InvestorQ : To what extent does the change in the volatility impact the value of a Call option? If the volatility increases, does it impact all call options similarly?

To what extent does the change in the volatility impact the value of a Call option? If the volatility increases, does it impact all call options similarly?

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. 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. 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. Let us look at simulated comparisons to understand this point better.

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

Input Data

Input Data

Stock Price now (P)

130.00

Stock Price now (P)

130.00

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

0.5443

d1

0.4335

d2

0.4577

d2

0.3180

Delta N(d1) Normal Cumulative Density Function

0.7069

Delta N(d1) Normal Cumulative Density Function

0.6677

Bank Loan N(d2)*PV(EX)

84.2001

Bank Loan N(d2)*PV(EX)

77.7705

Value of Call

7.6944

Value of Call

9.0263

(Note - Period is reduced to yearly decimals

Change in Value

17.31%

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 an OTM call is impacted when the volatility goes up by 10 bps from 30% to 40%. An OTM call option is one where the strike price is higher than the market price. Check the table below.

Input Data

Input Data

Stock Price now (P)

120.00

Stock Price now (P)

120.00

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

-0.3800

d1

-0.2597

d2

-0.4666

d2

-0.3752

Delta N(d1) Normal Cumulative Density Function

0.3520

Delta N(d1) Normal Cumulative Density Function

0.3975

Bank Loan N(d2)*PV(EX)

39.8844

Bank Loan N(d2)*PV(EX)

44.0366

Value of Call

2.3542

Value of Call

3.6687

(Note - Period is reduced to yearly decimals

Change in Value

55.83%

What can you infer from a comparison of the OTM, ITM and the ATM scenarios? As you move from ITM to ATM to OTM call options, the impact on the value of the call options is much larger. But the impact is much more in the OTM calls that near the money. As the call options keep going deep ITM or deep OTM, the relative impact on the value of the call option of a shift in the volatility keeps on gradually reducing. This is a very important aspect in understanding options trading.

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. 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. 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. Let us look at simulated comparisons to understand this point better.

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

Input DataInput DataStock Price now (P)

130.00

Stock Price now (P)

130.00

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 DataOutput DataPresent 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

0.5443

d1

0.4335

d2

0.4577

d2

0.3180

Delta N(d1) Normal Cumulative Density Function

0.7069

Delta N(d1) Normal Cumulative Density Function

0.6677

Bank Loan N(d2)*PV(EX)

84.2001

Bank Loan N(d2)*PV(EX)

77.7705

Value of Call7.6944Value of Call9.0263(Note - Period is reduced to yearly decimals

Change in Value17.31%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 DataInput DataStock 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 DataOutput DataPresent 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 Call4.5732Value of Call6.0067(Note - Period is reduced to yearly decimals

Change in Value31.35%Finally, let us now turn and look at how the option value of an OTM call is impacted when the volatility goes up by 10 bps from 30% to 40%. An OTM call option is one where the strike price is higher than the market price. Check the table below.

Input DataInput DataStock Price now (P)

120.00

Stock Price now (P)

120.00

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 DataOutput DataPresent 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

-0.3800

d1

-0.2597

d2

-0.4666

d2

-0.3752

Delta N(d1) Normal Cumulative Density Function

0.3520

Delta N(d1) Normal Cumulative Density Function

0.3975

Bank Loan N(d2)*PV(EX)

39.8844

Bank Loan N(d2)*PV(EX)

44.0366

Value of Call2.3542Value of Call3.6687(Note - Period is reduced to yearly decimals

Change in Value55.83%What can you infer from a comparison of the OTM, ITM and the ATM scenarios? As you move from ITM to ATM to OTM call options, the impact on the value of the call options is much larger. But the impact is much more in the OTM calls that near the money. As the call options keep going deep ITM or deep OTM, the relative impact on the value of the call option of a shift in the volatility keeps on gradually reducing. This is a very important aspect in understanding options trading.