ABSTRACT
This chapter discusses derivative asset pricing from the point of view of Arbitrage Pricing Theory (APT). Under idealized market conditions-i.e., neglecting transaction costs, liquidity constraints, or trading restrictions-the absence of arbitrage implies the existence of a probability measure such that the value of any derivative security is equal to the expectation of its discounted cash-flows. We discuss the Black-Scholes model from the APT point of view and revisit the important notion of dynamic hedging, which was introduced previously in the discrete framework (Chapter 3). In particular, we distinguish between dynamically complete and dynamically incomplete pricing models, and discuss an example involving stochastic volatility. At the end of the chapter we present a general connection that exists between expected values of diffusion processes and partial differential equations.
