Lecture 10

# Lecture 10 - ombining a stock position with an option...

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ombining a stock position with an option allows investor to put a cap or floor on payoff. But this has a more subtle implication it can allow us to take another view of put-call parity. Consider the payoff to buying a stock and buying a put with strike K. The payoff function of the stock, S 0 , is and the payoff function for the put, p , is so the payoff to the combined function is the purple line: . The payoff to this combination, which I've labeled "Z", looks remarkably like the payoff to

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buying a call, c , at some cost: . What could cost be? Recall our formula for put-call parity, that for a stock that does not pay dividends, p + S 0 = c + Ke -rT . What is the payoff to a portfolio with one put and one share of stock? That's the " p + S 0 " part. What is it equal to? A call, "c", plus some amount of cash, " Ke -rT ". So we could also derive our formula on put-call parity from the equivalence of the payoff functions. This is a taste of a more general result: if two portfolios give the same payoff functions, then if
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Lecture 10 - ombining a stock position with an option...

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