How does the time to expiry impact the value of the call option and what is the impact if the time to expiry is decreased. How does the call option get impacted?
Answer
Answer
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. 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)
0.16667
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^.5
0.0866
s*t^.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 Call
2.3542
Value of Call
4.1830
(Note - Period is reduced to yearly decimals
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 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. 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.