To understand the impact of volatility on option Greeks, let us start off with a base case scenario wherein the option is an ATM option. Consider the table below:

Underlying Price

180

The current market price of the stock, for example, the closing price of Tata Motors on the last traded day

Exercise Price

180

The price at which the underlying instrument will be exchanged. Also called Strike Price or the contract price

Today's Date

21-02-2019

Current Date or the date of the trade and this forms the base point for time to expiry

Expiry Date

28-03-2019

The Date on which the options contract expires which is routinely the last Thursday of the month

Historical Volatility

20%

The Historical Volatility of the asset's returns measured by the Variance of returns

Risk Free Rate

5.00%

The current risk free interest rate i.e. your return on cash held in the bank or the bare minimum returns expected

Dividend Yield

0.00%

The Annualized Dividend Yield which is measured by the quotient of the dividend per share and the stock price

DTE (Years)

0.10

The time left to expiry of the option expressed in terms of fractional years

Call Option

Theoretical Price

4.8797

Theoretical Value of the Call Option

Delta

0.5432

The amount that the theoretical price will change if the market moves up/down 1 point

Gamma

0.0356

The amount that the Delta will change if the market moves up/down 1 point

Theta

-0.0759

The amount that the theoretical price will change when 1 day passes or the time decay

Vega

0.2211

The amount that the theoretical price will change if the volatility of the asset moves up/down by 1 percentage point

Rho

0.0891

The amount that the theoretical price will change if interest rates move up/down by 1 percentage point

# 35 Days Expiry to the last Thursday of March 2019 series is assumed here.

Now let us look at a scenario wherein the volatility goes up higher from 20% to 30%. What is the impact on the value of the call option and the Option Greeks in this case?

Underlying Price

180

The current market price of the stock, for example, the closing price of Tata Motors on the last traded day

Exercise Price

180

The price at which the underlying instrument will be exchanged. Also called Strike Price or the contract price

Today's Date

21-02-2019

Current Date or the date of the trade and this forms the base point for time to expiry

Expiry Date

28-03-2019

The Date on which the options contract expires which is routinely the last Thursday of the month

Historical Volatility

30%

The Historical Volatility of the asset's returns measured by the Variance of returns

Risk Free Rate

5.00%

The current risk free interest rate i.e. your return on cash held in the bank or the bare minimum returns expected

Dividend Yield

0.00%

The Annualized Dividend Yield which is measured by the quotient of the dividend per share and the stock price

DTE (Years)

0.10

The time left to expiry of the option expressed in terms of fractional years

Call Option

Theoretical Price

7.0920

Theoretical Value of the Call Option

Delta

0.5391

The amount that the theoretical price will change if the market moves up/down 1 point

Gamma

0.0237

The amount that the Delta will change if the market moves up/down 1 point

Theta

-0.1072

The amount that the theoretical price will change when 1 day passes or the time decay

Vega

0.2213

The amount that the theoretical price will change if the volatility of the asset moves up/down by 1 percentage point

Rho

0.0862

The amount that the theoretical price will change if interest rates move up/down by 1 percentage point

# 35 Days Expiry to the last Thursday of March 2019 series is assumed here.

What exactly happens to all the option Greeks in this case? Let us go one by one. When the volatility goes up you get to see the theoretical value of the option go up which is obvious because the price of the option is positively correlated to volatility. However, the change in volatility has not impacted the Delta sensitivity in a big way. However, the Theta of the call option has gone up sharply due to the increase in volatility. That is because the volatility favours the buyer of the option and while it is the Theta that favours the seller of the option. Therefore an increase in volatility means that the call option loses value faster. What about Vega? The Vega has been not really impacted as the sensitivity of the option price to the volatility is not impacted. What could happen to the option Greeks of the call option if the volatility came down to 10%? Check the table below:

Underlying Price

180

The current market price of the stock, for example, the closing price of Tata Motors on the last traded day

Exercise Price

180

The price at which the underlying instrument will be exchanged. Also called Strike Price or the contract price

Today's Date

21-02-2019

Current Date or the date of the trade and this forms the base point for time to expiry

Expiry Date

28-03-2019

The Date on which the options contract expires which is routinely the last Thursday of the month

Historical Volatility

10%

The Historical Volatility of the asset's returns measured by the Variance of returns

Risk Free Rate

5.00%

The current risk free interest rate i.e. your return on cash held in the bank or the bare minimum returns expected

Dividend Yield

0.00%

The Annualized Dividend Yield which is measured by the quotient of the dividend per share and the stock price

DTE (Years)

0.10

The time left to expiry of the option expressed in terms of fractional years

Call Option

Theoretical Price

2.6753

Theoretical Value of the Call Option

Delta

0.5676

The amount that the theoretical price will change if the market moves up/down 1 point

Gamma

0.0705

The amount that the Delta will change if the market moves up/down 1 point

Theta

-0.0449

The amount that the theoretical price will change when 1 day passes or the time decay

Vega

0.2192

The amount that the theoretical price will change if the volatility of the asset moves up/down by 1 percentage point

Rho

0.0954

The amount that the theoretical price will change if interest rates move up/down by 1 percentage point

# 35 Days Expiry to the last Thursday of March 2019 series is assumed here.

Now how does the fall in volatility impact the value of the call option? Obviously, the value of the call option has come down which is natural with a fall in volatility. What about Delta? Delta has actually increased because the fall in volatility makes the intrinsic value of the option more important than the time value. What about the Theta or the time decay. Just rise in volatility works against the option seller, the fall in volatility works in favour of the option seller and this is apparent in the fall in Theta or the time decay. The Vega has however fallen very marginally despite the sharp fall in the volatility of the call option.

