Arbitrage Theory In Discrete And Continuous Time

In the ever-evolving world of finance, no-arbitrage theory remains a cornerstone for understanding asset pricing, risk management, and investment strategies. This book presents the key results of modern no-arbitrage theory in both discrete and continuous time settings. The book is structured in three parts.

The first part focuses on one-period financial market models. Although highly stylized, this framework provides a clear and explicit introduction to the fundamental features of a financial market, such as the absence of arbitrage and market completeness, as well as the tools used to effectively test these properties. Additionally, we explore how the absence of arbitrage imposes constraints on the pricing of new financial assets.

The second part transitions to multi-period financial market models, offering a more realistic depiction of financial markets. It introduces the fundamentals of discrete-time stochastic processes, extends the tools developed in the first part, and demonstrates how to price contingent claims with cash flows occurring at multiple dates.

In the third part, we refine the time structure further by moving into a continuous-time setting. After a primer on continuous-time stochastic processes and stochastic integration, we extend the no-arbitrage framework and rigorously examine pricing in the celebrated Black–Scholes model and in a few of its extensions.

Numerous numerical examples throughout the book support the reader's understanding and help visualize key concepts. Each part concludes with a comprehensive set of exercises and solutions, offering opportunities for practice and self-assessment.

Anna Battauz is an Associate Professor of Mathematical Methods for Economics and Finance at Bocconi University and she is the Director of the MSc in Finance program since the 2022/23 academic year. She earned her PhD in Mathematical Finance from the Scuola Normale Superiore in Pisa. Her research lies primarily in asset pricing, with a focus on derivatives pricing, asset allocation and optimal stopping strategies. With extensive teaching experience over two decades, Anna has taught a wide range of courses across academic levels, including Calculus, Quantitative Finance, Derivatives Pricing, Numerical Methods for Finance and Asset Pricing.

Fulvio Ortu is a Full Professor of Mathematical Methods for Economics and Finance at Bocconi University, where he also served as Dean of the PhD School, Vice-Rector and Dean for International Affairs and Head of the Department of Finance. He earned his PhD in Economics at the University of Chicago. Fulvio has published numerous papers in academic journals and his research interests include asset pricing, derivatives, mathematical finance and insurance. During his career, he has been teaching several different courses on Quantitative Finance and Derivatives Pricing, Investments and Asset Pricing at Bocconi as well as at Columbia University and the University of Southern California.

Francesco Rotondi is a tenured Lecturer in Mathematical Methods for Economics and Finance at Bocconi University, where he received his PhD in Economics and Finance with a dissertation on the pricing of American options. His research encompasses a broad spectrum of quantitative methods in finance, including mathematical finance, numerical methods, traditional econometrics, and modern machine learning techniques. His areas of application range from asset pricing and derivatives valuation to energy markets and quantitative investment strategies. Since joining Bocconi as a lecturer in 2021, he has taught several MSc-level courses in Empirical Finance, Computational Finance, and Financial Econometrics.