InvestorQ : To what extent does the change in the volatility impact the value of a Put option? If the volatility increases, does it impact Deep ITM and Deep OTM put options similarly?

To what extent does the change in the volatility impact the value of a Put option? If the volatility increases, does it impact Deep ITM and Deep OTM put options similarly?

The impact of change in volatility on the put option value will depend on whether the option is in-the money, at the money or out of the money. An in-the-money option is one where the option is profitable if exercised. For example, in case of a put options (which the right to sell) the option will be in the money if the market price of the stock is less than the strike price of the contract. On the other hand, the put option will be out of the money (OTM) if the market price of the stock is higher than the strike price. Let us look at simulated comparisons to understand this point better. However, here we are looking at deep ITM and deep OTM puts. A deep ITM put option will be one where the market price is substantially lower than the strike price. A deep OTM put option will be one where the market price is substantially higher than the strike price of the contract.

Let us first look at how the option value of a Deep ITM put is impacted when the volatility goes up by 10 bps from 30% to 40%.

Input Data

Input Data

Stock Price now (P)

90

Stock Price now (P)

90

Exercise Price of Option (EX)

125

Exercise Price of Option (EX)

125

Number of periods to Exercise in years (t)

0.08333

Number of periods to Exercise in years (t)

0.08333

Compounded Risk-Free Interest Rate (rf)

5.00%

Compounded Risk-Free Interest Rate (rf)

5.00%

Standard Deviation (annualized s)

30.00%

Standard Deviation (annualized s)

40.00%

Output Data

Output Data

Present Value of Exercise Price (PV(EX))

124.4803

Present Value of Exercise Price (PV(EX))

124.4803

s*t^0.5

0.0866

s*t^0.5

0.1155

d1

-3.7018

d1

-2.7511

d2

-3.7884

d2

-2.8666

Delta N(d1) Normal Cumulative Density Function

0.0001

Delta N(d1) Normal Cumulative Density Function

0.0030

Bank Loan N(d2)*PV(EX)

0.0094

Bank Loan N(d2)*PV(EX)

0.2583

Value of Put

34.4804

Value of Put

34.4893

(Note - Period is reduced to yearly decimals

Change in Value

0.03%

Let us now turn and look at how the option value of an ATM put is impacted when the volatility goes up by 10 bps from 30% to 40%. An ATM put option is one where the strike price and the market price are at the same level.

Input Data

Input Data

Stock Price now (P)

125

Stock Price now (P)

125

Exercise Price of Option (EX)

125

Exercise Price of Option (EX)

125

Number of periods to Exercise in years (t)

0.08333

Number of periods to Exercise in years (t)

0.08333

Compounded Risk-Free Interest Rate (rf)

5.00%

Compounded Risk-Free Interest Rate (rf)

5.00%

Standard Deviation (annualized s)

30.00%

Standard Deviation (annualized s)

40.00%

Output Data

Output Data

Present Value of Exercise Price (PV(EX))

124.4803

Present Value of Exercise Price (PV(EX))

124.4803

s*t^0.5

0.0866

s*t^0.5

0.1155

d1

0.0914

d1

0.0938

d2

0.0048

d2

-0.0217

Delta N(d1) Normal Cumulative Density Function

0.5364

Delta N(d1) Normal Cumulative Density Function

0.5374

Bank Loan N(d2)*PV(EX)

62.4791

Bank Loan N(d2)*PV(EX)

61.1650

Value of Put

4.0535

Value of Put

5.4869

(Note - Period is reduced to yearly decimals

Change in Value

35.36%

Finally, let us now turn and look at how the option value of a Deep OTM put is impacted when the volatility goes up by 10 bps from 30% to 40%. A Deep OTM put option is one where the strike price is substantially lower than the market price. Check the table below.

Input Data

Input Data

Stock Price now (P)

200

Stock Price now (P)

200

Exercise Price of Option (EX)

125

Exercise Price of Option (EX)

125

Number of periods to Exercise in years (t)

0.08333

Number of periods to Exercise in years (t)

0.08333

Compounded Risk-Free Interest Rate (rf)

5.00%

Compounded Risk-Free Interest Rate (rf)

5.00%

Standard Deviation (annualized s)

30.00%

Standard Deviation (annualized s)

40.00%

Output Data

Output Data

Present Value of Exercise Price (PV(EX))

124.4803

Present Value of Exercise Price (PV(EX))

124.4803

s*t^0.5

0.0866

s*t^0.5

0.1155

d1

5.5185

d1

4.1642

d2

5.4319

d2

4.0487

Delta N(d1) Normal Cumulative Density Function

1.0000

Delta N(d1) Normal Cumulative Density Function

1.0000

Bank Loan N(d2)*PV(EX)

124.4802

Bank Loan N(d2)*PV(EX)

124.4770

Value of Put

0.0000

Value of Put

0.0001

(Note - Period is reduced to yearly decimals

Change in Value

Negligible

What can you infer from a comparison of the Deep OTM, Deep ITM and the ATM scenarios? As you move either towards Deep ITM or Deep OTM put options, the impact on the value of the put options is very negligible when the volatility shifts upward. That is because the impact of this volatility rise on the time value of the option is very limited. But the impact is much more in the ATM puts as well as in cases where the ITM and OTM put options are near to the money. But, as the put options keep going deep ITM or deep OTM, the relative impact on the value of the put option resulting from a rise in the volatility becomes virtually negligible. This is a very important aspect in understanding options trading.

