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?

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 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.

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