# Volatility trading – Significance for options Part-I

Question: Why is Volatility significant for Options?

Answer: The value of an Option, apart from other factors, depends upon the Volatility of the underlying. Higher the Volatility of the underlying, higher the Option Premium.

Question: What is Volatility?

Answer: Volatility is the fluctuation in the price of the underlying. For example, the movement in the price of Satyam is quite high as compared to the Sensex. Thus, Satyam is more volatile than the Sensex.

Question: How do you measure Volatility?

Answer: Volatility is the standard deviation of the daily returns on any underlying.

Question: This is too complicated ! What is Daily Return?

Answer: Ok – let me restate in simple language. Every day, every scrip moves up or down by a certain percentage. For example, if Satyam closed at Rs 280 yesterday and today it closed at Rs 285, the percentage change is 5/280 x 100 = +1.79%. This percentage is called ‘daily return’.

Let me make a slightly elaborate calculation and show you.

 Day Satyam Closing Prices Daily Return 1 280 2 285 +1.79% 3 272 -4.56% 4 292 +7.33% 5 287 -1.71%

Fine, what next?

Now you find out the standard deviation of these Daily Returns.

Question: What is Standard Deviation?

Answer: Standard deviation is a measure of dispersion and comes from statistics. Dispersion indicates how widely ‘dispersed’ a set of data is. For example, if you look at heights of adult males in India, you will find that the heights of various people are not too far off from each other. While the average male is about five and a half feet tall, the others are not too far off. While some may be one feet above this average, others might be one feet below.

You are unlikely to find people twenty feet tall, nor two feet tall. Thus, if you were to work out the Standard Deviation of this data, this figure will be a small number, because the data is not too dispersed.

On the other hand, if you try and plot the wealth of various Indian males, you might find a wide dispersion, as somebody might have a wealth of Rs 100 while somebody else might possess Rs 1 crore. Thus, standard deviation of wealth will be high.

Question: How is it calculated?

Answer: In these days of computerized living, it might be simpler to use an Excel spreadsheet and key in the formula for standard deviation. You will get the figure in a second.

The technical formula goes like this:

Identify the basic data (in our case the percentage daily returns)

Work out the average

Work out the deviations of each observation from the average (these deviations might be positive or negative)

Take a square of these deviations

Sum up these squares

Divide the sum by the number of observations

Work out the square root of this number

Let me show you from the above example:

 Day Daily Return Deviation Square of Deviation 2 +1.79% +1.08% 0.011664% 3 -4.56% -5.27% 0.277729% 4 +7.33% +6.62% 0.438244% 5 -1.71% -2.42% 0.058564% Average +0.71% Sum 0.786201%

Divide the sum by the number of observations:  0.1966%

Square root of above:  4.43%

Thus the standard deviation of the above data comes to 4.43%.

This is the daily standard deviation, as it is based on daily returns data.

I have heard that Volatility is 50%, 80% etc. Your volatility is far lower at only 4%.

You have heard correct. What we have calculated above is the Daily Volatility. If you want to know the Annual Volatility, you should multiply with the square root of the number of working days in a year. For example, if one year has 256 working days, square root of 256 days is 16 days. Thus in the above case the Annual Volatility is 4.43% x 16 = 70.88%.

In a similar manner, if you want to know the Volatility of the next 9 days, the 9-day Volatility will be 4.43% x 3 = 13.29%.

Question: Having derived the Volatility, how do I interpret it?

Answer: The concept of Normal Distribution states that you can derive a deep understanding of possible movements in the share price from this figure of Volatility. The movement will be within 1 standard deviation 66% of the time, within 2 standard deviations 95% of the time and within 3 standard deviations 99% of the time.

Question: Can you elaborate using examples?

Answer: If Satyam’s closing price today is Rs 287, expected movement in the next one day can be tabulated as under:

 Number of Standard Deviations Percentage Price Movement Lower Price Higher Price Probability One 4.43% 13 274 300 66% Two 8.86% 26 261 313 95% Three 13.29% 38 325 249 99%

Similarly possible movement over the next nine days can be forecasted as under:

 Number of Standard Deviations Percentage Price Movement Lower Price Higher Price Probability One 13.29% 38 325 249 66% Two 26.58% 76 211 363 95% Three 39.87% 114 173 401 99%

Question: What are we predicting here?

Answer: Predicting is a rather difficult science. First of all, we are not looking at direction at all. We are not saying whether Satyam will move up or down. Secondly, we are forecasting possible maximum swing in magnitude irrespective of direction.

For example, we are saying that Satyam will close between Rs 249 to Rs 325 tomorrow and the probability of this happening is 99%. The implication is that the probability of Satyam closing below Rs 249 or above Rs 325 is 1%.

Question: How many days of data should we consider for calculating Volatility?

Answer: There is a difference of opinion among traders as to the number of days that should be considered. In the Indian context, we currently find that Options are available for 3 months. However, most of the trading happens in the first month. Thus, the relevant period for forecasting is one month or lower. Accordingly, it would be sensible to consider Volatility based on the past 10 trading days and for the past 20 trading days. Longer periods would perhaps not be relevant in the present context.

Question: How do we use Volatility in our trading strategies?

Answer: We will discuss this in our next column.

# Volatility – Significance for options Part-II

Question: Can we summaris our discussion last time?

Answer: In our last Article, we discussed the concept of Volatility, how is it calculated, how is it interpreted and what period of time should be reckoned for such calculations.

Question: How can these learnings be applied?

