to expiration, assuming other factors remain constant.

Theta of ATM, ITM & OTM Option
Theta is typically highest for ATM option, and is progressively declining as an option moves to ITM or OTM.
This makes sense because ATM options have the highest time value component, so they have more time value to lose over time compared to ITM or OTM options.

Effect of Time Remaining to Expiration on Theta
For ATM option, Theta will be higher as an option is approaching the expiration date.
In contrast, for ITM & OTM options, Theta will be lower as an option gets closer to expiration. The above effects are particularly observed in the last few weeks (about 30 days) before the expiration.

Impact of Implied Volatility (IV) on Theta
When Implied Volatility (IV) decreases, Theta will decrease, especially when it is approaching expiration.
On the other hand, when IV increases, Theta would also increase.

VEGA
Vega measures how sensitive an option’s price to the changes in Implied Volatility (IV). Vega estimates how much an option price will change as a result of 1% change in volatility.

A change in IV will have the same effect on both Calls and Puts options:
An increase in IV would increase an option’s price, whereas a decrease in IV will decrease an option’s price.
This is because higher volatility implies greater expected fluctuations in the stock price, which means a greater possibility for an option to move into your favor by the expiration date.

Vega of ATM, ITM & OTM Option
Vega will be the highest for ATM options, and would gradually get lower as options become more ITM and OTM.
That means, when there is a change in volatility, the value of ATM option would change the most. This makes sense because ATM option has the highest time value component, and that the changes in IV will only affect the time value portion of an option’s price.

Comparing between ITM & OTM options, the impact of volatility changes will be greater for OTM options than it is for ITM options.

Effect of Time Remaining to Expiration on Vega
Assuming all other things constant, Vega decreases when as time passes (as the option gets closer to the expiration).
Vega is relatively higher when there is more time remaining to expiration. This is because options with more time remaining to expiration have larger portion of time value, and it is the time value component that will affected by the changes in volatility.

Effect of Implied Volatility on Vega
Vega will be lower when IV decreases, especially for ITM and OTM options.
However, Vega is relatively stable / unchanged for ATM option.

Related Posts:
* Option Greeks
* Options Trading Basic – Part 1
* Options Trading Basic – Part 2
* Understanding Implied Volatility (IV)
* Understanding Option’s Time Value
* Learning / Understanding Candlestick Charts
* Learning Charts Patterns

Read More

Relationship between OPTIONS GREEK with DEGREE of MONEYNESS, IMPLIED VOLATILITY and TIME TO EXPIRATION: Summary – Part 1

Option Greeks have been one of the main topics that I have previously shared in details in this blog.
I’ve tried to explain each of option greek in a simple way for easy but yet deep understanding. It’s really not easy doing this, but I was very encouraged by many compliments and positive feedback from my readers. I'm happy that many people in fact have benefited from these Option Greeks articles. I'd really like to thank my readers for their continuous support. :)
Here I tried to summarize the main understanding of Options Greeks:

DELTA
Delta is an option greek that measures of the change in the option price due to a change in the underlying stock price.

Delta of ATM, ITM & OTM Options
The delta values for long position will be positive for Calls (0 to 1) & negative for Puts (0 to -1).
At-the-money (ATM) options have deltas around 0.5 (Calls: +0.5, Puts: -0.5).
Out-of-the-money (OTM) options have deltas between 0 to 0.5 (Calls: 0 to +0.5, Puts: 0 to -0.5).
In-the-money (OTM) options have deltas between 0.5 to 1 (Calls: +0.5 to +1, Puts: -0.5 to -1).

Effect of Time To Expiration on Delta:
As the time to expiration is nearing, the delta of ITM options increases (i.e. ITM option’s delta gets closer to 1 for Calls or to -1 for Puts) and the delta of OTM options decreases (i.e. OTM option’s delta gets closer to 0).

Impact of Implied Volatility on Delta:
When Implied Volatility (IV) increases, delta of OTM option will increase, whereas the delta of ITM option will decrease.
However, the delta of ATM option will always remain at around 0.5.

GAMMA
Gamma is an options greek that measures the rate of change of delta due to a one-point change in the price of the underlying stock.
In other words, Gamma estimates how much delta would change if the price of the underlying stock changes by $1.
So, gamma indicates how “stable” its corresponding delta is.
A high gamma means that the delta can change considerably for even a small move in the stock price.
Unlike delta, gamma for long position is always positive for both Calls and Puts. That means delta will increase as the underlying price increases, and delta will decrease as the underlying price decreases.

Gamma of ATM, ITM & OTM Options
Gamma is the largest for ATM options, and gradually decreases as it moves furthers towards ITM and OTM.
This means that the delta of ATM options changes the most when the stock price moves up or down, as compared to ITM & OTM options.

