**1.Basics of Call Options & Put Options**

Here we will learn about the basic characteristics of Put and Call options such as strike crisis, expiration dates, and how these values change with the changes in market prices.

We can define Option as a contract where a buyer has the right to sell 100 shares of stock at the options strike price at or before expiration.

**Strike Price**: The stock price in which an option buyer can purchase or sell 100 upon exercising the option.

**Expiration: ** The date an option ceases to trade on the market, and converts to shares of stock, or expires worthless.

Options are quoted on a per share basis and the minimum shares for a single option is 100 shares. Ie if the option price per share is $.0.50 the option value will be $50 ($0.50 multiplied by 100 shares).

From the buyers perspective, a call option means the right to buy 100 shares of stock at the call strike price before the expiration. If the call price is higher than the initial purchase then the buyer will benefit with a profit. For example, if a trader buys at $ 5 and the current price is $ 6 then the trader will have a profit of $100 making the total options value to $600. From the sellers perspective, the call option is an obligation to sell 100 shares of stock at call’s strike price. Sell will benefit when the call’s price is less than the initial sale price. Eg: If the trader sells the call option for $5 and when it falls to $ 3 then he can make a profit of $2 x 100, ie $200.

Call options value increase with the increase in stock price while it decreases with the decrease in the stock prices. Let’s see how the actual options price changes with the stock price change. Calls increase in value with the increase in stock values similarly, Call value decrease with the decrease in the stock value.

From the above, we can see that call option started near $5 and ended near $20. In this case, the buyer of the option started at $5 and ended at $20 will have a profit of $1500 and the seller of the option will have a $1500 loss. In a different case if a trader sold an option for $5 and later bought back for $ 20 then they will have a loss of $ 1500. So call buyers anticipate that the stock prices increase as it will increase the call price. Similarly, call sellers anticipate that the stock price decrease as it will decrease the call price.

Now let’s examine the PUT option from the buyers and sellers perspective. From the buyers perspective the PUT option is the right to sell 100 shares of stock at put’s strike price at or before expiry. Buyer will gain profit when put’s price is higher than the initial purchase price. From the sellers perspective, PUT option is the obligation to buy 100 shares of stock at the put’s strike price (if assigned). Sellers earn profits from PUT option when the prices fall than what they initially sold it for. Say a seller sells a put for $ 20 whose value is $2000 falls to $15, when they buy back earns a profit of %5 whose value would be $500 on such trade. Now we can examine how the PUT option reacts with the stock prices with a picture below.

Here, unlike the Call option, the PUT increases with the decrease in the value of stock price. Similarly, PUT decrease in value when the stock price goes up. As we can see from above picture the PUT started at $3 and rose to $6 and expired worthless. From the buyers perspective, they bought it for $3 rose to $6 which is a $300 increase in the actual value which represents a profit. Since the option expired worthless, they would have lost everything they paid for it. Now, from the seller’s point of view, they sold them for 3 dollars, which rose to $6 means they would $ 300 for this contract

**2: Option Strike Prices**

We will discuss in detail here about the strike prices from the Call and Put option perspectives. A Strike Price is basically price in which a buyer can purchase or sell 100 shares if they exercise the option. Only the option Buyer can exercise the option. For e.g., there is a call at the strike price of $ 110 and the call buyer exercises that option they will buy 100 shares for a $110 per share. If someone who owns 110 Put and exercises that 110 Put, sells 100 shares at $110 per share. For every option buyer, there has to be an option seller. So the person who sells the option.

We should be familiar with the three terms when we deal with options and they are ITM (in the money), ATM (at the money) and OTM (out of the money). We need to know the relationship between them in addition to what they mean with respect to Calls and Put. For ITM is when a Call has a strike price that is less than the stock price or when a Put has a strike price greater than stock price. ATM means that the call and put has the strike price is equal to stock price. OTM means the Call has the strike price greater than the stock price and Put has the strike price less than stock price. Let’s see these by hypothetically applying these terms.

