ABSTRACT

Introduction to Stochastic Finance with Market Examples, Second Edition presents an introduction to pricing and hedging in discrete and continuous-time financial models, emphasizing both analytical and probabilistic methods. It demonstrates both the power and limitations of mathematical models in finance, covering the basics of stochastic calculus for finance, and details the techniques required to model the time evolution of risky assets. The book discusses a wide range of classical topics including Black–Scholes pricing, American options, derivatives, term structure modeling, and change of numéraire. It also builds up to special topics, such as exotic options, stochastic volatility, and jump processes.

New to this Edition

  • New chapters on Barrier Options, Lookback Options, Asian Options, Optimal Stopping Theorem, and Stochastic Volatility
  • Contains over 235 exercises and 16 problems with complete solutions available online from the instructor resources
  • Added over 150 graphs and figures, for more than 250 in total, to optimize presentation
  • 57 R coding examples now integrated into the book for implementation of the methods

  • Substantially class-tested, so ideal for course use or self-study

With abundant exercises, problems with complete solutions, graphs and figures, and R coding examples, the book is primarily aimed at advanced undergraduate and graduate students in applied mathematics, financial engineering, and economics. It could be used as a course text or for self-study and would also be a comprehensive and accessible reference for researchers and practitioners in the field.

chapter |14 pages

Introduction

chapter Chapter 1|24 pages

Assets, Portfolios, and Arbitrage

chapter Chapter 2|26 pages

Discrete-Time Market Model

chapter Chapter 3|48 pages

Pricing and Hedging in Discrete Time

chapter Chapter 4|40 pages

Brownian Motion and Stochastic Calculus

chapter Chapter 5|20 pages

Continuous-Time Market Model

chapter Chapter 6|34 pages

Black–Scholes Pricing and Hedging

chapter Chapter 8|28 pages

Stochastic Volatility

chapter Chapter 9|22 pages

Volatility Estimation

chapter Chapter 10|24 pages

Maximum of Brownian Motion

chapter Chapter 11|26 pages

Barrier Options

chapter Chapter 12|22 pages

Lookback Options

chapter Chapter 13|30 pages

Asian Options

chapter Chapter 14|18 pages

Optimal Stopping Theorem

chapter Chapter 15|30 pages

American Options

chapter Chapter 16|30 pages

Change of Numéraire and Forward Measures

chapter Chapter 17|34 pages

Short Rates and Bond Pricing

chapter Chapter 18|30 pages

Forward Rates

chapter Chapter 19|22 pages

Pricing of Interest Rate Derivatives

chapter Chapter 20|36 pages

Stochastic Calculus for Jump Processes

chapter Chapter 21|22 pages

Pricing and Hedging in Jump Models

chapter Chapter 22|8 pages

Basic Numerical Methods