InvestorQ : To what extent does the change in the volatility impact the value of a put option? If the volatility decreases, does it impact all put options similarly, especially with focus on deep OTM and deep ITM put options? # To what extent does the change in the volatility impact the value of a put option? If the volatility decreases, does it impact all put options similarly, especially with focus on deep OTM and deep ITM put options? Answer 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 option (which is 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 and it will be deep in the money if the market price is substantially 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 and the put option will be deep out of the money if the market price is substantially higher than the strike price of the contract. Let us look at simulated comparisons to understand this point better.

Let us first look at how the option value of a Deep ITM put is impacted when the volatility goes down by 10 bps from 30% to 20%.

 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) 20.00% 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 0.0577 d1 -3.7018 d1 -5.5888 d2 -3.7884 d2 -5.6466 Delta N(d1) Normal Cumulative Density Function 0.0001 Delta N(d1) Normal Cumulative Density Function 0.0000 Bank Loan N(d2)*PV(EX) 0.0094 Bank Loan N(d2)*PV(EX) 0.0000 Value of Put 34.4804 Value of Put 34.4803 (Note - Period is reduced to yearly decimals Change in Value Negligible

Let us now turn and look at how the option value of an ATM put is impacted when the volatility goes down by 10 bps from 30% to 20%. 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) 20.00% 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 0.0577 d1 0.0914 d1 0.1010 d2 0.0048 d2 0.0433 Delta N(d1) Normal Cumulative Density Function 0.5364 Delta N(d1) Normal Cumulative Density Function 0.5402 Bank Loan N(d2)*PV(EX) 62.4791 Bank Loan N(d2)*PV(EX) 64.3898 Value of Put 4.0535 Value of Put 2.6203 (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 down by 10 bps from 30% to 20%. 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) 175 Stock Price now (P) 175 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) 20.00% 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 0.0577 d1 3.9767 d1 5.9289 d2 3.8901 d2 5.8712 Delta N(d1) Normal Cumulative Density Function 1.0000 Delta N(d1) Normal Cumulative Density Function 1.0000 Bank Loan N(d2)*PV(EX) 124.4740 Bank Loan N(d2)*PV(EX) 124.4802 Value of Put 0.0001 Value of Put 0.0000 (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 downward. That is because the impact of this volatility fall 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 fall in the volatility becomes virtually negligible. This is a very important aspect in understanding options trading.

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