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.
• Written specifically at the Master's level by experienced lecturers, so readers can dive in directly • The mathematics is rigorous but also motivated, so readers see how to apply what they learn • Clear, concise and short, so readers can master the whole topic
Contents
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.
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