Mathematical Finance: Theory Review and Exercises

Description

The book is conceived as a guide to solve exercises in Mathematical Finance and a complement to theoretical lectures. The potential audience consists of students in Applied Mathematics, Engineering and Economics, attending courses in Mathematical Finance. The most important subjects covered by this textbook are Pricing and Hedging of different classes of financial derivatives (European, American Exotic options, Fixed Income derivatives) in the most popular modeling frameworks, both in discrete and continuous time setting, like the Binomial and the Black-Scholes models. A Chapter on static portfolio optimization, one on pricing for more advanced models and one on Risk Measures complete the overview on the main issues presented in classical courses on Mathematical Finance. About one hundred exercises are proposed, and a large amount of them provides a detailed solution, while a few are left as an exercise to the reader. Every chapter includes a brief resume of the main theoretical results to apply. This textbook is the result of several years of teaching experience of both the authors. Preface to the Second Edition Preface to the First Edition Contents 1 Short Review of Probability and of Stochastic Processes 1.1 Review of Theory 1.2 Solved Exercises 1.3 Proposed Exercises 2 Portfolio Optimization in Discrete-Time Models 2.1 Review of Theory 2.2 Solved Exercises 2.3 Proposed Exercises 3 Binomial Model for Option Pricing 3.1 Review of Theory 3.2 Solved Exercises 3.3 Proposed Exercises 4 Absence of Arbitrage and Completeness of Market Models 4.1 Review of Theory 4.2 Solved Exercises 4.3 Proposed Exercises 5 Itô's Formula and Stochastic Differential Equations 5.1 Review of Theory 5.2 Solved Exercises 5.3 Proposed Exercises 6 Partial Differential Equations in Finance 6.1 Review of Theory 6.2 Solved Exercises 6.3 Proposed Exercises 7 Black-Scholes Model for Option Pricing and Hedging Strategies 7.1 Review of Theory 7.2 Solved Exercises 7.3 Proposed Exercises 8 American Options 8.1 Review of Theory 8.2 Solved Exercises 8.3 Proposed Exercises 9 Exotic Options 9.1 Review of Theory 9.2 Solved Exercises 9.3 Proposed Exercises 10 Interest Rate Models 10.1 Review of Theory 10.2 Solved Exercises 10.3 Proposed Exercises 11 Pricing Models Beyond Black-Scholes 11.1 Review of Theory 11.2 Solved Exercises 11.3 Proposed Exercises 12 Risk Measures: Value at Risk and Beyond 12.1 Review of Theory 12.2 Solved Exercises 12.3 Proposed Exercises References Index