AN ACTUARIAL APPROACH TO OPTION PRICING UNDER THE PHYSICAL MEASURE AND WITHOUT MARKET ASSUMPTIONS

As the title may indicate, this paper uses merely probabilistic and ac tuarial considerations for pricing options. There are no economical co nsiderations involved, and our approach is valid even when an equilibr ium price measure does not exist (arbitrage, non-equilibrium) or is no t unique (incompleteness). We only make use of the physical measure th at generates the pay-out distributions. The approach does not in gener al carry over to general derivative securities, since we use an interp retation of the securities under consideration as being potential loss es or claims from the issuers point of view. Under this interpretation we calculate the price of the security as the fair premium needed to insure the potential loss. As a special case of our formula we derive the Black and Scholes formula. (C) 1998 Elsevier Science B.V. All righ ts reserved.