From the above table, we can the see that the stock price is trading at $150 along with different strike prices. Focusing on the call section we can see that the Call is ITM (in the money) when the strike prices are below the current stock price. The calls are OTM (out of the money) when the strike prices are greater than the current stock price. For the Puts it is completely reverse, that is they are OTM when the strike prices are below the current stock price ($150) and they are ITM when the strike prices are above the current strike price. For both Calls and Puts, we can see they are ATM when the strike price is equal to current stock price. If we have for example the current strike price equals to 148 or 152 they will be still considered ATM since they are near the current stock price.

Comparing option Call strike prices to the premium they have. ITM have the highest price whereas OTMs will have the lowest prices. From the below chart we can see the SPY has the value $227 which means any option with the strike price below the $227 is considered to be in the money. As we can see when we go towards to the lower strike prices the Call premium increases. OTM call options are calls with the strike prices calls above the current stock price ($227). We can observe that at higher and higher strike prices the call’s premium gets cheaper and cheaper which means there is no value buying the stock at the current stock prices.

Put Strike vs the Put Premium

This is completely opposite what we have observed for the call strike vs its premium. As we know Puts are ITM when the current strike price is above the current stock price. We can observe this by the following picture.

Any put with the strike price above $227 in ITM. We can see that any put with the strike price is ITM (in the money) and the premium gets more and more expensive at higher strike prices. It is because there is more value being able to buy shares at the higher price than the current market price. On the other hand, OTM puts are any puts with a strike price below the current stock price. As we go towards the lower side the premium gets cheaper and cheaper as there is no value selling shares at the lower price.

**2: Options Expiration.**

We’ll now discuss expiration and what calls and puts expire with the expiration how we can choose the expiration with considerations doing so.

Expiration is a date that represents the final day the option can be traded before settling to its final value. Options that are ITM at expiration will expire too long or short shares, while OTM option will expire without having any value and they will disappear from the account. Looking at the various scenarios where we encounter the expirations.

When we long a Call option that expires ITM, it will have 100 shares of long stock. If we short a Call ITM expiry, it will expire to negative 100 shares, ie short stock position of 100 shares.

If we long a Put option ITM at expiration then it will expire to -100 shares per contract which is a short stock position of 100 shares. If we short a put option ITM at expiry that will expire to 100 shares, a long stock of 100 shares. If we long or short a Call or Put options out of the money at expire will expire to 0 ie it is worthless. We can easily remember this. If there is a bullish options position which expires ITM that will expire to +100 shares. So a bullish options position would be a long call or short Put. Similarly, if there is a bearish option position which expires ITM, will expire to -100 shares of stock.

Various expiration types are Monthly (standard), Weekly or Quarterly. We can check these types and when they would expire with a tabular representation below.

Most of the time we trade the standard expiration cycle which occurs on the 3^{rd} Friday every month. Any other expiration cycle that does not land on the 3^{rd} Friday will be considered a non-standard expiration cycle. Weekly and Quarterly are the non-standard expiration cycles. The quarterly cycle occurs at the final trading day of March, June, September or December. If they fall on any Holiday, will be moved up by 1 trading day.

Knowing about the longest term expiration cycle. As an example AAPL expiration cycle on Dec 9th, 2016.

We can see there is 770 days expiration duration which is 2 years approximately could be the longest expiration cycle. We can also observe that most of them short-term ie weekly expiration cycles and the long-term expiration cycles being the monthly cycles. With these kinds of cycles which one would be the best expiration cycle to choose from?

First, we need to choose our strategy. Options are typically used for short-term positions. If we depend on time decay for profits, stay near-term. In stock replication strategies, go for a long-term to minimize decay.

We need to consider the liquidity for choosing the expiration. The most trading activities take place in the near term expiration cycles and most of the open option contracts are in the near term expiration cycles. They have most volume and open interest too.

