Till time, we have discuss Delta, Gamma and Theta from Greek letters. Now, we are going to discuss new letter call Vega, before we start new concept lets us learn definition of **Vega is the rate of change of option premium with respect to change in volatility. **But what is volatility? most important and crucial part of Greek Letter i.e. Volatility. Most Complex concept of Option learning is Volatility. Many common answer heard till time i.e. up and down movement of stock.

But let's understand entire concept and use of it here. Volatility is measurement of Risk. Higher the volatility higher would be risk. It can be estimated by standard deviation and Standard Deviation is the square root of variance.

What is simple meaning of Volatility ? with Example,

Volatility suggest expected movement of underlying over a period of one year. Example: Nifty Volatility is 15% it shows nifty can move 15% in any direction. TCS and INFY Volatility is 25% it shows in a period of one year both stock can go up 25% or down by 25%.

Practical Example:

Today's Date: 26th Aug. 2019

Nifty spot = 11057.85

Nifty volatility = 16.65% (India VIX)

SBIN Spot = 280.25

SBIN Volatility = 38%

Given this information, can you predict the likely range within which Nifty and SBIN will trade 1 year from now?

Of course we can, let us put the numbers to good use –

Underlying | Upper Move | Lower Move |

Nifty | 12899 | 9217 |

SBIN | 387 | 174 |

Calculation : =11057.85 + (11057.85*16.65%) &

11057.85 - (11057.85*16.65%)

Calculation: = 280.25 + (280.25*38%) & 280.25 - (280.25*38%)

So the above calculations suggest that in the next 1 year, given Nifty’s volatility, Nifty is likely to trade anywhere between **9217 and 12899** with all values in between having varying probability of occurrence and SBIN with all values in between 174 to 387 anywhere in between this values.

Some outcome we can derived here.....

We can derived nifty range for 1 year same way we can derived for 1 month or few days range or likely series of expiry.

Once, we derived range we can easily sell out of money option which expire worthless

How do we calculate Volatility? using MS Excel

We calculated Nifty’s range estimating its volatility as 16.5% , what if the volatility changes? we can calculate at every level.

**Learning so Far.....**

Vega measures the rate of change of premium with respect to change in volatility

Volatility is not just the up down movement of markets

We can estimate the range of the stock price given its volatility

Larger the range of a stock, higher is its volatility risk.

Volatility is a measure of risk

Volatility is estimated by standard deviation

Standard Deviation is the square root of variance

**Calculation of Volatility:**

So let us get to work straight away.

>

**Step 1** – **Download the historical closing prices**

It will Look like below Screenshot

Click on above box to download historical data of SBIN.

Do make sure you get the data for the last 1 year. The dates that I have selected here is from 27th Aug 2018 to 26th AUG 2019.

It will Look like below Picture....

Once you get this, click on ‘Download file in CSV format’ (highlighted in the Black box), and

You now have the required data on Excel. Of course along with the closing prices, you have tons of other information as well. Just remove data without box drawn in above image. Take close and Date with security name. Series I have taken for reference else many company having Bonds and debenture also.

Here is a snapshot of how my excel sheet looks at this stage –

**Step 2** – **Calculate Daily Returns**

We know that the daily returns can be calculated as –

Return = (Ending Price / Beginning Price) – 1

**Return = LN (Ending Price / Beginning Price)**, where LN denotes Logarithm to Base ‘e’, note this is also called ‘Log Returns’.

Here is a snap shot showing you how I’ve calculated the daily log returns of SBIN in above Excel Picture. Once you arrive at LN value then next step is to calculate

**Step 3 **– **Use the STDEV Function**

It will look like Below,

Once this is done, Excel will instantly calculate the daily standard deviation volatility of SBIN for you. I get the answer as 0.00189 which when converted to a percentage reads as 1.89%.

This means the daily volatility of SBIN is 1.89% !

The value we have calculated is SBIN’s daily volatility, but what about its annual volatility?

Likewise to convert the annual volatility to daily volatility, divide the annual volatility by square root of time.

So in this case we have calculated the daily volatility, and we now need SBIN’s annual volatility. We will calculate the same here –

Daily Volatility = 1.89%

Time = 365

Annual Volatility = 1.89% * SQRT (365)

= 36%

In fact I have calculated the same on excel, have a look at the image below –

Let's Check SBIN Contract on NSE Website:

As per NSE’s calculation SBIN’s daily volatility is about 2.23% and Annualized Volatility is about 42.68%.

So why is there a slight difference between our calculation and NSE’s? – One possible reason could be that we are using spot price while NSE is using Futures price.

Anyway Our motive is to learn the volatility calculation here, Not to check why the difference is arise. May be huge gap of Cash and Future is the reason.

We are still learning volatility basis before touching concept of Vega it is much necessary to learn Volatility calculation.

