Financial Mathematics: A Comprehensive Treatment
by Roman N. Makarov, Giuseppe Campolieti
Financial Mathematics
- Preliminaries
- Preface
- Part I Introduction to Pricing and Management of Financial Securities
- Chapter 1 Mathematics of Compounding
- Chapter 2 Primer on Pricing Risky Securities
- Chapter 3 Portfolio Management
- 3.1 Expected Utility Functions
- 3.2 Portfolio Optimization for Two Assets
- 3.3 Portfolio Optimization for N Assets
- 3.4 The Capital Asset Pricing Model
- 3.5 Exercises
- Figure 3.1
- Chapter 4 Primer on Derivative Securities
- 4.1 Forward Contracts
- 4.2 Basic Options Theory
- 4.3 Basics of Option Pricing
- 4.4 Exercises
- Figure 4.1
- Part II Discrete-Time Modelling
- Chapter 5 Single-Period Arrow–Debreu Models
- 5.1 Specification of the Model
- 5.2 Analysis of the Arrow–Debreu Model
- 5.3 No-Arbitrage Asset Pricing
- 5.4 Pricing in an Incomplete Market
- 5.5 Change of Numéraire
- 5.6 Exercises
- Figure 5.1
- Chapter 6 Introduction to Discrete-Time Stochastic Calculus
- 6.1 A Multi-Period Binomial Probability Model
- 6.2 Information Flow
- 6.3 Conditional Expectation and Martingales
- 6.4 Exercises
- Figure 6.1
- Chapter 7 Replication and Pricing in the Binomial Tree Model
- 7.1 The Standard Binomial Tree Model
- 7.2 Self-Financing Strategies and Their Value Processes
- 7.3 Dynamic Replication in the Binomial Tree Model
- 7.4 Pricing and Hedging Non-Path-Dependent Derivatives
- 7.5 Pricing Formulae for Standard European Options
- 7.6 Pricing and Hedging Path-Dependent Derivatives
- 7.7 American Options
- 7.8 Exercises
- Figure 7.1
- Table 7.11
- Chapter 8 General Multi-Asset Multi-Period Model
- Chapter 5 Single-Period Arrow–Debreu Models
- Part III Continuous-Time Modelling
- Chapter 9 Essentials of General Probability Theory
- Chapter 10 One-Dimensional Brownian Motion and Related Processes
- Chapter 11 Introduction to Continuous-Time Stochastic Calculus
- 11.1 The Riemann Integral of Brownian Motion
- 11.2 The Riemann–Stieltjes Integral of Brownian Motion
- 11.3 The Itô Integral and Its Basic Properties
- 11.4 Itô Processes and Their Properties
- 11.5 Itô's Formula for Functions of BM and Itô Processes
- 11.6 Stochastic Differential Equations
- 11.7 The Markov Property, Feynman–Kac Formulae, and Transition CDFs and PDFs
- 11.8 Radon–Nikodym Derivative Process and Girsanov's Theorem
- 11.9 Brownian Martingale Representation Theorem
- 11.10 Stochastic Calculus for Multidimensional BM
- 11.11 Exercises
- Figure 11.1
- Chapter 12 Risk-Neutral Pricing in the (B, S) Economy: One Underlying Stock
- Chapter 13 Risk-Neutral Pricing in a Multi-Asset Economy
- Chapter 14 American Options
- Chapter 15 Interest-Rate Modelling and Derivative Pricing
- Chapter 16 Alternative Models of Asset Price Dynamics
- Part IV Computational Techniques
- Chapter 17 Introduction to Monte Carlo and Simulation Methods
- 17.1 Introduction
- 17.2 Generation of Uniformly Distributed Random Numbers
- 17.3 Generation of Nonuniformly Distributed Random Numbers
- 17.4 Simulation of Random Processes
- 17.5 Variance Reduction Methods
- 17.6 Exercises
- References
- Figure 17.2
- Table 17.1
- Chapter 18 Numerical Applications to Derivative Pricing
- 18.1 Overview of Deterministic Numerical Methods
- 18.2 Pricing European Options
- 18.3 Pricing Early-Exercise and Path-Dependent Options
- Figure 18.2
- Table 18.1
- Appendix: Some Useful Integral Identities and Symmetry Properties of Normal Random Variables
- Glossary of Symbols and Abbreviations
- References
- Chapter 17 Introduction to Monte Carlo and Simulation Methods
Financial Mathematics Series
Aims and scope:
The field of financial mathematics forms an ever-expanding slice of the financial sector. This series aims to capture new developments and summarize what is known over the whole spectrum of this field. It will include a broad range of textbooks, reference works and handbooks that are meant to appeal to both academics and practitioners. The inclusion of numerical code and concrete realworld examples is highly encouraged.
Series Editors
M.A.H. Dempster |
Dilip B. Madan |
Rama Cont |
Published Titles
American-Style Derivatives; Valuation and Computation, Jerome Detemple
Analysis, Geometry, and Modeling in Finance: Advanced Methods in Option Pricing, Pierre Henry-Labordère
Computational Methods in Finance, Ali Hirsa
Credit Risk: Models, Derivatives, and Management, Niklas Wagner
Engineering BGM, Alan Brace
Financial Mathematics: A Comprehensive Treatment, Giuseppe Campolieti and Roman N. Makarov
Financial Modelling with Jump Processes, Rama Cont and Peter Tankov
Interest Rate Modeling: Theory and Practice, Lixin Wu
Introduction to Credit Risk Modeling, Second Edition, Christian Bluhm, Ludger Overbeck, and Christoph Wagner
An Introduction to Exotic Option Pricing, Peter Buchen
Introduction to Risk Parity and Budgeting, Thierry Roncalli
Introduction to Stochastic Calculus Applied to Finance, Second Edition, Damien Lamberton and Bernard Lapeyre
Monte Carlo Methods and Models in Finance and Insurance, Ralf Korn, Elke Korn, and Gerald Kroisandt
Monte Carlo Simulation with Applications to Finance, Hui Wang
Nonlinear Option Pricing, Julien Guyon and Pierre Henry-Labordère
Numerical Methods for Finance, John A. D. Appleby, David C. Edelman, and John J. H. Miller
Option Valuation: A First Course in Financial Mathematics, Hugo D. Junghenn
Portfolio Optimization and Performance Analysis, Jean-Luc Prigent
Quantitative Finance: An Object-Oriented Approach in C++, Erik Schlögl
Quantitative Fund Management, M. A. H. Dempster, Georg Pflug, and Gautam Mitra
Risk Analysis in Finance and Insurance, Second Edition, Alexander Melnikov
Robust Libor Modelling and Pricing of Derivative Products, John Schoenmakers
Stochastic Finance: An Introduction with Market Examples, Nicolas Privault
Stochastic Finance: A Numeraire Approach, Jan Vecer
Stochastic Financial Models, Douglas Kennedy
Stochastic Processes with Applications to Finance, Second Edition, Masaaki Kijima
Structured Credit Portfolio Analysis, Baskets & CDOs, Christian Bluhm and Ludger Overbeck
Understanding Risk: The Theory and Practice of Financial Risk Management, David Murphy
Unravelling the Credit Crunch, David Murphy
Proposals for the series should be submitted to one of the series editors above or directly to:
CRC Press, Taylor & Francis Group
3 Park Square, Milton Park
Abingdon, Oxfordshire OX14 4RN
UK
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