If we look at the left graph above for AAPL option volume by Expiration, the near time expiration is 0(zero) day ie, that expiration is on the same exact day. Here staying in the 7 and 42-day expiration cycles will be beneficial since there are more people trading this cycle. Means it will be easy to enter and exit our options position.

In the right graph AAPL option, open interest by expiration means how many contracts are open between 2 parties in those options. Looking at the 7 and 42-day cycles we can observe significant open interest. a 406-day cycle has 931K open interest contract we can see the volume is low compared to 7 and 42 standard monthly cycles. We can say that the 1^{st} and 2^{nd} standard monthly cycles are the most liquid means we need to stick to those options when we are trading short-term option positions.

**4: Intrinsic and Extrinsic Value.**

Every option has 2 price values known as intrinsic value and extrinsic values.

-> Intrinsic value is the value of exercising an option as opposed to buying or selling shares at the current market price. It is the value of an option at expiration. If the current stock price is at $200 and Call strike price at $150 then intrinsic value of that call is $ 50, because the value of buying shares at 150 as opposed to 200 is worth $ 50. Similarly, if we do it with call strike price at $175 then the intrinsic value of that call would be $25. If the strike price of the call is $210, the intrinsic value will be $0.

-> Extrinsic value is the portion of an option price that exceeds its intrinsic value. Also, it is the premium associated with the potential for an option to become more valuable before it expires. This is also called as Time Value. For eg, if the stock price is $200 with the Call strike price at $150 the intrinsic value of this call is $50. But if the calls price is $52 then the additional value is called extrinsic value. If the intrinsic value is $25 having the call price $30 then we have $5 as extrinsic value. With the call strike price $210 it has no intrinsic value, still, has $2 extrinsic value. $ 210 Call has no value in this case but it has the potential if the stock price is increased to $ 220 which will have $ 10 intrinsic value.

Let’s see how extrinsic and intrinsic values change using a picture below.

Here is a call with a strike price of $ 105. Whenever the stock is trading above 105 we can say this has an intrinsic value. When it is equal to or below 105 it has (no intrinsic) an extrinsic value. As the expiration nears the extrinsic value diminishes leaving only intrinsic value.

**5: Exercise and Assignment.**

Here we are going to learn about what happens to calls and puts when the option buyer exercises and what happens to the person who shorts that option, how to gauge early assignment risks if we are short in the money options.

EXERCISE AND ASSIGNMENT: Option buyers have the right to exercise their options at or before expiration. When an option is exercised, a trader who is short that option is assigned.

For a CALL if exercised Call buyer purchases 100 shares at the strike price. If assigned the seller has the obligation to sell -100 shares at the strike price.

For a PUT buyer if exercised sells 100 shares at the strike price. If assigned Put seller assigned 100 shares at the strike price. Demonstrating this with an example:

If 105 Call buyer exercises the option, the purchase of 100 shares for $ 105/share. If it is a call seller who is assigned -100 shares for $ 105/share.

For 75 Put buyer exercising the option, they sell the 100 shares for $75/share. Now, someone who has short that 75 put will have the obligation to buy 100 shares for $75 per share.

There are two important things that are to be noted about Exercising and Assignment. One is at expiration in the money options are automatically exercised. For eg, we have a Call at strike rate of $100.01 or higher at expiration that 100 call will be automatically exercised. Similarly, if we have Put 50 it will be automatically exercised if the stock priced is 49.99 or lower at expiration. The option buyer necessarily doesn’t need to exercise the option. If they let, in the money options expired will be automatically assigned.

Considerations for Excising options: Even if you don’t have enough capital to hold the long or short stock position associated with your option position, you can still be exercised or assigned into the stock position. As an example, if we have $10000 in our account and a couple of weeks ago we bought a 500 call option and now the stock at expiration is 499 if we think the option is going to expire worthlessly we take it back from a loss. If it is $500.50 that long call is automatically exercised at expiration. If we are going to buy 100 shares of stock for $500/ share. It makes $50000 but if we have only $10000 in our account we need to close or our booking agent should do it.

