Mathematical Finance in Continuous Time

Abstract

This chapter discusses the general principles of continuous-time financial market models. In the first section we use a rather general model, which will serve also as a reference in the later chapters. A thorough discussion of the benchmark multi-dimensional Black-Scholes model is the topic of the second section. We discuss the valuation of several standard and exotic contingent claims in the continuous-time Black-Scholes model in the third section. After examining the relation between continuous-time and discrete-time models we close with a discussion of futures and currency markets.