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Advanced Binomial Trees - Binomial Model and Risk-Neutral pricing

4 important questions on Advanced Binomial Trees - Binomial Model and Risk-Neutral pricing

Why would an american call on a dividend paying stock be exercised early?

Economic intuition: if the american call is not exercised

The strike price is paid later: +
The stock is received later: ~
Asymmetric payoff profile: -

high stock prices: profit
low stock prices: losses are capped, but the investor foregoes the dividend: - (because you will not receive the underlying and thus the dividend)

Early exercise can be reasonable in order to avoid the dividend 'loss' (exercise immediately before the dividend payment)

When is it favorable to exercise and american call on a dividend paying stock?

The left term means the amount that we could earn if we would not exercise the option and invest the amount in the MMA --> if the interest that we could earn from doing this is higher than the dividend we receive, we do not exercise. If vice versa, we could exercide early