In the case of dividends, the modified formula can be derived in similar manner to above, but with the modification that one portfolio consists of going long a call, going short a put, and D T bonds that each pay 1 dollar at maturity T the bonds will be worth D t at time t ; the other portfolio is the same as before - long one share of stock, short K bonds that each pay 1 dollar at T.
History[ edit ] Forms of put-call parity appeared in practice as early as medieval ages, and was formally described by a number of authors in the early 20th century.
Michael Knoll, in The Ancient Roots of Modern Financial Paritate în opțiuni The Early History of Regulatory Arbitrage, describes the important role that put-call parity played in developing the equity of redemptionthe defining characteristic of a modern mortgage, in Medieval England.
In the 19th century, financier Russell Sage used put-call parity to create synthetic loans, which had higher interest rates than the usury laws of the time would have normally allowed.
His book was re-discovered by Espen Gaarder Haug in the early s and many references from Nelson's book are given in Haug's book "Derivatives Models on Models". London: Engham Wilson but in less detail than Nelson Mathematics professor Vinzenz Bronzin paritate în opțiuni derives the put-call parity in and uses it as part of his arbitrage argument to develop a series of mathematical option models under a series of different distributions.
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The work of professor Bronzin was just recently rediscovered by professor Wolfgang Hafner and professor Heinz Zimmermann. The original work of Bronzin is a book written in German and is now translated and published in English in an edited work by Hafner and Zimmermann "Vinzenz Bronzin's option pricing models", Springer Verlag.
Implications[ edit ] Put—call parity implies: Equivalence of calls and puts: Parity implies that a call and a put can be used interchangeably in any delta-neutral portfolio.
Equivalence of calls and puts is very important when trading options.