Effect of Time To Expiration on Gamma
As the time to expiration gets nearer, the gamma of ATM options increases (is relatively higher), whereas the gamma of deep ITM and deep OTM options normally decreases (is relatively lower).

Impact of Implied Volatility (IV) on Gamma
When the Implied Volatility decreases, the gamma of ATM options increases, whereas the gamma for deep ITM or OTM options decreases.
When the Implied Volatility is very low, the gamma of ATM options is relatively high, while the gamma for deep ITM / OTM options is relatively low (close to 0).
This is because when the volatility is low, the time value portion of an option is low. However, time value of ATM option is still higher relative to ITM & OTM options, hence the gamma of ATM option is higher as compared to ITM & OTM options.

On the other hand, when IV is high, gamma tends to be stable for ATM option as well as ITM and OTM options. This is because when volatility is high, the time value of deep ITM / OTM options are already quite substantial. As a result, the increase in the time value of deep ITM / OTM options as they go nearer the money will be less dramatic. Therefore, gamma tends to be stable across all strike prices in this case.

Continue to Part 2.

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The Impact of IMPLIED VOLATILITY (IV) on OPTIONS GREEKS: Summary

The Impact of Implied Volatility (IV) on DELTA
Assuming all other factors constant, when Implied Volatility increases, the time value portion of an option will increase.
As a result, the delta of OTM (Out-of-The-Money) options will go up, whereas the delta of ITM (In-The-Money) options will go down.
Nevertheless, the delta of ATM (At-The-Money) options will always remain at around 0.5.

Why is it so?
As discussed previously, IV has a very big impact on the option price. However, IV would affect only the time value component of an option's price, not on the Intrinsic Value.
Therefore, when there is significant movement in Implied Volatility, ATM and OTM options will be greatly affected as compared to ITM options.

However, although ATM will be significantly affected by IV movement, the delta of ATM options will always be around 0.5.

The Effect of Implied Volatility (IV) on THETA
When Implied Volatility (IV) decreases, Theta will be lower, especially when it is approaching expiration.
On the other hand, when IV increases, Theta would be higher.

Why is it so?
As discussed earlier in this post, Time Value as the price that people are willing to pay for the chance / uncertainty as to whether or not an option will finish ITM.
The more uncertain, the higher the time value will be.
An option that is far OTM has almost no chance of finishing ITM. As such, it will not command a high time value.
An option that is already deep ITM is almost certain that it will finish ITM, hence time value is smaller.
But ATM or near ATM options have more uncertainty as to whether or not the options will finish ITM, and therefore these options have a higher time value.

When IV decreases, such uncertainty will be lower, particularly when the option is nearing to expiration. This lower uncertainty will then be reflected in lower time value. Since Theta is the decrease of time value due to the passage of time, Theta will naturally be lower because it has less time value to lose over the remaining time to expiration.

For more detailed discussion, go to: Options Greek.

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The Impacts of TIME REMAINING TO EXPIRATION on OPTIONS GREEKS: Summary

The Effect of Time Remaining To Expiration on DELTA
Delta is a measure of the change in the option price resulting from a change in the underlying stock price.

An option’s Delta does change as one trading day passes. This is often called as “Delta Decay”.
As the expiration is nearing (time to expiration gets shorter), the time value portion of an option is declining (time decay effect).
This causes the delta of ITM (In-The-Money) options to increase (i.e. ITM option’s delta gets closer to 1 for Calls or to -1 for Puts) and the delta of OTM (Out-of-The-Money) options to decrease (i.e. OTM option’s delta gets closer to 0).

As a result:
For ITM options, for the same strike price, the longer days to expiration, the lower the delta. Hence, a next month ITM option will have a lower delta than the current month option.
On the other hand, for OTM options, for the same strike price, the longer days to expiration, the higher the delta. So, a next month OTM option will have higher delta than the current month option.

The Impact of Time Remaining to Expiration on THETA
As mentioned earlier, as the expiration is nearing (fewer days to expiration), the time value portion of an option will be declining due to “time decay” effect.
And Theta is a measure of the Time Decay, i.e. the rate of decline of option’s time-value resulting from the passage of time.

Theta (time decay) increases as an option gets closer to expiration.
Theta would increase sharply (resulting in time value decrease at an accelerating rate) in the last few weeks before expiration (particularly in the last 30 days before expiration). Therefore, this can severely undermine a long option holder's position.

However, please note here that Theta increase sharply (Time Value decreases at accelerating rate) as expiration nears is true only for ATM option.

For both ITM & OTM options, on the other hand, Theta decreases as an option is approaching expiration.
As a result, for both ITM & OTM options, Time Value actually decreases at a decelerating rate as expiration nears.


