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Say you have a call option whose current value is $4.73$ and has a $\delta = .43$. Let's say dividend is increased by $.37$. I would expect the option to increase in value by ($.43*.37$) since the stock's price will go up by $.37$.

Sheldon Natenburg in Option Volatility and Pricing Workbook chapter 7, question 6c. expects the value to go down by the amount calculated above. Why is that?

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  • $\begingroup$ What happens when a stock goes ex-dividend? Its price per share adjusts (decreases) by the exact amount of the dividend... $\endgroup$
    – amdopt
    Oct 4 '20 at 15:14
  • $\begingroup$ So I guess the question is which date is being referred to? I imagine that the author is referring to the announcement date? (that's when the dividend is increased) $\endgroup$
    – Darby Bond
    Oct 4 '20 at 16:20
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In your example, I believe it's assumed that the exercise date is after the dividend date. If the dividend date is after the exercise date, nothing happens. The value would decrease, consider the following timeline:

  • $t=0$: You have a call option worth $4.73$ and a stock worth $S_0$
  • $t=1$: The increase in dividend is announced but dividends are not paid out yet.
  • $t=1 + \varepsilon$: The price of the option changes.
  • $t=2$: The dividend is paid.
  • $t=3$: Expiration date.

At $t=2$, the price of the stock would decrease by $.37$ more than was expected at $t=0$. This implies a downward adjustment of the option price at $t=3$ and one can expect that the price of the option from $t=1$ to $t=1+\varepsilon$ to decrease. It's less likely to end in the money and if it ends in the money the payoff would be lower, ceteris paribus.

Dividend decisions don't change company value as a first order effect. A decision to change dividends might give a signal to the market which has an effect on the price but the size and sign of that signal are hard to determine in general. Dividends come from the assets of the company so a dividend decrease the company value by the amount that is paid out. Otherwise it would be free lunch.

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  • $\begingroup$ At $t=2$, the price of the stock will decrease by $.37$ which is more than expected, but wouldn't the price increase by $.37$ between $t=1$ and $t = 1 + \epsilon$ anyway so there is no change to the price at $t=2$ after the dividend is paid? $\endgroup$
    – Darby Bond
    Oct 4 '20 at 17:01
  • $\begingroup$ No. Dividends come from the assets of the company so a dividend decrease the company value by the amount that is paid out. Otherwise it would be free lunch. $\endgroup$
    – Bob Jansen
    Oct 4 '20 at 17:02
  • $\begingroup$ Sorry to ask, but how would it lead to a free lunch? $\endgroup$
    – Darby Bond
    Oct 4 '20 at 17:39
  • $\begingroup$ The company pays out a dividend. Nothing happens to the stock price. Shareholders just gave themselves the dividend and their stock still has the same value. $\endgroup$
    – Bob Jansen
    Oct 4 '20 at 17:42
  • $\begingroup$ I see. But while increasing dividend reduces the value of the company, doesn't it increase the value of the share (using dividend discount model)? $\endgroup$
    – Darby Bond
    Oct 4 '20 at 19:04

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