By Melvyn S. Berger, Marion Berger
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Additional info for Perspectives in Nonlinearity: An Introduction to Nonlinear Analysis
These simple payoff diagrams are composed of straight lines connected via kinks. 2, which in turn results from the choices embedded within the option contract . The terminal payoffs to the short positions are nowhere positive-in exchange for the up-front cash flow generated by shorting the option; the converse is tr ue for the long positions. Zero payoffs are drawn as very slightly different from zero, so that they can be seen . 3 on page 59-or a deep in-t he-money Europeanstyle call on a stock with a high dividend yield-see discussion on page 109).
First, when pulling quotes, unless done in real t ime, there is no guarantee that they are coincident. Second, an option need not t rade to have a quoted bid and ask. You can have zero volume, but the market maker (or the market maker's autoquote machine) keeps moving the quotes during the day. 5 Fourth, RTH for index options can differ from those for equity options. vSixth, deep in-the-money European-style calls can trade at a discount to exercise value when there are dividends during the life of the call , but that discount is small when dividends are small or when interest rates are large.
Thus, the European call on the higher-dividend stock is the less valuable of the pair of options. How does the ability to exercise early and capture a dividend alter the above argument when we consider an American call? 4 that the only t ime the holder of an American call considers early exercise is just prior to t he stock going ex-dividend , and at that time the option has only its exercise value: 5 - X . It follows that there are three distinct cases when applying the identical stock/different dividend argument to American-style calls.