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If an underlying doesn't pay dividends (for our purpose defined as any distribution to the underlying's holder) directly or indirectly (e.g. options on futures) how does put-call parity change from the usual assumption of a European option?

In particular, I'm thinking of bond options like the 10-year Treasury Note. Clearly options like these are worth more but how much more and what factors are required to evaluate put-call parity?

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2 Answers 2

There is an interesting article entitled American Put Call Symmetry from the mid 90s that might be what you want.

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In John Hull's Option's, Futures and Other Derivatives, it states in the chapter "Properties of Stock Options" that from put-call parity, it follows for American options that $$ S_0 - K \le C - P \le S_0 - K e^{-rT} $$ where $C$ and $P$ are the American call and put prices.

In the book, the derivation is left as an exercise.

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