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- The basics of call option
- The Option Jargons
- Call Option - Buying
- Call option -Selling/Writting
- Buying the Put Option
- Selling the Put option
- Call & Put Option - Summary
- Option contract - Moneyness concept
- Delta - 'The option Greek' Section -1
- Delta - Section 2
- Delta - Section 3
- Gamma - Section 1
- Gamma - Section 2
- Concept of 'Theta"
- The Basics of Volatility
- Calculation of Volatility (Historical )
- A study to Volatility and Normal Distribution
- Application of Volatility
- Vega - Basics
- Understanding the Greek Interaction
- A Guide to 'Greek Calculator'
- Re-calling Call & Put Option
- Bringing to a conclusion
- Physical Settlement

These chapters provide a solid foundation to better understand volatility. Now we know what volatility is, how to calculate it, and how to use it for trading strategies. Now it is time to get back to the main topic - Option Greek, and specifically the 4 Option Greek "Vega". Before we dive deeper into Vega we need to talk about Quentin Tarantino.

Quentin Tarantino is a huge favorite of mine and his films. Quentin Tarantino is one of Hollywood's most talented directors. He is responsible for super-cult films like Pulp Fiction, Kill Bill and Reservoir Dogs. I recommend you to watch his films. You may love them as much as I do.

It's well-known that Quentin Tarantino keeps all production details secret until the movie trailer is released. The trailer will reveal the movie's name, star cast details, storyline, location, and other information. This is not true for the movie he's directing, "The Hateful Eight", which will be released in December 2015. Everything about "The Hateful Eight", including the storyline, cast and location, has been leaked. This means that people know what to expect from Tarantino. Given that the majority of information about the movie has been leaked, wild speculations are rife about its box office success.

This could be the subject of some analysis.

**Past movies**We know that almost all Tarantino's movies have been successful. We can reasonably predict that "The Hateful Eight" will be a big box-office hit based on his previous directorial performances.**Movie Analysts' forecast**– These are professional Hollywood movie analysts who have a deep understanding of the business side of cinema. These analysts predict that "The Hateful Eight" may not be a hit (unlike his previous films), as the majority of details about the movie are already failing to excite the audience.**Social Media**- You'd be surprised at how many people are excited about 'The Hateful Eight', even though they know what to expect. According to the reaction on Social Media, "The Hateful Eight" is likely to be a big hit.**The final outcome**- We will know whether the movie is a success or not once it is released. This is obviously the final verdict, and we will have to wait until the movie is out.

We don't really care about the fate of the movie, but I will be watching .

You may wonder why we're even talking about Quentin Tarantino when there is a chapter on Options and Volatility. This is my attempt (hopefully not lame!) to explain the three types of volatility available - Historical Volatility and Forecasted Volatility. So let's get going.

**Historical Volatility** This is similar to how we judge the box office success for 'The Hateful Eight' on the basis of Tarantino's previous directorial ventures. Stock market world uses historical volatility to calculate the closing prices of stock/index. We discussed how to calculate historical volatility in Chapter 16. Historical volatility is easy to calculate, and it helps us with most day-to-day requirements. Historical volatility, for example, can be used in an option calculator to determine a quick and dirty option price. (More details on this are in the next chapters

**Forecasted Volatility**is akin to a movie analyst trying to predict the fate of "The Hateful Eight". Analysts forecast volatility in the stock market. Forecasting volatility is the act of forecasting volatility over a desired time period.

But, you don't need to predict volatility. There are many options strategies that can be profitable, but the profitability of each strategy is dependent on how volatile you expect it to be. If you have a view on volatility, such as that volatility will increase by 12.34% in the next seven trading sessions, you can create option strategies to profit from this view.

At this stage, you need to realize that it is not necessary to have an opinion on the direction of the stock market. You can also view volatility. Professional options traders tend to trade on volatility, not market direction. This is something I must mention: Many traders find that forecasting volatility is more efficient than forecasting the market direction.

Now clearly having a mathematical/statistical model to predict volatility is much better than arbitrarily declaring "I think the volatility is going to shoot up". A few statistical models are good, such as the 'Generalized AutoRegressive Conditionsal Heteroskedasticity Process (GARCH). It sounds scary, but it is what it is. There are many GARCH processes that forecast volatility. If you're interested in this field, I can tell you right away that GARCH (11,1) and GARCH (2,2) are better suited for forecasting volatility.

**Implied volatility (IV** is like people's perceptions on social media. It doesn't matter what historical data or predictions the movie analyst makes about 'The Hateful Eight. The movie seems to have people excited, which is a sign of how it will fare. The implied volatility is also a measure of market participants' expectations about volatility. On one hand, we have historical and forecasted volatilities which can be described as'manufactured'. However, on the other we have implied volatility that is in a sense "consensual". Implied volatility is the consensus volatility reached among all market participants regarding the expected amount of underlying volatility over the remaining life options. The premium price reflects implied volatility.

