Discrete Models of Financial Markets

This book explains in simple settings the fundamental ideas of financial market modelling and derivative pricing, using the no-arbitrage principle. Relatively elementary mathematics leads to powerful notions and techniques - such as viability, completeness, self-financing and replicating strategies, arbitrage and equivalent martingale measures - which are directly applicable in practice. The general methods are applied in detail to pricing and hedging European and American options within the Cox–Ross–Rubinstein (CRR) binomial tree model. A simple approach to discrete interest rate models is included, which, though elementary, has some novel features. All proofs are written in a user-friendly manner, with each step carefully explained and following a natural flow of thought. In this way the student learns how to tackle new problems.

Preface; 1. Introduction; 2. Single-step asset pricing models; 3. Multi-step binomial model; 4. Multi-step general models; 5. American options; 6. Modelling bonds and interest rates; Index.

This first volume explains in simple settings the fundamental ideas of financial market modelling and derivative pricing, using the no-arbitrage principle. All proofs are written in a user-friendly, step-by-step manner and following a natural flow of thought. In this way the student learns how to tackle new problems.

Marek Capinski has published over 50 research papers and nine books. His diverse interests include mathematical finance, corporate finance and stochastic hydrodynamics. For over 35 years he has been teaching these topics, mainly in Poland and in the UK, where he has held visiting fellowships. He is currently Professor of Applied Mathematics at AGH University of Science and Technology in Krakow.
Ekkehard Kopp is Emeritus Professor of Mathematics at the University of Hull, where he taught courses at all levels in analysis, measure and probability, stochastic processes and mathematical finance between 1970 and 2007. His editorial experience includes service as founding member of the Springer Finance series (1998–2008) and the Cambridge University Press AIMS Library series. He has authored more than 50 research publications and five books.