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? Answer 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. 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.

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