InvestorQ : What happens to the value of the call and put options under Black & Scholes when the strike price goes down or shifts down?
Arya Nanda made post

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

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Deepa Salunkhe answered.
3 years ago
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What happens if the excise price goes down. For example instead of buying an 1100 RIL strike, we have instead decided to shift to a 1080 RIL strike price. 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. Check the table below:

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)

? 1,080

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

0.408

d2

0.109

d2

0.321

N(d1)

0.578

N(d1)

0.658

N(d2)

0.544

N(d2)

0.626

Call Price (Vc)

? 45.77

Call Price (Vc)

? 57.41

-d1

-0.196

-d1

-0.408

-d2

-0.109

-d2

-0.321

N(-d1)

0.422

N(-d1)

0.342

N(-d2)

0.456

N(-d2)

0.374

Put Price (Pp)

? 31.21

Put Price (Pp)

? 22.95

While the market price has remained the same, we have moved the option strike down by 20 points from 1100 to 1080. When the strike price goes down, the advantage works against the put option and in favour of the call option. There is a simple reason for that. In the first scenario above on the left side, the call option was OTM because the market price was below the strike price. With the shift in the excise price downward, the option now becomes an in the money call option. That is the reason that the call option is benefiting from a downward shift in the excise price. At the same time, the put option is losing out on the value as is evident from the above table.
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