When exercising an option the extrinsic value is lost this result most of the options are not exercised. Let’s say we have a stock price at $100, 95 option Call is trading at $7.00 we know that this has an as intrinsic value of 5 and extrinsic value of $2 which is considered to be a loss. It means exercising this option will be lead to an overall loss of $200. If we exercise the option 100 Call with option price $5, it will have $0 intrinsic value, and the loss from exercising this option would be $500. If we exercise the option Call 70 with the option price $30.10, the intrinsic value will be $30 and extrinsic value of .10 the loss from exercising this option would be $10. Here we can note that while exercising the option 100 call with the stock price at $100 the profit for this trade is 0. However, as we have given up the $5.00 option as premium we effectively lose $500.00.

**Who gets assigned?**: We might be wondering who gets assigned to a short option. Ie if there are 5000 option contracts and one contract is exercised who gets that option assigned to? The actual process that happens is random. When the options are exercised the OCC (Options clearing corporation) receives a notification which in turn uses the random procedure to select an account with short positions in those exercised options. It will go to the pool of accounts with OCC members which randomly selects accounts from that pool. Once the accounts are selected they process the assignment notifications on the brokerage firm if we are assigned to the options. The picture below explains this process in detail.

**Assessing Early Assignment Risks**

Many traders worry about getting assigned before expiration. Let us see various scenarios in which option assignment are done in general.

When a short option is out of money or in the money with mostly extrinsic value, in this situation the likelihood of early assignment is Extremely Low.

When the option is on the money with little extrinsic value then the likelihood of assignment of an option is More.

Before a stock’s ex-dividend date: a short call is in the money and has less extrinsic value than the dividend. In this scenario, the likelihood of assignment is High to Very High.

**6: The Bid-Ask Spread.**

The Bid-Ask spread is most important as it represents a hidden cost of entering and exiting the trading positions.

Ask or the best asking price is the lowest price someone is willing to sell an asset for, and it’s the price you have to pay to buy a stock or option immediately.

The Mid price is just the midpoint between the bid and ask. It’s advisable to always try and buy or sell at the mid-price.

Bid or the best bidding price is the highest price someone is willing to pay for an asset, and it’s the price you have to sell for if you want to sell immediately.

The Bid-Ask spread is said to be the hidden cost of trading, ie the loss from the buying at the ask and selling at the bid. For example

If we are buying shares of stock with the bidding price at $100.02 and Ask price at $100.03, the Bid-Ask spread, in this case, would be 0.1 penny. Here for 100 shares there would be a loss of $1

For call option, if the bidding price is $ 5.10 with ask price at $6.30, the bid-ask spread on this call option would be $1.20. The loss here would be $120 per contract.

For Put option, the bidding price at $4.30, Ask price at $4.35 the bid-ask spread, in this case, would be $0.5 we would lose $5 per contract. So, trading products with narrow bid-ask spread make it very easy for us to enter and exit the trading positions without incurring huge costs. There are 3 factors that contribute option’s bid-ask spread.

- Whether the option is in the money, at the money or out of the money.
- The option’s number of days until expiration.
- Market volatility.

Let’s visualize these with some examples.

Here we can see the money options around 205 stretches. Also, we can see options which are close to at the money have the narrowest bid-ask spread whereas ITM Calls and ITM puts have the widest bid-ask spreads. This is because the ITMs are more and more expensive so it will be wider on more expensive options. In addition to this ITM options have less trading volume which also contributes to a wider bid-ask spread. In the case of OTM (out of the money) options, they get cheaper and cheaper as it moves further out of the money. Now we look at the options at 365 days.

Here we can see the At the money options have bid-ask spreads of around 15 to 20 cents while the OTM options have Bid-ask spreads of around 15 cents. Here we can notice ATM and ITM have the higher Bid-Ask spreads. Factors contributing this are longer transactions are more expensive, therefore will have wider bid-ask spreads. Also, longer trading options have generally low trading volumes than near-term options that contribute to a wider bid-ask spread.