Answer: Study of past prices of a scrip will enable you to arrive at ‘historical’ volatility. Option prices as you are aware, depend on Volatility to a high degree. However, Option prices may or may not reflect ‘historical’ volatility.

Study of past prices of a scrip will enable you to arrive at ‘historical’ volatility. Option prices as you are aware, depend on Volatility to a high degree. However, Option prices may or may not reflect ‘historical’ volatility.

Question: Why not?

Answer: It is possible that market participants believe that Volatility in future is expected to rise. Thus, historical Volatility may have been 50%, but it is widely believed that the scrip will become more Volatility resulting in a higher level of say 60%. Accordingly, the Option might be priced on the basis of 60% forecasted Volatility.

Question: How will I know this?

Answer: If you study the price of the Option as actually quoted in the market, you will realize what is the ‘implied’ Volatility. For example, if the following Option is theoretically studied:

Stock Price Rs 280

Strike Price Rs 260

Volatility 50% annual

Days to Expiry 20 days

Interest Rate 12% annual

The price of the Option applying Black-Scholes Model comes to Rs 26.28. But the actual price of that Option in the market might be (say) Rs 29.50.

Question: What does this imply?

Answer: This could imply that the market is not going by the historical Volatility of 50%, but is imputing another Volatility to that Option going forward. You can use the same calculator, but now instead of providing the Volatility figure yourself, you can provide the Option price instead. Now if you work backwards and find out what is the Volatility that would support the price of Rs 29.50, that Volatility comes to 65%.

Question: So how can I use this understanding?

Answer: You are facing a situation where historical Volatility of the scrip is 50%, but the implied Volatility is 65%. Various possibilities for this divergence can emerge. One possibility is that the market is expecting the future Volatility of the scrip to increase and is accordingly factoring in such expectations. Another possibility is that the market is mis-pricing the Option and that the Option value will come back to around Rs 26.28 shortly. The third possibility could be that there is some news about the company that could affect the price favourably and this news is being reflected in the Options become more expensive to begin with and in a short time, the underlying scrip will also reflect this phenomenon.

Depending on what you see from these possibilities (and there could be others too), you could take an appropriate stand.

For example, if you believe that Volatility will rise, you could go in for Option Strategies that could suit such an event happening. If you believe that the Option is being mispriced, as an aggressive player, you could sell such Options with a belief that you could buy them back at a later date. Such a strategy would need to be supported by a hedging strategy as mere selling of Options will leave with unlimited risk.

If you believe that there is some positive ‘news’, you might be tempted to buy the Options inspite of high Volatility (or buy the underlying).

Question: What if the Implied Volatility is lower than Historical Volatility?

Answer: This is also possible. It could indicate that the Option itself is being underpriced in the market (which could make it a good buy on its own merit). It could indicate that the market believes that the days of high Volatility in that scrip are over and it will now trade a lower level. Another possibility is that there is some bad news whereby the underlying stock price is expected to move down and the Option has first started reflecting this possibility.

Question: What should I do to fine tune my understanding?

Answer: If you are a serious derivatives market player, you should track historical Volatility very closely. It is recommended that you work out 10 day and 20 day moving Volatilities on a continuous basis. A moving daily trend would be very useful.

Once you have this set of numbers, you could compare with Implied Volatility to arrive at a more definitive conclusion. For example, you could find the following information:

10 day Volatility Today (of last 10 days):  61%

20 day Volatility Today (of last 20 days):  57%

Max 10 day Volatility in the last 6 months:  62%

Max 20 day Volatility in the last 6 months:  59%

Implied Volatility Today:  71%

This set of data reveals that the current Implied Volatility is way beyond historical levels and the likelihood of some positive news in the scrip is probable. If you plan to sell the Option on the assumption that it is overpriced, that strategy is dangerous and should be dropped.

On the other hand, if the data shows up as under:

10 day Volatility Today (of last 10 days):  51%

20 day Volatility Today (of last 20 days):  47%

Max 10 day Volatility in the last 6 months:  72%

Max 20 day Volatility in the last 6 months:  67%

Implied Volatility Today:  61%

This would indicate the possible overpricing of the Option at current levels, but as the Implied Volatility is within the maximum levels reached in the recent past, there does not appear to be abnormal behaviour in the price. Advanced players could consider selling such Options which have a ‘statistical edge’ and if necessary covering the position with some other Option or Future. Selling such Options needs further discussion, which we will try and explore in later articles in this series.

If you are anyway considering selling the Option (for reasons other than Volatility reasons enumerated here), you could think that this is an appropriate time for selling the Option as the edge will help you in increasing your profit to a small degree.

Question: How much does Volatility affect an Option’s price?

Answer: It does affect the price quite significantly. Some examples are provided below:

Days to expiry:  30 days

Interest Rate:  12% per annum

At The Money Option:

Stock Price:  260

Strike Price:  260

 Volatility Annualised Option Price 50% 16.09 60% 19.03 70% 21.98 80% 24.92

In the Money Option:

Stock Price:  300

Strike Price:  260

 Volatility Annualised Option Price 50% 45.46 60% 47.44 70% 49.69 80% 52.14

Out of the Money Option:

Stock Price:  240

Strike Price:  260

 Volatility Annualised Option Price 50% 7.15 60% 9.72 70% 12.35 80% 15.03

You can see that the price of the Option is significantly affected in all three types of Options.

Question: What are the Advanced applications of Volatility trading?

Answer: Volatility trading is a subject in itself. Strategies like delta neutral and gamma neutral fall within its ambit. We will discuss them after understanding basic strategies.