Pricing An Option on a Dividend Paying Stock Using The Binomial Tree Method - Trading Tutorial

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These classes are all based on the book Trading and Pricing Financial Derivatives, available on Amazon at this link.
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This is the sixth video in our series on pricing options, to watch the whole series as a playlist, click here:

Options on Dividend Paying Underlyings

For an American-style call option, early exercise can make sense whenever the benefits of being long the underlying outweighs the cost of giving up the option early (the benefits of being long the underlying outweigh the foregone time value of the option). For example, on the day before an ex-dividend date, it may make sense to exercise an equity call option early in order to collect the dividend. In general, equity call options should only be exercised early on the day before an ex-dividend date, and then only for deep in-the-money options when the dividend is sufficiently large.

Todays video illustrates a scenario where a dividend of $2.50 per share is expected to be paid immediately prior to expiration of an option. Call option holders, though holding "bullish" or "long" positions with respect to the underlying asset, are not eligible to collect dividends paid on the underlyings. Therefore, if a long American call option holder expects at T0 and at T1 that a dividend will be paid on the underlying stock just prior to the option's maturity at T2, they can evaluate whether or not it is optimal to early-exercise. Analyzing potential early exercise at T0 shows there is no benefit to early exercising since the option is not in-the-money. At T1, the up node is in-the-money, the American call holder evaluates if holding or early-exercising is optimal. Early-exercising has a value at T1 in the up node of $3.00 ($30 share price less $30 strike). Using the European options binomial tree pricing formula fu in the up node, the call option is valued at only $2.73. This valuation difference came about because the expected value of the spot at T2 is reduced by $2.50 just prior to expiration. This dividend payment is of sufficient size, in this case (it is not always optimal to early-exercise on dividend-paying stocks, prior to expiration, it depends on the relative size of the dividend), that the underlying asset's price drop due to the dividend payment makes early-exercise the optimal strategy.