InvestorQ : How does the time to expiry impact the value of the put option and what is the impact if the time to expiry is increased. How does the put option get impacted?

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

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. 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 time 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)

0.16667

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)

30.00%

Output Data

Output Data

Present Value of Exercise Price (PV(EX))

124.4803

Present Value of Exercise Price (PV(EX))

123.9627

s*t^0.5

0.0866

s*t^0.5

0.1225

d1

-0.3800

d1

-0.2040

d2

-0.4666

d2

-0.3265

Delta N(d1) Normal Cumulative Density Function

0.3520

Delta N(d1) Normal Cumulative Density Function

0.4192

Bank Loan N(d2)*PV(EX)

39.8844

Bank Loan N(d2)*PV(EX)

46.1167

Value of Put

6.8345

Value of Put

8.1457

In the above illustration, we have kept all the other parameters the same but we have increased the time to expiry. Effectively, we have increased the time to expiry from 1 month to 2 months. The impact of this is an increase in the value of the put option. Time to expiry is directly related to the time value. As the time to expiry is increased the time value of the put option also increases and thus the total value of the put option also increases. 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, an increase in the time to expiry impacts the calls and puts in a similar manner.

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. 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 time 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)

0.16667

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)

30.00%

Output DataOutput DataPresent Value of Exercise Price (PV(EX))

124.4803

Present Value of Exercise Price (PV(EX))

123.9627

s*t^0.5

0.0866

s*t^0.5

0.1225

d1

-0.3800

d1

-0.2040

d2

-0.4666

d2

-0.3265

Delta N(d1) Normal Cumulative Density Function

0.3520

Delta N(d1) Normal Cumulative Density Function

0.4192

Bank Loan N(d2)*PV(EX)

39.8844

Bank Loan N(d2)*PV(EX)

46.1167

Value of Put6.8345Value of Put8.1457In the above illustration, we have kept all the other parameters the same but we have increased the time to expiry. Effectively, we have increased the time to expiry from 1 month to 2 months. The impact of this is an increase in the value of the put option. Time to expiry is directly related to the time value. As the time to expiry is increased the time value of the put option also increases and thus the total value of the put option also increases. 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, an increase in the time to expiry impacts the calls and puts in a similar manner.