What happens to the value of the call and put options under Black & Scholes when the time to expiry of the stock goes up or moves up?
Answer
Answer
How does time to expiry of an option impact the value of an option? For example, if we shift from a 1 month option to a 2 month option, what is likely to be the impact on the value of the option? Let us look at the table below to understand the cause-effect relationship.
Inputs
Inputs
Stock Price Now (Ps)
? 1,110
Stock Price Now (Ps)
? 1,110
Standard Dev - Annual (s)
30.00%
Standard Dev - Annual (s)
30.00%
Risk free Rate - Annual (R)
6.00%
Risk free Rate - Annual (R)
6.00%
Exercise Price (E)
? 1,100
Exercise Price (E)
? 1,100
Time To Maturity - Years (T)
0.0833
Time To Maturity - Years (T)
0.1667
Dividend yield (d)
1.00%
Dividend yield (d)
1.00%
Outputs
Outputs
d1
0.196
d1
0.203
d2
0.109
d2
0.081
N(d1)
0.578
N(d1)
0.581
N(d2)
0.544
N(d2)
0.532
Call Price (Vc)
? 45.77
Call Price (Vc)
? 63.74
-d1
-0.196
-d1
-0.203
-d2
-0.109
-d2
-0.081
N(-d1)
0.422
N(-d1)
0.419
N(-d2)
0.456
N(-d2)
0.468
Put Price (Pp)
? 31.21
Put Price (Pp)
? 44.64
In the above instance we have evaluated a rise in time to expiry of the option. What happens to the value of the option when the time to expiry goes up? You will notice that when we move the expiry of the option from 1 month to two months, the value of the call and the put option goes up. The reason is quite simple. Higher time means greater scope for the price to move in your favour. If the price moves against you then anyways you have the option of letting your option expire worthless.