**Bid-Ask Spread Vs Market Volatility: **

Naturally, as markets become more volatile Bid-Ask spreads will typically widen out because the stock prices will be more volatile. It means the options prices on that stock will also be more volatile. With more uncertainty around prices would widen out.

When a market becomes volatile the VIX index will also tend to increase because more market volatility means more people are going to buy options and pay higher premiums for options to either hedge of speculating on the option positions.

**7: Volume and Open Interest**

Volume is the number of contracts or shares traded in a given period. Trading platforms typically display the volume for a trading day.

Open Interest is the number of contracts that are open between two parties.

From the picture below:

We can see here the estimated product volumes for the year. From the above graph, we can notice that SPY has 648 million options contract for the year 2016. We can understand that more options volume means easiest entry and exit.

An open interest is the number of contracts that open between two parties, but not yet closed. When two parties open positions, open interest increase. Explaining this with an example. Let’s say Trader A buys 5 contracts to open and trader B buys 5 contracts to open. Since both have open orders open interest will increase by +5. Let’s say B buys 5 contracts to Close and C Sells 5 contracts to Open. Since only one of the order is a closing order and one is open order, open interest actually will not change.

Let’s say trader A and C want to get out of the contracts so A sells 5 Contracts to Close and C Buy 5 Contracts to Close, open interest will decrease here to -5.

**Importance of Volume and Open Interest**

Open interest and Volume indicate the amount of trading activity for a particular stock or option. Sticking to high volume and open interest products will make it easier to enter and exit positions with bid-ask spreads will be typically narrower.

**Options that have most volume and Open Interest**

Let’s look at the trading day in 2016 from above picture has 50 expiration days. We can see open interest and volume at each strike price. ATM strike price at 200 has by far the most volume on this trading day, also it has the significant open interest. Strike prices that are away from the ATM strike prices the volumes are coming down similarly the open interest also decrease. We can also notice that the strike prices that are divisible by 5 have the more open interest like 175, 180, 190 etc than other strikes. It is interesting to see that market prefers to trade at evenly divisible by 5 strikes, and sticking to that strike will give liquidity advantage because it will be easy to enter and exit the positions.

**Volume and open interest in terms of days of expiration:**

Here we can see that, in terms of volume most volume is occurring in the first 3 expiration cycles, ie with 4, 25 and 46 days to go. 4 and 46 days are standard monthly cycles and those have most open interest and volume combinations. Always keep in mind that the first two expiration cycles will tend to have highest volumes and most open interest. Let’s see with another example from the picture below.

Here also the most volume is taking place on 4^{th} and 46th-day expiration cycles. The most open interest is in the 382 expiration cycle which does not have significant volume.

**8: Order Types**

__Market Order__: Market orders guarantee immediate fills, but not the full price. As a result market orders tend to result in unfavorable fill prices. Let’s see this with an example.

Here the asking price is $5.50 and the bid price is $4.50. If we go for market buy order it is likely that we will get filled with asking price of $5.50. Another side of this is if we go for the market sells order it’s likely that we get filled with a bidding price of $4.50. Here we get very little chance of getting at mid-price of $5.00 because

__Limit Order__: These orders are used to execute trades at a specific price or better.

Example.

We see that the current price of the stock is $50/share, we want to buy it when it reaches $42.50. Now this order will not be filled unless it reaches $42.50 or lower. This may not happen in a single trading day, so we might be using a GTC order which will remain active between 30 and 60 days.

Here the current stock price is $40 and we want to exit when the price reaches $45 or higher.

__GTC Order or Good-til-Canceled__: These orders are limit orders that remain active until cancelled.

Stop-Loss Order: These are used to immediately execute a trade when a stock or options trade at a specific price. Example for Stop-Loss Sell order

If we purchased the stock at $50 and want to stop the loss when the shares trade below the $40, we need to sell the shares when the shares are at $40. This will be automatically executed at whatever the market price the share is at.

