InvestorQ : How does the volatility or standard deviation impact the value of the call option and what is the impact if the standard deviation or volatility is decreased. How does the call option get impacted? # How does the volatility or standard deviation impact the value of the call option and what is the impact if the standard deviation or volatility is decreased. How does the call option get impacted? Answer 1 year ago

The volatility is important because it determines the time value of the option. Higher the volatility, higher is the time value of the option and lower is the time to expiry lower is the time value of the option. That is because there is greater probability of the option prices moving in your favour when there is more volatility in the stock and less chances of the price moving in your favour as the volatility reduces. Let us see this example in practical terms when volatility is reduced from 30% to 25%.

 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) 25.00% 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 0.0722 d1 -0.3800 d1 -0.4718 d2 -0.4666 d2 -0.5440 Delta N(d1) Normal Cumulative Density Function 0.3520 Delta N(d1) Normal Cumulative Density Function 0.3185 Bank Loan N(d2)*PV(EX) 39.8844 Bank Loan N(d2)*PV(EX) 36.5004 Value of Call 2.3542 Value of Call 1.7226 (Note - Period is reduced to yearly decimals

In the above illustration, we have kept all the other parameters the same but we have reduced the volatility of the stock price. Effectively, we have decreased the volatility from 30% to 25%. The impact of this is a reduction in the value of the call option. Volatility is directly related to the time value. As the volatility is increased the time value of the call option also increases and thus the total value of the call option also increases. The reverse operates when the volatility is reduced as it reduces your chances of being profitable in your options trade. We all know that the value of the call option is the sum total of the intrinsic value of the option and the time value of the option. That is how a reduction in the volatility reduces the value of a call option.

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