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 decreased. How does the put option get impacted?
Debbie Mascarenhas made post

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

Answer
user profile image
Neelam Naik answered.
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 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 time left for expiry and less chances of the price moving in your favour as the time to expiry reduces. 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)

0.04167

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))

124.7399

s*t^0.5

0.0866

s*t^0.5

0.0612

d1

-0.3800

d1

-0.6020

d2

-0.4666

d2

-0.6632

Delta N(d1) Normal Cumulative Density Function

0.3520

Delta N(d1) Normal Cumulative Density Function

0.2736

Bank Loan N(d2)*PV(EX)

39.8844

Bank Loan N(d2)*PV(EX)

31.6334

Value of Put

6.8345

Value of Put

5.9376

In the above illustration, we have kept all the other parameters the same but we have reduced the time to expiry. Effectively, we have decreased the time to expiry from 1 month to 15 days or half a month. The impact of this is a reduction 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 call option also increases and thus the total value of the call option also increases. The reverse operates when the time to expiry 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 time to expiry reduces the value of a put option.