The IV is more valuable than the other types of volatility.

India VIX, which you may have seen on the NSE website, is the official 'Implied Volatility’ index. India VIX is calculated using a mathematical formula. Here is a explaining how India VIX was calculated.

If the calculations seem overwhelming to you, here's a quick overview of India VIX ( *I have reprinted some points from NSE's whitepaper*).

- NSE calculates India VIX using Nifty Options' order book
- India VIX is calculated using the best bid-ask rates of Nifty options contracts for the next month and near-month.
- India VIX is an indicator of investor's perception about the market's volatility in near term (30 calendar days).
- The expected volatility is higher if the India VIX value is higher and vice versa
- Markets that are volatile tend to move quickly and the volatility index tends toward rising.
- When markets are less volatile, volatility indexes fall. India VIX and other volatility indices are often referred to as "Fear Index" because the volatility index increases. However, it is important to be cautious as markets can swing sharply in any direction. Volatility indices are used by investors to measure market volatility and help them make investment decisions.
- Volatility Index differs from NIFTY, a market index. NIFTY is a measure of market direction and is calculated using the price movements of the underlying stocks, whereas India VIX measures expected volatility and uses the order book for the NIFTY options. India VIX, on the other hand, is an annualized percentage. Nifty is a number.

NSE also publishes the implied volatility at different strike prices for all options that are traded. These implied volatilities can be tracked by looking at the option chain. Here is an example of the option chain for Cipla with all IV's clearly marked.

(IMAGE 1)

A standard options calculator can calculate the Implied Volatilities. In the next chapters, we will cover how to calculate IV and how to use IV to set up trades. We will now turn our attention to understanding Vega.

**Realized volatility** is very similar to what we will see in the movie. Realized volatility also involves looking back at the past and finding out what volatility occurred during the expiry sequence. Realized volatility is important, especially when you compare today's implied volatilities with the historical implied volatility. This angle will be explored in greater detail when we discuss "Option Trading Strategies".

You may have noticed that when there are strong winds or thunderstorms, the voltage in your home fluctuates violently. This can lead to a surge in the voltage and damage to electronic equipment.

The stock/index price swings heavily when volatility increases. This is why a stock that trades at Rs.100 can suddenly start to move between 90 and 110. All PUT option writers begin to panic when the stock reaches 90. This is because the Put options have a good chance at expiring in the cash. All CALL option writers will panic if the stock reaches 110. This is because all Call options have a good chance to expire in the money.

Option premiums are more likely to be in the money regardless of whether volatility rises for Calls and Puts. Think about it: If the spot trades at 475, and you have 10 days before expiration, 500 CE options could be written. There is no intrinsic value, but there is some value in time. Assume that the option trades at Rs.20. You would be willing to write the option. I think you could write the options and get the Rs.20/- premium. But what if volatility is higher over the next 10 days? Maybe election results or corporate results will be scheduled simultaneously. You can still write the option for Rs.20. You might not. As you all know, with volatility increasing, an option could easily expire "in the money" and you may lose all your premium money. What would motivate option writers to create options if they were afraid of volatility? A higher premium would, evidently. You could consider writing an option instead of Rs.20 if the premium was 30, 40 or more.

This is what happens when volatility increases (or is expected increase). Option writers begin to fear that they might be writing options that could potentially make them 'in the cash'. However, fear can be overcome with a price. Option writers expect higher premiums when writing options are available. Therefore, premiums for call and put options will go up as volatility increases.

The graphs below highlight the same point.

(image 2

(image 3)

The premium value in Rupees is represented by the Y axis. Volatility (in%) can be shown on the X axis. As we can see, premiums rise when volatility increases.For Put as well as Call this is true. These graphs go further than that. They show you how option premium changes with volatility and days until expiry.

Take a look at the CE chart. The blue line shows the change of premium relative to volatility change when there are 30 days remaining for expiry. The green and red lines represent the change in premium relative to volatility change when there are 15 days and 5 days respectively.

To keep this in perspective, here's a few observations. These observations are common for both Call or Put options.

- Referring to the Blue Line - When there are 30 days before expiry (start of series), and volatility increases from 15%-30%, the premium rises from 97 to 193. This represents a 95.5% increase in premium.
- Referring back to the Green Line - If volatility rises between 15% and 30% (15 days before expiry) the premium will rise from 67 up to 100. This is approximately half of the change in premium.
- Referring to Red line: When there are five days before expiry (towards end of series), and volatility increases from 15%-30%, the premium rises from 38 to 56. This represents approximately 47% increase in premium

We can draw few conclusions if we keep the above observations in mind.

