31 lines
1.7 KiB
Plaintext
31 lines
1.7 KiB
Plaintext
Dividends and Option Pricing
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The preceding discussion demonstrated how dividends affect stock traders.
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There’s one problem: we’re option traders! Option holders or writers do not
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receive or pay dividends, but that doesn’t mean dividends aren’t relevant to
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the pricing of these securities. Observe the behavior of a conversion or a
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reversal before and after an ex-dividend date. Assuming the stock opens
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unchanged on the ex-date, the relationship of the price of the synthetic stock
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to the actual stock price will change. Let’s look at an example to explore
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why.
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At the close on the day before the ex-date of a stock paying a $0.25
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dividend, a trader has an at-the-money (ATM) conversion. The stock is
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trading right at $50 per share. The 50 puts are worth 2.34, and the 50 calls
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are worth 2.48. Before the ex-date, the trader is
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Long 100 shares at $50
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Long one 50 put at 2.34
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Short one 50 call at 2.48
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Here, the trader is long the stock at $50 and short stock synthetically at
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$50.14—50 + (2.48 − 2.34). The trader is synthetically short $0.14 over the
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price at which he is long the stock.
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Assume that the next morning the stock opens unchanged. Since this is
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the ex-date, that means the stock opens at $49.75—$0.25 lower than the
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previous day’s close. The theoretical values of the options will change very
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little. The options will be something like 2.32 for the put and 2.46 for the
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call.
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After the ex-date, the trader is
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Long 100 shares at $49.75
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Long one 50 put at 2.32
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Short one 50 call at 2.46
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Each option is two cents lower. Why? The change in the option prices is
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due to theta. In this case, it’s $0.02 for each option. The synthetic stock is
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still short from an effective price of $50.14. With the stock at $49.75, the |