Please refer to “More Understanding about Options Time Value” for further discussion about this.

The Effect of Time Remaining to Expiration on VEGA
Vega is a measure the sensitivity of an option’s price to changes in Implied Volatility (IV).
Assuming all other things unchanged, Vega decrease as an option gets closer to expiration.

Vega is higher when there is more time remaining to expiration. This makes sense because options with more time remaining to expiration have larger portion of time value, and it is the time value that is affected by changes in volatility.

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Options Greeks and Position in the Market (Long vs. Short): Summary

DELTA and the position in the market:
* Long calls have positive delta; short calls have negative delta.
* Long puts have negative delta; short puts have positive delta.
* Long stock has positive delta; short stock has negative delta.

Positive delta means that the option’s value will increase when the underlying stock price increases, and will decrease when the stock price decreases (positive relationship).
Negative delta means that the option’s value will increase when the underlying stock price drop, and will decrease when the stock price rises (negative relationship).

For Calls, the value of delta ranges from 0 to 1, whereas for Puts from -1 to 0.
Calls have a positive delta because Call premiums increases when the underlying stock price increases, and vice versa, assuming all other factors remain the same.
In contrast, Puts have a negative delta because the Put option price drops when the stock price goes up, and vice versa.

GAMMA and the position in the market:
* Both long calls and long puts always have positive gamma.
* Both short calls and short puts always have negative gamma.
* Stock has zero gamma because its delta is always 1.00 – it never changes.

Positive Gamma means the delta will increase when the underlying stock price increases, and will decrease when the stock price decrease (positive relationship).
Negative Gamma means the delta will decrease when the underlying stock price rises, and will increase when the stock price drops (negative relationship).

What does “long calls and long puts have positive gamma” mean?
What does “short calls and short puts have negative gamma” mean?
Please refer to the following post for further discussion about this:
Option Greek: GAMMA

THETA and the position in the market:
* Long calls and long puts always have negative theta.
* Short calls and short puts always have positive theta.
* Stock has zero theta – its value is not eroded by time.

Positive theta means that the option value will increase as the time passes, while negative theta means the option value will fall as the time passes.
Therefore, it makes sense that long options have negative theta and short options have positive theta.
If options are continuously losing their time value as days pass, a long option position will lose money because of theta, whereas a short option position will make money because of theta.

VEGA and the position in the market:
* Long calls and long puts both always have positive vega.
* Short calls and short puts both always have negative vega.
* Stock has zero vega – it’s value is not affected by volatility.

Positive vega means the option price increases when volatility increases, and decreases when volatility decreases.
Negative vega means the option price decreases when volatility increases, and increases when volatility decreases.

RHO and the position in the market:
Long calls and short puts have positive rho.
Short calls and long puts have negative rho.

Positive rho means the option price increases when the interest rate increases, and decreases when the interest rate decreases.
Negative rho means the option price decreases when the interest rate increases, and increases when the interest rate decreases.

For more detailed discussion, go to: Option Greeks.

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Options Greeks vs. OTM, ATM & ITM Options: Summary

1) Option Greeks: DELTA
Delta is a measure of the change in the option price resulting from a change in the underlying stock price.

The delta values will be positive for Calls & negative for Puts.

At-the-money (ATM) options have (absolute) deltas around 0.5.
Out-of-the-money (OTM) options have (absolute) deltas between 0 to 0.5.
In-the-money (OTM) options have (absolute) deltas between 0.5 to 1.




2) Option Greeks: GAMMA
Gamma is a measure the rate of change of delta due to a one-point change in the price of the underlying stock.

Unlike delta, gamma is always positive for both Calls and Puts.

Gamma is the highest for the ATM options, and gradually gets lower as it moves furthers towards ITM and OTM.
That means that the delta of ATM options changes the most when the stock price moves up or down, as compared to ITM & OTM options.

3) Option Greeks: THETA
Theta is a measure of the rate of decline of option’s time-value resulting from the passage of time (TIME DECAY).

Theta is typically highest for ATM options, and is progressively lower as options are ITM and OTM.
This makes sense because ATM options have the highest time value component, so they have more time value to lose over time than an ITM or OTM option.

4) Option Greeks: VEGA
Vega is a measure the sensitivity of an option’s price to changes in Implied Volatility (IV).

Vega is highest for ATM options, and is gradually lower as options are ITM and OTM.This means that the when there is a change in volatility, the value of ATM options will change the most. This makes sense because ATM options have the highest time value component, and changes in Implied Volatility would only affect the time value portion of an option’s price.




For more detailed discussion, please refer to the following post:
Option Greeks

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