Part I Introduction to Pricing and Management of Financial Securities
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
-
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