Example for Stop-Loss buy order,

If we short some shares for $70/share, but we want to buy those back if the shares rise to $75 we need to use Stop-Loss-Buy order with a specified price of $75. This will also take place automatically price when the current market price reaches $75.

Section 2: Implied Volatility

**Implied Volatility Basics:**

Implied volatility is the expected magnitude of a stock’s future price changes, as implied by the stock’s option prices. Let’s see how implied volatility in options prices is connected. We are looking at the 2 stocks with similar prices with same options on each of those stocks. Let’s say PEP (PEPSI) is trading at $102 with options to expire in 37 days having 105 Call Price. If 105 calls on PEP is $0.80 while the 100 Put is at $1.17. So, PEP’s implied volatility, in this case, is 16.41%.

Looking at UNP having similar prices whose value is $103.60. With the same DTE (Days to expire), ie 37 days, the 105 call is trading for $2.72. and 100 PUT is trading for $1.92. Here the UNP’s option prices are higher compared to PEP’s option prices. It has an implied volatility of 30.94%.

__Conceptualizing Implied Volatility__

Market participants typically use options for one of the two reasons. (1) Hedging against moments in the stock or IV or (2) Speculating on moments in the stock or IV.

If options buyers willing to pay more or options sellers demand more will lead to increase in Option Price in higher implied volatility with larger expected moments in the markets in future.

If option buyers pay less or option sellers to demand less, this will lead to decrease in options prices in lower implied volatility with smaller expected moments in future.

**Implied Volatility and Probability: **It represents one standard deviation change in the stock price. One standard and deviation encompasses about 68% of the occurrences around the average (the current stock price)

One year Standard Deviation Range Formula:

*Stock Price (plus or minus) (Stock Price X Implied Volatility)*

Let’s look at the examples for how expected range formula applied various stocks.

On the date Sep 28, 2016, NFLX has the stock price of $97.50 with IV (implied volatility) of 44% along with 1-year standard deviation range between $54.60 and $140.40 which we get using the formula stated above. With this, we can notice the probability of 68% in between the range. Taking GPRO stock with a stock price of $16.50 having IV of 84%. This calculates to the 1 year expected a range between $2.64 and $30.36 which means the GPRO is going to be out of the business or the stock price may double.

Let’s now visualize 1 SD stock price range:

Here we are looking at a graph with $100 stock with 25% IV which says that there is 68% of a chance plus/minus 25% probability moment from the current price.

Looking at the 2 SD stock price range:

With implied volatility, we can easily calculate 2 SD Stock Price Range which we get by multiplying the stock price and IV times 2.

In this case, $100 stock with IV (implied volatility) of 25% will result in 2 SD range of $50 from the current stock price. In this 2 SD range, there is 95% of occurring is between $50 and $150 in 1 year time.

Now let’s look at the difference between high and low IV stock.

Calculate Expected Ranges for any time frame.

For 1 year ranges, calculating the stock price by its implied volatility will do. Other time periods will be calculated with the formula below:

Stock Price X Implied Volatility X

For example, a $250 stock with implied volatility has a 30 day expected range of

$250 X 15% X = (Plus/Minus) $10.75

On that same stock, the one day expected range would be

$250 X 15% X = (Plus/Minus) $1.96

**What is VIX Index?**

VIX index is created by Chicago Board of Options Index (CBOI) which tracks the 30 days implied volatility of the options on the S&P 500 index (SPX). People option use this expiration cycle for SPX options that expire between 23 and 37 days. Using those expiration cycles people find out the most active products.

This index is also treated as a fear index as option prices tend to rise in times of market turbulence. Options prices on the SPX tend to rise because more people are hedging their positions and more people are willing to pay a higher premium for options because they expect the markets to be more volatile. Knowing the VIX number is an indication of overall market sentiment. When the VIX is low it is the indication that market is very complacent and if it is very high indicates there is a lot of fear in the market position. Another important thing people use VIS is that it helps them to select the strategies for current market environments. That is when there are cheap option prices it means low VIX so people choose Net Long Premium Strategies. With the high option, prices mean high VIX leads people to choose Net Short Premium Strategies.

