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? # 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 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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