InvestorQ : How does the volatility impact the value of the put option and what is the impact if the volatility is increased. How does the put option get impacted?
Aditi Sharma made post

How does the volatility impact the value of the put option and what is the impact if the volatility is increased. How does the put option get impacted?

Answer
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shrinidhi Rajan answered.
1 year ago


The volatility or standard deviation is important because it determines the time value of the option. Higher the volatility, higher is the time value of the option and lower the volatility or standard deviation, 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 implicit in the stock and less chances of the price moving in your favour as there is less volatility in the stock. Let us see this example in practical terms when standard deviation goes up from 30% to 36%.

Input Data

Input Data

Stock Price now (P)

120

Stock Price now (P)

120

Exercise Price of Option (EX)

125

Exercise Price of Option (EX)

125

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^0.5

0.0866

s*t^0.5

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 Put

6.8345

Value of Put

7.6174

In the above illustration, we have kept all the other parameters the same but we have increased the volatility of the stock returns as measured by standard deviation. Effectively, we have increased the volatility of the stock from 30% to 36%. The impact of this is increase in the value of the put option. Volatility is directly related to the time value. As the volatility is increased the time value of the put option also increases and thus the total value of the put 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 put 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 put option.