InvestorQ : How does the time to expiry impact the value of the call option and what is the impact if the time to expiry is increased. How does the call option get impacted? # How does the time to expiry impact the value of the call option and what is the impact if the time to expiry is increased. How does the call option get impacted? Answer 2 years ago
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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) 120.00 Stock Price now (P) 120.00 Exercise Price of Option (EX) 125.00 Exercise Price of Option (EX) 125.00 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^.5 0.0866 s*t^.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 Call 2.3542 Value of Call 1.1978 (Note - Period is reduced to yearly decimals

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 call 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 call 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 call option.
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