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

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

The volatility is important because it determines the time value of the option. Higher the volatility in the price of the stock, 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 volatility in the stock price. The same rule applies to put option also because put and call options are based on the probability of the prices moving in your favour and that means volatility should work in favour of options price. Let us see this example in practical terms.

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)

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^0.5

0.0866

s*t^0.5

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 Put

6.8345

Value of Put

6.2029

In the above illustration, we have kept all the other parameters the same but we have reduced the volatility. Effectively, we have reduced the volatility from 30% to 25%. The impact of this is decrease in the value of the put option. Volatility is directly related to the time value. As the volatility is reduced the time value of the put option also reduces and thus the total value of the put option also reduces. 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. Interestingly, a reduction in the volatility represented by the standard deviation impacts the calls and puts in a similar manner. The volatility and the time to expiry are the only two factors that impact calls and puts in the same direction.

The volatility is important because it determines the time value of the option. Higher the volatility in the price of the stock, 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 volatility in the stock price. The same rule applies to put option also because put and call options are based on the probability of the prices moving in your favour and that means volatility should work in favour of options price. Let us see this example in practical terms.

Input DataInput DataStock 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)

25.00%

Output DataOutput DataPresent 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

0.0722

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 Put6.8345Value of Put6.2029In the above illustration, we have kept all the other parameters the same but we have reduced the volatility. Effectively, we have reduced the volatility from 30% to 25%. The impact of this is decrease in the value of the put option. Volatility is directly related to the time value. As the volatility is reduced the time value of the put option also reduces and thus the total value of the put option also reduces. 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. Interestingly, a reduction in the volatility represented by the standard deviation impacts the calls and puts in a similar manner. The volatility and the time to expiry are the only two factors that impact calls and puts in the same direction.