Book contents
- Frontmatter
- Contents
- Preface
- Part I Point Processes
- Part II Optimal Control in Discrete Time
- Part III Optimal Control in Continuous Time
- Part IV Non-Linear Filtering Theory
- Part V Applications in Financial Economics
- 16 Basic Arbitrage Theory
- 17 Poisson-Driven Stock Prices
- 18 The Simplest Jump-Diffusion Model
- 19 A General Jump-Diffusion Model
- 20 The Merton Model
- 21 Determining a Unique Q
- 22 Good-Deal Bounds
- 23 Diversifiable Risk
- 24 Credit Risk and Cox Processes
- 25 Interest-Rate Theory
- 26 Equilibrium Theory
- References
- Index of Symbols
- Subject Index
20 - The Merton Model
from Part V - Applications in Financial Economics
Published online by Cambridge University Press: 27 May 2021
Book contents
- Frontmatter
- Contents
- Preface
- Part I Point Processes
- Part II Optimal Control in Discrete Time
- Part III Optimal Control in Continuous Time
- Part IV Non-Linear Filtering Theory
- Part V Applications in Financial Economics
- 16 Basic Arbitrage Theory
- 17 Poisson-Driven Stock Prices
- 18 The Simplest Jump-Diffusion Model
- 19 A General Jump-Diffusion Model
- 20 The Merton Model
- 21 Determining a Unique Q
- 22 Good-Deal Bounds
- 23 Diversifiable Risk
- 24 Credit Risk and Cox Processes
- 25 Interest-Rate Theory
- 26 Equilibrium Theory
- References
- Index of Symbols
- Subject Index
Summary
This chapter is devoted to the classical Merton jump–diffusion model which is analyzed using martingale methods. Given the standard Merton assumption, we derive pricing formulas for a standard call option as well as for an asset-or-nothing option.
- Type
- Chapter
- Information
- Point Processes and Jump DiffusionsAn Introduction with Finance Applications, pp. 220 - 226Publisher: Cambridge University PressPrint publication year: 2021