Geodesic
A Note on the Call--Put Parity and a Call--Put Duality
Teoriâ veroâtnostej i ee primeneniâ, Tome 46 (2001) no. 1, pp. 181-183

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Along with the well-known "call–put parity" relation that makes it possible to express the rational price of a put option in terms of the rational price of a call option, we introduce a "call–put duality" relation. This new concept offers a simple explanation of the relationship between the rational price of a put option and a call option, not only for options of the European type, but also for options of the American type.
Keywords: call–put parity, Black–Merton–Scholes model, call–put duality, American call–put option, European call–put option, optimal stopping problem, free-boundary problem. 
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G. Peskir; A. N. Shiryaev. A Note on the Call--Put Parity and a Call--Put Duality. Teoriâ veroâtnostej i ee primeneniâ, Tome 46 (2001) no. 1, pp. 181-183. http://geodesic.mathdoc.fr/item/TVP_2001_46_1_a14/