Standard Deviation represents volatility, represents risk.

we can Use NSE INDIA for data Collection source

Calculate Various function using LN, STDEV and SQT of time.

We can compare Calculation with NSE Volatility based on Future Price

** NORMAL DISTRIBUTION WITH NIFTY RELATION :**

l The bell curve above suggests that with reference to the mean (average) value –

68% of the data is clustered around mean within the 1^{st} SD, in other words there is a 68% chance that the data lies within the 1^{st} SD

95% of the data is clustered around mean within the 2^{nd} SD, in other words there is a 95% chance that the data lies within the 2^{nd} SD

99.7% of the data is clustered around mean within the 3rd SD, in other words there is a 99.7% chance that the data lies within the 3^{rd} SD

Since we know that Nifty’s daily returns are normally distributed, the above set of properties is applicable to Nifty. So what does it mean?

**so, Nifty lies in 1st SD is 68% probability **

**Nifty lies in 2nd SD is 95% and **

**nifty lies in 3rd SD is 99.7%.**

Let's Discuss Example:

Date = 26^{th} August 2019

Number of days for expiry = 5

Nifty current market price = 11057.85

Daily Average Return = 0.05%

Annualized Return = 14%

Daily SD = 0.95%

Annualized SD = 16.5%

Given this I would now like to identify the range within which Nifty will trade until expiry i.e 5 days from now –

5 day SD = Daily SD *SQRT (5)

= 0.95% * SQRT (5)

= **2.12%**

5 day average = Daily Avg * 5

= 0.05% * 5 = **0.25%**

These numbers will help us calculate the upper and lower range within which Nifty is likely to trade over the next 5 days –

Upper Range = 5 day Average + 5 day SD

= 0.25% + 2.12%

= 2.37%, to get the upper range number –

= 11057.85 * 2.37% = 262

= **11319.85**

Lower Range = 5 day Average – 5 day SD

= 0.25% – 2..12%

= 1.87% to get the lower range number –

= 11057.85 * - 1.87% = -206.8

= **10851.05**

The calculation suggests that Nifty is likely to trade anywhere in the region of **11319.85**** ****to 10851.05. **How sure are we about this, well we know that there is a 68% probability for this calculation to work in our favor. In other words there is 32% chance for Nifty to trade outside 10851 and 11319 range. This also means all strikes outside the calculated range ‘may’ go worthless.

Here, Both call and Put Option chain Image is posted below.....

If I have to select option strike out of above image with expiry of just 4 days, I will go for 1 SD away the strike i.e. 11300 or above it.

Example: 11350 Strike call available at 5.45 Rs. per lot, Many of us will think why to short such small amount option reason is simple short one lot of 11350 will give almost (5.45*75)= Rs. 400 while Margin requirement say 75000 per lot almost 750 P.M. comes 1% here only 3 days to go and 400 Rs. premium received it means almost 4% return.

I would like to short option before expiry of one week where Theta favors more.Few Point I want to clarify here is.....

**Put Options:** Always avoid shorting put as panic spreads more than greed. In any sudden move our short option will become ATM and ITM in no time in panic period.

**Call Option:** To make my 11350 Call ATM or ITM Nifty has to move almost 300 POINTS from current level in 3 days, there has to excess Greed over market. it is not easy to move sharply in one direction. Better to short call instead of Put.

**Strike:** It is safe to assume pick any strike above 1 SD , decide premium to margin %, Time to expiry before selecting Strike.

**Time:** always select last Friday before a week expiry i.e. on 29th AUG. 2019 is expiry day, short 5th Sep. 2019 Call on 30th AUG.2019, As we learn in Theta chapter regarding Theta favors more on expiry period.

**Events:** Avoid trading during event period, this days FM announcing various relaxation to the investor and derivative trader for tax issue and package to bank. Even during Election, Policy and global event one should skip shorting option for that week.

**Loss:** Get out position once option becomes OTM to ATM, As on expiry period Delta use to fluctuate more.

**Expense:** Keep account where Brokerage use to minimum, this days lot of brokerage house provide huge scheme for option trader.

**Capital Allocation:** Try to take exposure of 5-8% of portfolio, Don't Overweight much on shorting option better to allocate fund in various option. you can read various option of investment in India

I am equity Friend invested 100% in Equity and same class like....

30% to mutual fund having 3 scheme consist of one ELSS

40% to direct equity holding almost 5 stocks

20% investment based on opportunity or Event based trading like IPO, ETFs and BUY BACK etc

10% with option trading

**Selection:**

I always prefer to short options of BANK NIFTY, NIFTY or Stock having full of liquidity like RELIANCE, TCS, INFY, such bluechip stocks only.

**Summary:**

We discuss Historical Volatility Calculation, Nifty range selection, identification of Strike, Probability of normal distribution of option expiry and allocation of fund and avoid time of trading.

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