InvestorQ : How does the volatility impact the value of the call option and what is the impact if the volatility of the price increases. How does the call option get impacted?

How does the volatility impact the value of the call option and what is the impact if the volatility of the price increases. How does the call option get impacted?

1 year ago

The time to expiry is important because it determines the time value of the option. Higher the time to expiry, higher 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 time left for expiry. Let us see this example in practical terms when volatility is increased by 20%.

 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) 36.00% 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 0.1039 d1 -0.3800 d1 -0.3008 d2 -0.4666 d2 -0.4047 Delta N(d1) Normal Cumulative Density Function 0.3520 Delta N(d1) Normal Cumulative Density Function 0.3818 Bank Loan N(d2)*PV(EX) 39.8844 Bank Loan N(d2)*PV(EX) 42.6790 Value of Call 2.3542 Value of Call 3.1371

In the above illustration, we have kept all the other parameters the same but we have increased the volatility by 20%. Effectively, we have increased the volatility from 30% to 36%. The impact of this is an increase in the value of the call option. Volatility is directly related to the time value as greater the volatility means more chances of being profitable within the same period of time. 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. 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.

But what would happen if we increased the volatility by another 20%. This would effectively take the volatility higher from 36% to 43.2%. Obviously the value of call will increase further but will it be more than the first 20% move or the less than the first move. Let us look at 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) 43.20% 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 0.1247 d1 -0.3800 d1 -0.2316 d2 -0.4666 d2 -0.3563 Delta N(d1) Normal Cumulative Density Function 0.3520 Delta N(d1) Normal Cumulative Density Function 0.4084 Bank Loan N(d2)*PV(EX) 39.8844 Bank Loan N(d2)*PV(EX) 44.9142 Value of Call 2.3542 Value of Call 4.0978 (Note - Period is reduced to yearly decimals

While the value of the call goes up further with the higher volatility, the subsequent 20% increase in volatility has a lesser impact on the call value as the elasticity of time value of the call option tends to saturate after a point of time.

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