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?

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. 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.

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