A partial introduction to financial asset pricing theory.
The paper offers an overview of the semimartingale theory results about financial asset pricing in continuous time, based on the well-established arbitrage-free market approach. In the standard review part, the author concentrates on the exact conditions of the arbitrage-free asset pricing in terms of the existence and uniqueness of the equivalent martingale measure for the given semimartingale price process. The traditional application to European option pricing via a self-financing replicating investment strategy is spelled out. In the less ``textbook'' part of the paper, pricing of general lookback (path-dependent) options is put in connection with the Clark-Ocone formula for Brownian functionals. Specifically, prices of American options are characterized by means of the Snell envelope of the option payoff process. A result from specialized literature about an alternative American put option pricing formula, which connects the put price to the solution of a backward stochastic differential equation with an obstacle, is explained.
backwards stochastic differential equation
scientific article; zbMATH DE number 2102366
scientific article