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?
Aditi Sharma made post

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
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shrinidhi Rajan answered.
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.