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Delta of an American put
why does an american put have higher delta than a european put of similar makeup? is this always so.?
Delta of an American put
Intuitively it makes sense because thevalues and deltas will be asymptotically equal far out-of-the-money.Then, as you decrease the stock price, the delta of the Americanmust be higher (more negative) in order to force the price to bestrictly higher than the Euro-style one.I don't know if this is a theorem. If it is, you might be able toprove it from the 'early exercise' representation which splitsthe amer. put value into the euro-style value plus a correction term.regards,
Delta of an American put
another way to see this, in addition to the intuition alan described:the expected time to optimal exercise of an american put on stock decreases as it goes from otm to itm. as expected time to expiration decreases, delta moves closer to -1.