To understand the impact of volatility on option Greeks, let us start off with a base case scenario wherein the option is an ATM option. Consider the table below:

Underlying Price

180The current market price of the stock, for example, the closing price of Tata Motors on the last traded dayExercise Price

180The price at which the underlying instrument will be exchanged. Also called Strike Price or the contract priceToday's Date

21-02-2019Current Date or the date of the trade and this forms the base point for time to expiryExpiry Date

28-03-2019The Date on which the options contract expires which is routinely the last Thursday of the monthHistorical Volatility

20%The Historical Volatility of the asset's returns measured by the Variance of returnsRisk Free Rate

5.00%The current risk free interest rate i.e. your return on cash held in the bank or the bare minimum returns expectedDividend Yield

0.00%The Annualized Dividend Yield which is measured by the quotient of the dividend per share and the stock priceDTE (Years)

0.10

The time left to expiry of the option expressed in terms of fractional years

Call OptionTheoretical Price

4.8797Theoretical Value of the Call OptionDelta

0.5432The amount that the theoretical price will change if the market moves up/down 1 pointGamma

0.0356The amount that the Delta will change if the market moves up/down 1 pointTheta

-0.0759The amount that the theoretical price will change when 1 day passes or the time decayVega

0.2211The amount that the theoretical price will change if the volatility of the asset moves up/down by 1 percentage pointRho

0.0891The amount that the theoretical price will change if interest rates move up/down by 1 percentage point# 35 Days Expiry to the last Thursday of March 2019 series is assumed here.

Now let us look at a scenario wherein the volatility goes up higher from 20% to 30%. What is the impact on the value of the call option and the Option Greeks in this case?

Underlying Price

180The current market price of the stock, for example, the closing price of Tata Motors on the last traded dayExercise Price

180The price at which the underlying instrument will be exchanged. Also called Strike Price or the contract priceToday's Date

21-02-2019Current Date or the date of the trade and this forms the base point for time to expiryExpiry Date

28-03-2019The Date on which the options contract expires which is routinely the last Thursday of the monthHistorical Volatility

30%The Historical Volatility of the asset's returns measured by the Variance of returnsRisk Free Rate

5.00%The current risk free interest rate i.e. your return on cash held in the bank or the bare minimum returns expectedDividend Yield

0.00%The Annualized Dividend Yield which is measured by the quotient of the dividend per share and the stock priceDTE (Years)

0.10

The time left to expiry of the option expressed in terms of fractional years

Call OptionTheoretical Price

7.0920Theoretical Value of the Call OptionDelta

0.5391The amount that the theoretical price will change if the market moves up/down 1 pointGamma

0.0237The amount that the Delta will change if the market moves up/down 1 pointTheta

-0.1072The amount that the theoretical price will change when 1 day passes or the time decayVega

0.2213The amount that the theoretical price will change if the volatility of the asset moves up/down by 1 percentage pointRho

0.0862The amount that the theoretical price will change if interest rates move up/down by 1 percentage point# 35 Days Expiry to the last Thursday of March 2019 series is assumed here.

What exactly happens to all the option Greeks in this case? Let us go one by one. When the volatility goes up you get to see the theoretical value of the option go up which is obvious because the price of the option is positively correlated to volatility. However, the change in volatility has not impacted the Delta sensitivity in a big way. However, the Theta of the call option has gone up sharply due to the increase in volatility. That is because the volatility favours the buyer of the option and while it is the Theta that favours the seller of the option. Therefore an increase in volatility means that the call option loses value faster. What about Vega? The Vega has been not really impacted as the sensitivity of the option price to the volatility is not impacted. What could happen to the option Greeks of the call option if the volatility came down to 10%? Check the table below:

Underlying Price

180The current market price of the stock, for example, the closing price of Tata Motors on the last traded dayExercise Price

180The price at which the underlying instrument will be exchanged. Also called Strike Price or the contract priceToday's Date

21-02-2019Current Date or the date of the trade and this forms the base point for time to expiryExpiry Date

28-03-2019The Date on which the options contract expires which is routinely the last Thursday of the monthHistorical Volatility

10%The Historical Volatility of the asset's returns measured by the Variance of returnsRisk Free Rate

5.00%The current risk free interest rate i.e. your return on cash held in the bank or the bare minimum returns expectedDividend Yield

0.00%The Annualized Dividend Yield which is measured by the quotient of the dividend per share and the stock priceDTE (Years)

0.10

The time left to expiry of the option expressed in terms of fractional years

Call OptionTheoretical Price

2.6753Theoretical Value of the Call OptionDelta

0.5676The amount that the theoretical price will change if the market moves up/down 1 pointGamma

0.0705The amount that the Delta will change if the market moves up/down 1 pointTheta

-0.0449The amount that the theoretical price will change when 1 day passes or the time decayVega

0.2192The amount that the theoretical price will change if the volatility of the asset moves up/down by 1 percentage pointRho

0.0954The amount that the theoretical price will change if interest rates move up/down by 1 percentage point# 35 Days Expiry to the last Thursday of March 2019 series is assumed here.

Now how does the fall in volatility impact the value of the call option? Obviously, the value of the call option has come down which is natural with a fall in volatility. What about Delta? Delta has actually increased because the fall in volatility makes the intrinsic value of the option more important than the time value. What about the Theta or the time decay. Just rise in volatility works against the option seller, the fall in volatility works in favour of the option seller and this is apparent in the fall in Theta or the time decay. The Vega has however fallen very marginally despite the sharp fall in the volatility of the call option.