In the case of dividends, the modified formula can be paritate opțiuni 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 paritate opțiuni 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 Innovation: 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 paritate opțiuni 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 paritate opțiuni Haug's book "Derivatives Models on Models".
London: Engham Wilson but in less detail than Nelson Mathematics professor Vinzenz Bronzin also 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. 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.