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In 1973 F. Black and M. Scholes published their pathbreaking paper [BS73] onoptionpricing. Thekeyidea—attributedtoR. Mertoninafootnoteofthe Black-Scholes paper — is the use of trading in continuous time and the notion of arbitrage. The simple and economically very convincing “principle of - arbitrage” allows one to derive, in certain mathematical models of ?nancial markets(suchastheSamuelsonmodel,[S65],nowadaysalsoreferredtoasthe “Black-Scholes” model, based on geometric Brownian motion), unique prices for options and other contingent claims. This remarkable achievement by F. Black, M. Scholes and R. Merton had a profound e?ect on ?nancial markets and it shifted the paradigm of de- ing with ?nancial risks towards the use of quite sophisticated mathematical models. It was in the late seventies that the central role of no-arbitrage ar- ments was crystallised in three seminal papers by M. Harrison, D. Kreps and S. Pliska ([HK79], [HP81], [K81]) They considered a general framework, which allows a systematic study of di?erent models of ?nancial markets. The Black-Scholes model is just one, obviously very important, example emb- ded into the framework of a general theory. A basic insight of these papers was the intimate relation between no-arbitrage arguments on one hand, and martingale theory on the other hand. This relation is the theme of the “F- damental Theorem of Asset Pricing” (this name was given by Ph. Dybvig and S. Ross [DR87]), which is not just a single theorem but rather a general principle to relate no-arbitrage with martingale theory.
Content Level »Professional/practitioner
Keywords »Arbitrage - Black-Scholes - Finance - Hedging - JEL: G12, G13 - Martingale - Numéraire - Probability space - Stochastic Processes - change of numeraire - fundamental theorem of asset pricing - local martingale - stochastic process - superreplication