InvestorQ : To what extent does the change in the volatility impact the value of a Put option? If the volatility increases, does it impact all put options similarly?
Tisha Malhotra made post

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

Answer
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Ria Jain answered.
1 year ago


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.

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

Input Data

Input Data

Stock Price now (P)

120

Stock Price now (P)

120

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

-0.3800

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 Put

6.8345

Value of Put

8.1490

(Note - Period is reduced to yearly decimals

Change in Value

19.23%

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

Input Data

Input Data

Stock Price now (P)

130

Stock Price now (P)

130

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

0.5443

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 Put

2.1747

Value of Put

3.5065

(Note - Period is reduced to yearly decimals

Change in Value

61.24%

What can you infer from a comparison of the OTM, ITM and the ATM scenarios? As you move from ITM to ATM to OTM put options, the impact on the value of the put options is much bigger. This is specifically applicable to near money option which is what we have considered in this case. But the impact is much more in the OTM puts that are near the money compared to ITM options that are near the money. As the put options keep going deep ITM or deep OTM, the relative impact on the value of the put option of a shift in the volatility keeps on gradually reducing. This is a very important aspect in understanding options trading.