InvestorQ : What happens to the value of the call and put options under Black & Scholes when the strike price goes up?
Anjana Aiyar made post

What happens to the value of the call and put options under Black & Scholes when the strike price goes up?

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Arya Nanda answered.
3 years ago
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What happens if the excise price goes up. For example instead of buying an 1100 RIL strike, we have instead decided to shift to an 1120 RIL strike. Would that really impact the value of the call and put option? The answer is that it surely will and let us also see how. It is all about the relationship between the strike price and the market price. It is this gap that is the key to determining the shift in value of the option.

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)

? 1,120

Time To Maturity - Years (T)

0.0833

Time To Maturity - Years (T)

0.0833

Dividend yield (d)

1.00%

Dividend yield (d)

1.00%

Outputs

Outputs

d1

0.196

d1

-0.012

d2

0.109

d2

-0.099

N(d1)

0.578

N(d1)

0.495

N(d2)

0.544

N(d2)

0.461

Call Price (Vc)

? 45.77

Call Price (Vc)

? 35.78

-d1

-0.196

-d1

0.012

-d2

-0.109

-d2

0.099

N(-d1)

0.422

N(-d1)

0.505

N(-d2)

0.456

N(-d2)

0.539

Put Price (Pp)

? 31.21

Put Price (Pp)

? 41.12

While the market price has remained the same, we have moved the option strike up by 20 points from 1100 to 1120. When the strike price goes up, the advantage works against the call option and in favour of the put option. There is a simple reason for that. In the first scenario above on the left side, the put option was OTM because the market price was above the strike price. With the shift in the excise price, the option now becomes an in the money put option. That is the reason that the put option is benefiting from an upward shift in the excise price. At the same time, the call option is losing out on the value as is evident from the above table.
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