Mathematical finance : theory, modeling, implementation /
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| Author / Creator: | Fries, Christian, 1970- |
|---|---|
| Imprint: | Hoboken, N.J. : Wiley-Interscience, c2007. |
| Description: | xxii, 520 p. : ill. ; 25 cm. |
| Language: | English |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/7195935 |
Table of Contents:
- 1. Introduction
- 1.1. Theory, Modeling and Implementation
- 1.2. Interest Rate Models and Interest Rate Derivatives
- 1.3. How to Read this Book
- 1.3.1 Abridged Versions.
- 1.3.2 Special Sections.
- 1.3.3 Notation.
- I. Foundations
- 2. Foundations
- 2.1. Probability Theory
- 2.2. Stochastic Processes
- 2.3. Filtration
- 2.4. Brownian Motion
- 2.5. Wiener Measure, Canonical Setup
- 2.6. Ito Calculus
- 2.6.1. Ito Integral
- 2.6.2. Ito Process
- 2.6.3. Ito Lemma and Product Rule
- 2.7. Brownian Motion with Instantaneous Correlation
- 2.8. Martingales
- 2.8.1. Martingale Representation Theorem
- 2.9. Change of Measure (Girsanov, Cameron, Martin)
- 2.10. Stochastic Integration
- 2.11. Partial Differential Equations (PDE)
- 2.11.1. Feynman-Kac Theorem
- 2.12. List of Symbols
- 3. Replication
- 3.1. Replication Strategies
- 3.1.1. Introduction
- 3.1.2. Replication in a discrete Model
- 3.2. Foundations: Equivalent Martingale Measure
- 3.2.1. Challenge and Solution Outline
- 3.2.2. Steps towards the Universal Pricing Theorem
- 3.3. Excursus: Relative Prices and Risk Neutral Measures
- 3.3.1. Why relative prices?
- 3.3.2. Risk Neutral Measure
- II. First Applications
- 4. Pricing of a European Stock Option under the Black-Scholes Model
- 5. Excursus: The Density of the Underlying of a European Call Option
- 6. Excursus: Interpolation of European Option Prices
- 6.1. No-Arbitrage Conditions for Interpolated Prices
- 6.2. Arbitrage Violations through Interpolation
- 6.2.1. Example (1): Interpolation of four Prices
- 6.2.2. Example (2): Interpolation of two Prices
- 6.3. Arbitrage-Free Interpolation of European Option Prices
- 7. Hedging in Continuous and Discrete Time and the Greeks
- 7.1. Introduction
- 7.2. Deriving the Replications Strategy from Pricing Theory
- 7.2.1. Deriving the Replication Strategy under the Assumption of a Locally Riskless Product
- 7.2.2. The Black-Scholes Differential Equation
- 7.2.3. The Derivative V(t) as a Function of its Underlyings S i (t)
- 7.2.4. Example: Replication Portfolio and PDE under a Black-Scholes Model
- 7.3. Greeks
- 7.3.1. Greeks of a European Call-Option under the Black-Scholes model
- 7.4. Hedging in Discrete Time: Delta and Delta-Gamma Hedging
- 7.4.1. Delta Hedging
- 7.4.2. Error Propagation
- 7.4.3. Delta-Gamma Hedging
- 7.4.4. Vega Hedging
- 7.5. Hedging in Discrete Time: Minimizing the Residual Error (Bouchaud-Sornette Method)
- 7.5.1. Minimizing the Residual Error at Maturity T
- 7.5.2. Minimizing the Residual Error in each Time Step
- III. Interest Rate Structures, Interest Rate Products And Analytic Pricing Formulas. Motivation and Overview
- 8. Interest Rate Structures
- 8.1. Introduction
- 8.1.1. Fixing Times and Tenor Times
- 8.2. Definitions
- 8.3. Interest Rate Curve Bootstrapping
- 8.4. Interpolation of Interest Rate Curves
- 8.5. Implementation
- 9. Simple Interest Rate Products
- 9.1. Interest Rate Products Part 1: Products without Optionality
- 9.1.1. Fix, Floating and Swap
- 9.1.2. Money-Market Account
- 9.2. Interest Rate Products Part 2: Simple Options
- 9.2.1. Cap, Floor, Swaption
- 9.2.2. Foreign Caplet, Quanto
- 10. The Black Model for a Caplet
- 11. Pricing of a Quanto Caplet (Modeling the FFX)
- 11.1. Choice of Numeraire
- 12. Exotic Derivatives
- 12.1. Prototypical Product Properties
- 12.2. Interest Rate Products Part 3: Exotic Interest Rate Derivatives
- 12.2.1. Structured Bond, Structured Swap, Zero Structure
- 12.2.2. Bermudan Option
- 12.2.3. Bermudan