How to identify the change in VIX index:

From the above graph we can see that the VIX is below 15 which rose back to 27.5 then fell to 12.5 then rose back to 27.5. Here we can notice that VIX is always changing on a day to day basis, ie the option prices on SPX are changing simultaneously on a day to day basis. The reasons for fluctuations in VIX and option prices are changes in stock prices actually. When the market falls the VIX tends to rise because more people will buy SPX options for safety and people are willing to pay more for speculative purposes because they expect the market to be more volatile. The change in VIX is not always caused by the price actions but due to upcoming news events. This news may move the market in a big way then people will follow with speculative positions or hedges because they do not like the insurgency of potential market moves.

__What Does VIX represent?__

It represents 1 standard deviation (68% probability) expected a range for the S&P in one year. The VIX is expressed as an annualized percentage. We can calculate the expected range with the following formula.

S&P 500 one year expected range = S&P 500 Price Plus/Minus S&P 500 Price X VIX/100

For example, if S&P 500 price is currently trading at $1500 with the VIX at 10 the 1 year expected range (in %) is plus/minus 10%. So the 1 year expected range would be $1350 to $1650.

These ranges are 68% probability ranges. With the SPX at $ 2000 and VIX at 50, the 50% expected range is just the 68% probability range. Basically, it means there is a 68% chance that S&P 500 would be between $1000 and $3000 in the next year. Also, there is a 32% chance that the SPX is below %1000 and above %3000.

There is a well-documented relationship between VIX index and S&P 500, ie VIX tend to change relatively to S&P 500. For example, if S&P 500 falls the VIX tends to increase because more people will buy for speculative purposes or to hedge risks. When S&P 500 rises or remain intact the VIX tends to decrease because moments will no longer occur as the stock prices will rise people feel complacent. There is no need to buy protection in a hurry. We see the comparison of VIX index, S&P500 price and 1-year range using the graph below:

We can see two shaded regions in the charts, A and B. In the region A we can see the S&P 500 is trading relatively flat then collapses from $2100 to $ 1850. During this same period, the VIX increases from 15 to 30. The expected range when the VIX is at 15 is just below 350, but when the market falls and VIX rises to almost 30, the expected range also rises to 500.

On the shaded region B, the S&P 500 starts at $1850 and suddenly rises to $2050 which means the VIX changed from 27 to 15 ie rising market means falling VIX. As the VIX is falling the 1 year expected range also falls.

__Correlating the VIX index and S&P 500: __

Here in 1-year duration, we can see most of the time the relation between the two is below -.80. Ie there is a strong inverse relationship between the two factors.

History of VIX index

The lowest closing was at 9.31, average at 19.69 and highest at 80.86 in 2008. We can see that mostly it stays below 20 ie 61% of the time from 1991 it closed below 20 though it spiked every now and then temporarily which also very common.

**The Expected Move**

The expected move is one standard deviation expected price range for a stock in future. Suppose, if the stock’s expected move is 5%, then the stocks price is expected to be + or – 5% from its current price in 30 days. (with 68% certainty ). To calculate expected moves for any stock we need 3 variables. They are

- The current stock price
- The stock’s implied volatility (matched with the time period in the calculation).
- The desired time frame for the expected move.

__Reason to match the implied volatility to the time period.__

It is very important to use the implied volatility closest to your calculation period because different expiration cycles have different implied volatilities. If we calculate any 70 days expected move we would not want to use the 7 day IV of 27.50%. because that would give an expected move which is overstated compared to the 24.5 % volatility.

A formula to calculate the Expected Move:

Expected move = Stock Price X Implied Volatility X

For example, if we have $200 stock and with different DTEs, IVs, Expected moves as below

Let’s visualize the above numbers through a graph:

For the 7 days duration expiration, the expected move is between $207.62 and $192.38. Going to 35 days to expiration, the expected stock price range is between $184.36 and $215.64 with expected move of plus/minus $15.64. The expected range for the stock gets larger and larger as the days to expire increase because there will be more uncertainty prevails with larger days to expire.