- The graphs below show a 100% increase in volatility, from 15% to 30%, and the effect it has on premiums. This is how we can capture and understand volatility's effect on premium and time. These observations are valid even if volatility moves in smaller amounts, such as 20% or 30%. The only difference is that the premium move will be proportional.
- The increase in volatility has the greatest effect when there are more days before expiry. This means that if volatility is high at the beginning of a series, premiums will be plum. It might be a good idea for you to write these options and collect premiums. Invariably, premiums cool down when volatility is low. You could also pocket the differential in premium
- If there are fewer days before expiry, volatility increases and premiums go up. However, it is not as dramatic as if there are more days until expiry. You might be wondering why long options aren't working in volatile environments. Take a look to the expiry dates.

One thing is certain: premiums rise with volatility. But the question is, "by how much?" The Vega confirms this.

The Vega is an option's rate of change (premium) for every percentage change in volatility. The vega, which can be used for calls or puts, is a positive number that indicates how options increase in value as a result of volatility increases. If an option has a volatility of 0.15, it will lose 0.15 for every % in volatility.

Perhaps it is time to reexamine the course this module on Option Trading took and the direction it will go (over the next few chapters).

The basic structure of options was first covered. Next, we looked at the Call and Put options from the buyers and sellers perspectives. Then we moved on to understanding the moneyiness of options and a few technicalities in relation to options.

We also understood the option Greeks, such as the Delta and Gamma, Theta and Vega, along with a small series of Normal Distributions and Volatility.

Our understanding of Greeks at this point is only one-dimensional. We know, for example, that option premiums change based on delta as the market moves. In reality, however, multiple factors work simultaneously. On one hand, volatility can be high, while markets move heavily. The options premiums could also fluctuate wildly, with the option liquidity getting sucked into and out all the time. This is what markets do every day. For new traders, this can prove to be quite overwhelming. They may quickly rebrand the markets to 'Casino' because it can seem overwhelming. Varsity is the best place to point out if you hear such negative comments about the markets.

However, I want to emphasize that all of these Greeks manifest themselves on premiums and that premiums vary on an individual basis. It is crucial for traders to understand the 'inter Greek' interactions. We will talk about the topic in next chapter. The next chapter will provide a basic understanding about the Black & Scholes pricing formula and how to apply it.

The following article appeared in on 31 August 2015.

This is a very recent event. Everyone who is remotely involved in the stock market will know that the Indian stock markets experienced a sharp decline of close to 5.92% on August 24, 2015. This was the worst single-day drop in Indian stock market history. The onslaught was not kind to any of the top stocks, and all suffered a decline of 8-10%. These panic days are common in equity markets.

However, something strange happened in the options market on 24 thAugust 2015. Here are some data points.

The Nifty fell by 4.92%, or approximately 490 points.

(image 4)

India VIX jumped by 64%

(image 5)

However, call option premiums have risen!

(image 6)

Options traders will be familiar with the fact that call option premiums decrease when the market falls. Option strikes above 8650 performed better than call option premiums lower than 8600. However, they did show a decline in value. The premiums did not fall as expected, but increased by 50 to 80%. This has puzzled many traders. The move is being blamed on market manipulation and rate-rigging. This can be explained with option theory logic.

We know that option premiums can be affected by sensitivity factors, also known as the Option Greeks. Delta, as we know, measures the sensitivity of an option premium to changes in the underlying.Let's take a look at what happens when the Delta for a call options is 0.75. The premium will then increase/decrease by 0.75 for every 1 point decrease in the underlying. The Nifty lost 490 points on August 24, 2018. All call options that have a "noticeable Delta" (e.g. 0.2,0.33,0.6, etc.) also declined. A decline in the underpinning tends to cause Delta in in-the-money’ options (as was the situation on 24th August, when all strike below 8600). Consequently, all premiums fell.

Options that are 'out of the money' usually have a delta of 0.1 or less. This means that no matter what the underlying moves, the premium for an option will remain very restrictive. All options above 8600 were considered 'out-of-the-money' options, meaning they had low delta values and options that were not within the market. These call options didn't lose much premium value despite the huge fall in the market.

This explains why certain call option values did not decline, but why premiums went up. Vega, the option Greek that captures market volatility on premiums for options, is the answer.

Volatility increases, and so does the Vega. This is independent of calls or puts. Option premiums tend to rise with an increase in Vega. The volatility in Indian markets jumped 64% on the 24 th Aug. Participants in the Indian markets were not prepared for this increase in volatility. Consequently, all options saw their Vega increase and consequently, their premiums increased. Vega has a particularly strong effect on 'Out-of-the-money' options. The option premiums for these out-of-the-money options were not affected by the low delta value of the call options. However, the Vega value was high and this increased the option premium.

On 24 th August 2015, we witnessed the extraordinary - call option premium increased 50 - 80 percent on a day that markets crashed 5.92%.

- Historical volatility is measured using the closing prices for the stock/index
- Forecasted volatility is predicted by volatility forecasting models
- Implied volatility is the market participants' expectation of volatility
- India VIX is the implied volatility for the next 30 day period
- Vega is the ratio of premium change to volatility.
- When volatility rises, all options see an increase in premium
- Volatility is most noticeable when there are more days before expiry.