InvestorQ : How does a change in the stock price actually impact the Greeks pertaining to the call options?
Dhwani Mehta made post

How does a change in the stock price actually impact the Greeks pertaining to the call options?

Answer
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Arya Nanda answered.
1 year ago


Let us understand this point with the help of an ATM call option on Tata Motors. We are referring to the Tata Motors call option of Rs.180 strike when the market price of the stock is also at Rs.180. 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

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.

Instead of an ATM call, let us assume that this was an ITM call where the market price was greater than the strike price. How does that impact the Option Greeks?

Underlying Price

200

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

21.0374

Theoretical Value of the Call Option

Delta

0.9648

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

Gamma

0.0063

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

Theta

-0.0373

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

Vega

0.0481

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

Rho

0.1649

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 are your quick inferences here? The price of the call option has gone up because it has become more in-the-money in this case. What about the Greeks? There has been a sharp rise in the Delta which means that the call option price has become more sensitive to the changes in the market price. At the same time, the theta or the time decay has come down because the impact of time reduces as the stock becomes intrinsically more valuable. What is interesting is that the Vega has fallen sharply. That is because, when the stock becomes sharply in the money, the role of volatility reduces and it is the intrinsic value that begins to matter more. That shows the reduced impact of volatility which is shown by the fall in Vega.

Now, instead of an ITM call, let us assume that this was an OTM call where the market price was less than the strike price. How does that impact the Option Greeks?

Underlying Price

160

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

0.1407

Theoretical Value of the Call Option

Delta

0.0365

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

Gamma

0.0081

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

Theta

-0.0121

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

Vega

0.0396

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

Rho

0.0055

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 are your quick inferences in this case of an OTM call option where the stock price is lower than the strike price? The price of the call option has obviously come down sharply as the OTM option has limited value despite the time to expiry being 35 days. What about the Greeks? There has been a sharp fall in the Delta which means that the call option price has become almost insensitive to the changes in the market price. At the same time, the theta or the time decay has also fallen sharply because the impact of time becomes negligible when the option itself has very limited value due to being OTM. What is interesting is that the Vega is still around the same level. That is because, the time to expiry of 35 days means that there is still sufficient volatility potential in the stock despite it being deep out of the money at this point of time.