PRICING SECURITIES IN INCOMPLETE MARKETS BY MERTON'S FORMULA

                       Mogens Bladt

                    IIMAS, UNAM, Mexico


In this talk we present an actuarial argument for Merton's
formula with risk-neutral preferences. This formula was first
derived by Samuelson (1965) and later extended by Merton and
Samuelson (1969) for options. We derive the formula for a
general derivative security and apply it to an incomplete
market where prices of a security is fitted by a Levy process.
Comparison to competing methods for pricing in incomplete
markets via the Esscher transform or exponential tilting is
performed. The main advantage of Merton's formula is that it
operates under the original distributional measure. Hence the
pricing principle is not affected by incompleteness of the
market.