InvestorQ : What happens to the value of the call and put options under Black & Scholes when the time to expiry of the stock goes down or moves down?
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What happens to the value of the call and put options under Black & Scholes when the time to expiry of the stock goes down or moves down?

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Anamika Sodhani answered.
3 years ago
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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 time to expiry of just 15 days, 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)

0.0417

Dividend yield (d)

1.00%

Dividend yield (d)

1.00%

Outputs

Outputs

d1

0.196

d1

0.212

d2

0.109

d2

0.151

N(d1)

0.578

N(d1)

0.584

N(d2)

0.544

N(d2)

0.560

Call Price (Vc)

? 45.77

Call Price (Vc)

? 33.54

-d1

-0.196

-d1

-0.212

-d2

-0.109

-d2

-0.151

N(-d1)

0.422

N(-d1)

0.416

N(-d2)

0.456

N(-d2)

0.440

Put Price (Pp)

? 31.21

Put Price (Pp)

? 21.25

In the above instance we have evaluated a fall in time to expiry of the option. What happens to the value of the option when the time to expiry goes down? You will notice that when we move the time to expiry of the option from 1 month to 15 days, the value of the call and the put option goes down. The reason is quite simple. Lower time to maturity means lower 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. That is why longer dated options are normally always working in favour of the value of the call and the put option.
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