InvestorQ : To what extent does the change in the volatility impact the value of a Call option? If the volatility decreases, 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 decreases, does it impact all call options similarly? Answer 1 year ago

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 down by 10 bps from 30% to 20%.

 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) 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^.5 0.0866 s*t^.5 0.0577 d1 0.5443 d1 0.7804 d2 0.4577 d2 0.7226 Delta N(d1) Normal Cumulative Density Function 0.7069 Delta N(d1) Normal Cumulative Density Function 0.7824 Bank Loan N(d2)*PV(EX) 84.2001 Bank Loan N(d2)*PV(EX) 95.2329 Value of Call 7.6944 Value of Call 6.4804 (Note - Period is reduced to yearly decimals Change in Value -15.78%

Let us now turn and look at how the option value of an ATM call is impacted when the volatility goes down by 10 bps from 30% to 20%. 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) 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^.5 0.0866 s*t^.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 Call 4.5732 Value of Call 3.1401 (Note - Period is reduced to yearly decimals Change in Value -31.34%

Finally, let us now turn and look at how the option value of an OTM call is impacted when the volatility goes down by 10 bps from 30% to 20%. 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) 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^.5 0.0866 s*t^.5 0.0577 d1 -0.3800 d1 -0.6060 d2 -0.4666 d2 -0.6638 Delta N(d1) Normal Cumulative Density Function 0.3520 Delta N(d1) Normal Cumulative Density Function 0.2723 Bank Loan N(d2)*PV(EX) 39.8844 Bank Loan N(d2)*PV(EX) 31.5462 Value of Call 2.3542 Value of Call 1.1239 (Note - Period is reduced to yearly decimals Change in Value -52.26%

What can you infer from a comparison of the OTM, ITM and the ATM scenarios when the volatility has fallen by 10 bps? As you move from ITM to ATM to OTM call options, the negative impact on the value of the call options is much larger. But the impact is much more in the OTM calls that are 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.

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