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.
Author(s): Emanuela Rosazza Gianin, Carlo Sgarra
Series: UNITEXT, 149
Edition: 2
Publisher: Springer
Year: 2023
Language: English
Pages: 317
City: Cham
Tags: Option Pricing; Arbitrage Theory; Derivatives Hedging; Mathematical Finance; Stochastic Financial Models
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
