InvestorQ : What happens to the value of the call and put options under Black & Scholes when the dividend yields on the index move down due to a cut in the dividend rates?
Lavanya Subramanian made post
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What happens to the value of the call and put options under Black & Scholes when the dividend yields on the index move down due to a cut in the dividend rates?

Answer
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ishika Banerjee answered.
3 years ago
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You can, of course, argue that option holders do not receive dividends. Then why does dividend impact the value of the option. The reason is that dividends impact the value of the stock and therefore the value of the option. Check the table below as to what happens when the dividend yield of the stock goes down.

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)

0.0833

Dividend yield (d)

1.00%

Dividend yield (d)

0.50%

Outputs

Outputs

d1

0.196

d1

0.201

d2

0.109

d2

0.114

N(d1)

0.578

N(d1)

0.580

N(d2)

0.544

N(d2)

0.545

Call Price (Vc)

? 45.77

Call Price (Vc)

? 46.04

-d1

-0.196

-d1

-0.201

-d2

-0.109

-d2

-0.114

N(-d1)

0.422

N(-d1)

0.420

N(-d2)

0.456

N(-d2)

0.455

Put Price (Pp)

? 31.21

Put Price (Pp)

? 31.01

In the above illustration, the dividend yields have gone down from 1% to 0.50%. Dividend yield is the quotient of the dividend per share and the price per share. Let us see how that impacts the value of the option. When a company pays dividends it is partial liquidation of the assets of the company. When the dividend yield reduces it means that greater value is being retained in the company rather than being paid out. That increases the value of the company and that means the price will also go up in this case. If the price goes up, the intrinsic value of the call option also goes up and the intrinsic value of the put option will come down. Of course, the impact is quite marginal as is evident in the above illustration.
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