**Trading VIX Options.**

The VIX index is the index that tracks the 30 days implied volatility of SPX options. VIX options are some of the liquid options that are available in the market for options traders. The VIX can’t be traded directly, but there are options on the VIX that can be traded. In 2016, VIX options had an average daily volume of 587000 contracts or 148 million contracts through the entire year.

__VIX Options Nuances__

There are important nuances that we need to be aware of before trading VIX options:

- VIX options are not priced to the VIX index, they are priced to the VIX futures with the same settlement date.
- VIX options settle to a Special Opening Quotation (VRO), a VIX-style calculation on the morning of settlement.
- Long-term VIX options are less sensitive than the short term VIX index.

__VIX options pricing and VIX Futures__

Since VIX no tradable shares, VIX options are not priced in line with the level of VIX index. Let’s compare the prices and intrinsic value of ITM options on equities and the VIX.

From the above table, we can see that AAPL trading at $109.40, January 200 Put, Options price, in this case, is $90.60 and intrinsic value is $90.60. In case of TSLA also the Options price ($218.55) is also trading more than its intrinsic value ($218.15). Looking at the VIX at January 50 put there is a problem because the options price is not at least its intrinsic value.

Now compare this with the January VIX Future which is trading at 16.60. Looking at the Jan 50 Put, the options price is $33.50 while the intrinsic value is at $33.40. Comparing VIX options to VIX futures with the graph below.

Along synthetic VIX consists of buying stock positions using VIX options. So it consists of buying a Call option and selling a Put option in the same strike price and in the same expiration cycles. If the trader entered for debit (Dr) the effective cost of synthetic position is the strike price first the Debit. If the cost of the synthetic is a Credit (Cr) then the effective cost of the position is strike price minus Credit. The green line indicates the strike price plus the Debit or minus the Credit on each trading days.

__Why are VIX options priced to the VIX futures?__

As we have known that there are no tradable VIX shares which mean there is no put-call parity between VIX options and VIX index. The VIX futures are considered to be the tradable shares of the VIX.

VIX futures and options both settles to VRO, which keeps their prices in line with one another. Let’s see the VIX option settlement examples.

While the opening VIX value on the morning of settlement may seem like it should be identical to the VIX settlement value (VRO), it will likely differ. From the table below:

We can see the VIX opening price is 23.40 where VRO came in at 23.76, based on this VRO a 15 Call would sell to $8.76 which is $876. A 17 Put is OTM, this option will expire worthlessly,

With the VIX opening at 15.96 and VRO at 16.22, a Call option with the strike price would settle for $6.22 whose value would be $622. A 30 Put would settle $13.78 option or $1378 in premium. VIX options are cash-settled, meaning on the morning of settlement each option will sell to the amount of its intrinsic value and disappear from the traders’ account.

__Why not trade long-term VIX options?__

Let’s say that the VIX is at 10 right now and we think that in the next 300 days the VIX is going to rise to 15 or 20 because the VIX of 10 is not sustainable.

If volatility is high or low, many new traders wonder why they shouldn’t just place trades in the longest-term VIX options cycles to allow for ample time to be profitable.

Let’s visualize why VIX options with longer durations are less sensitive than short-term VIX options.

Here we have a period between Sep and Nov 2008. We are looking at the changes in Oct, Nov and Dec VIX futures. We can observe from above that the VIX rose from 22.5 to 70 in few months for Sep VIX. The October VIX rose from 22.5 to 65 at the highest point. Looking at the Nov Future it started from 22.5 but only rose to 47.5. December VIX future started the same lever and only rose to 35. From this, we can notice that short-term VIX Future contracts are more sensitive than the changes in the VIX index. It is the reverse with the longer term VIX futures contracts.