Intermediate Financial Theory, 3rd Edition

Chapter 15

An Intuitive Overview of Continuous Time Finance

Chapter 15 extends the concept of asset pricing from discrete to continuous time.

Keywords

Closed-form pricing; random walks; Brownian motion; continuous time processes; Wiener process; sawtooth pattern; stochastic differential equation; Ito’s lemma; nowhere-differentiable; inblunded variation

Chapter Outline

15.1 Introduction 443

15.2 Random Walks and Brownian Motion 444

15.3 More General Continuous Time Processes 448

15.4 A Continuous Time Model of Stock Price Behavior 449

15.5 Simulation and Call Pricing 451

15.5.1 Ito processes 451

15.5.2 Binomial Model 453

15.6 Solving Stochastic Differential Equations: A First Approach 454

15.6.1 The Behavior of Stochastic Differentials 454

15.6.2 Ito’s ...