The impact of change in volatility on the put option value will depend on whether the option is in-the money, at the money or out of the money. An in-the-money option is one where the option is profitable if exercised. For example, in case of a put options (which the right to sell) the option will be in the money if the market price of the stock is less than the strike price of the contract. On the other hand, the put option will be out of the money (OTM) if the market price of the stock is higher than the strike price. Let us look at simulated comparisons to understand this point better. However, here we are looking at deep ITM and deep OTM puts. A deep ITM put option will be one where the market price is substantially lower than the strike price. A deep OTM put option will be one where the market price is substantially higher than the strike price of the contract.

Let us first look at how the option value of a Deep ITM put is impacted when the volatility goes up by 10 bps from 30% to 40%.

Input DataInput DataStock Price now (P)

90

Stock Price now (P)

90

Exercise Price of Option (EX)

125

Exercise Price of Option (EX)

125

Number of periods to Exercise in years (t)

0.08333

Number of periods to Exercise in years (t)

0.08333

Compounded Risk-Free Interest Rate (rf)

5.00%

Compounded Risk-Free Interest Rate (rf)

5.00%

Standard Deviation (annualized s)

30.00%

Standard Deviation (annualized s)

40.00%

Output DataOutput DataPresent Value of Exercise Price (PV(EX))

124.4803

Present Value of Exercise Price (PV(EX))

124.4803

s*t^0.5

0.0866

s*t^0.5

0.1155

d1

-3.7018

d1

-2.7511

d2

-3.7884

d2

-2.8666

Delta N(d1) Normal Cumulative Density Function

0.0001

Delta N(d1) Normal Cumulative Density Function

0.0030

Bank Loan N(d2)*PV(EX)

0.0094

Bank Loan N(d2)*PV(EX)

0.2583

Value of Put34.4804Value of Put34.4893(Note - Period is reduced to yearly decimals

Change in Value0.03%Let us now turn and look at how the option value of an ATM put is impacted when the volatility goes up by 10 bps from 30% to 40%. An ATM put option is one where the strike price and the market price are at the same level.

Input DataInput DataStock Price now (P)

125

Stock Price now (P)

125

Exercise Price of Option (EX)

125

Exercise Price of Option (EX)

125

Number of periods to Exercise in years (t)

0.08333

Number of periods to Exercise in years (t)

0.08333

Compounded Risk-Free Interest Rate (rf)

5.00%

Compounded Risk-Free Interest Rate (rf)

5.00%

Standard Deviation (annualized s)

30.00%

Standard Deviation (annualized s)

40.00%

Output DataOutput DataPresent Value of Exercise Price (PV(EX))

124.4803

Present Value of Exercise Price (PV(EX))

124.4803

s*t^0.5

0.0866

s*t^0.5

0.1155

d1

0.0914

d1

0.0938

d2

0.0048

d2

-0.0217

Delta N(d1) Normal Cumulative Density Function

0.5364

Delta N(d1) Normal Cumulative Density Function

0.5374

Bank Loan N(d2)*PV(EX)

62.4791

Bank Loan N(d2)*PV(EX)

61.1650

Value of Put4.0535Value of Put5.4869(Note - Period is reduced to yearly decimals

Change in Value35.36%Finally, let us now turn and look at how the option value of a Deep OTM put is impacted when the volatility goes up by 10 bps from 30% to 40%. A Deep OTM put option is one where the strike price is substantially lower than the market price. Check the table below.

Input DataInput DataStock Price now (P)

200

Stock Price now (P)

200

Exercise Price of Option (EX)

125

Exercise Price of Option (EX)

125

Number of periods to Exercise in years (t)

0.08333

Number of periods to Exercise in years (t)

0.08333

Compounded Risk-Free Interest Rate (rf)

5.00%

Compounded Risk-Free Interest Rate (rf)

5.00%

Standard Deviation (annualized s)

30.00%

Standard Deviation (annualized s)

40.00%

Output DataOutput DataPresent Value of Exercise Price (PV(EX))

124.4803

Present Value of Exercise Price (PV(EX))

124.4803

s*t^0.5

0.0866

s*t^0.5

0.1155

d1

5.5185

d1

4.1642

d2

5.4319

d2

4.0487

Delta N(d1) Normal Cumulative Density Function

1.0000

Delta N(d1) Normal Cumulative Density Function

1.0000

Bank Loan N(d2)*PV(EX)

124.4802

Bank Loan N(d2)*PV(EX)

124.4770

Value of Put0.0000Value of Put0.0001(Note - Period is reduced to yearly decimals

Change in ValueNegligibleWhat can you infer from a comparison of the Deep OTM, Deep ITM and the ATM scenarios? As you move either towards Deep ITM or Deep OTM put options, the impact on the value of the put options is very negligible when the volatility shifts upward. That is because the impact of this volatility rise on the time value of the option is very limited. But the impact is much more in the ATM puts as well as in cases where the ITM and OTM put options are near to the money. But, as the put options keep going deep ITM or deep OTM, the relative impact on the value of the put option resulting from a rise in the volatility becomes virtually negligible. This is a very important aspect in understanding options trading.