The impact of change in volatility on the call option value will depend on whether the option is in-the money, at the money or out of the money. Even within ITM and OTM options, the impact will depend on whether the ITM is deep ITM or near ITM. Similarly, the impact on the OTM options will also depend on whether it is deep OTM or near OTM. An in-the-money option is one where the option is profitable if exercised. For example, in case of a call options (which the right to buy) the option will be in the money if the market price of the stock is more than the strike price of the contract and it will be deep in the money if the market price is substantially higher than the strike price. On the other hand, the call option will be out of the money (OTM) if the market price of the stock is lower than the strike price and deep OTM if the market price is substantially lower than the strike price. Let us look at simulated comparisons to understand this point better.

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

Input Data

Input Data

Stock Price now (P)

180.00

Stock Price now (P)

180.00

Exercise Price of Option (EX)

125.00

Exercise Price of Option (EX)

125.00

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^.5

0.0866

s*t^.5

0.1155

d1

4.3019

d1

3.2517

d2

4.2153

d2

3.1363

Delta N(d1) Normal Cumulative Density Function

1.0000

Delta N(d1) Normal Cumulative Density Function

0.9994

Bank Loan N(d2)*PV(EX)

124.4787

Bank Loan N(d2)*PV(EX)

124.3737

Value of Call

55.5198

Value of Call

55.5230

(Note - Period is reduced to yearly decimals

Change in Value

0.01%

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

Input Data

Input Data

Stock Price now (P)

125.00

Stock Price now (P)

125.00

Exercise Price of Option (EX)

125.00

Exercise Price of Option (EX)

125.00

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^.5

0.0866

s*t^.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 Call

4.5732

Value of Call

6.0067

(Note - Period is reduced to yearly decimals

Change in Value

31.35%

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

Input Data

Input Data

Stock Price now (P)

80.00

Stock Price now (P)

80.00

Exercise Price of Option (EX)

125.00

Exercise Price of Option (EX)

125.00

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^.5

0.0866

s*t^.5

0.1155

d1

-5.0619

d1

-3.7711

d2

-5.1485

d2

-3.8866

Delta N(d1) Normal Cumulative Density Function

0.0000

Delta N(d1) Normal Cumulative Density Function

0.0001

Bank Loan N(d2)*PV(EX)

0.0000

Bank Loan N(d2)*PV(EX)

0.0063

Value of Call

0.0000

Value of Call

0.0002

(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 call options, the impact on the value of the call options very negligible when the volatility shifts. That is because the impact of this movement on the time value of the option is very limited. But the impact is much more in the ATM calls as well as in cases where the ITM and OTM call options are near to the money. But, as the call options keep going deep ITM or deep OTM, the relative impact on the value of the call option resulting from a shift in the volatility becomes virtually negligible. This is a very important aspect in understanding options trading.