Was Fermat's Theorem Really Proven?

[jason1990]

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Without doing the math I'm guessing that in that example, with stock price of $130, a put with strike of $90 would be priced the same as a call with strike of $170.

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A call with strike $170 is worth $30 if up, $0 if down. Hedge it by taking $16 from pocket, borrowing $10, and buying 1/5 share for $26. Your 1/5 share is worth $40 if up, $10 if down, and you owe $10. So the call has price $16.

A put with strike of $90 is worth $0 if up, $40 if down. Hedge it by taking $18.67 from pocket, borrowing 4/15 share, and selling it for $34.67. You have $53.33. If up, this buys you exactly 4/15 share to settle your debt. If down, 4/15 share costs $13.33, leaving you with $40. So the put has price $18.67.

Put-call parity only applies when comparing calls and puts with the same strike price.