Option valuation under stochastic volatility : with Mathematica code /
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| Author / Creator: | Lewis, Alan L. |
|---|---|
| Imprint: | Newport Beach, CA : Finance Press, c2000. |
| Description: | vii, 350 p. : ill. ; 23 cm. |
| Language: | English |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/4377135 |
Table of Contents:
- Preface
- Historical Volatility of the SandP 500 Index
- 1.. Introduction and Summary of Results
- Summary of Results
- The Hedging Argument of Black and Scholes
- The Drift Cancellation and Option Sensitivities
- The Hedging Argument under Stochastic Volatility
- The Martingale Approach
- App. 1.1. Parameter Estimators for the GARCH Diffusion Model
- App. 1.2. Solutions to PDEs
- 2.. The Fundamental Transform
- Assumptions
- The Transform-based Solution
- Some Models with Closed-form Solutions
- Analytic Characteristic Functions
- A Bond Price Analogy and Option Price Bound
- App. 2.1. Recovery of the Black and Scholes Solution
- App. 2.2. Mathematica Code for Chapter 2
- App. 2.3. General Properties of Option Prices
- 3.. The Volatility of Volatility Series Expansion
- Assumptions
- General Steps in the [xi] - expansion
- The Two Series for a Parameterized Model
- App. 3.1. Details of the Volatility of Volatility Expansion
- 4.. Mixing Solutions and Applications
- The Basic Mixing Solution
- Connection between Mixing Densities and the Fundamental Transform
- A Monte Carlo Application
- Arbitrary Payoff Functions
- A More General Model without Correlation
- 5.. The Smile
- Introduction and Summary of Results
- The Symmetric Case
- The Correlated Case
- Deducing the Risk-adjusted Volatility Process from Option Prices
- App. 5.1. Calculating Volatility Moments
- App. 5.2. Working with Differential Operators in Mathematica
- App. 5.3. Additional Mathematica Code for Chapter 5
- App. 5.4. Calculating with the Mixing Theorem
- 6.. The Term Structure of Implied Volatility
- Deterministic Volatility
- Deterministic Volatility II: a Transform Perspective
- Stochastic Volatility--The Eigenvalue Connection
- Example I. The Square Root Model
- Example II. The 3/2 Model
- Example III. The Garch Diffusion Model
- A Variational Principle Method
- A Differential Equation (Dsolve) Method
- App. 6.1. Mathematica Code for Chapter 6
- 7.. Utility-based Equilibrium Models
- A Representative Agent Economy
- Examples
- The Pure Investment Problem with a Distant Planning Horizon
- Preference Adjustments to the Volatility of Volatility Series Expansion
- The Effect of Risk Attitudes on Option Prices
- 8.. Duality and Changes of Numeraire
- Put-Call Duality
- Introduction to the Change of Numeraire
- Mathematics of the Change of Numeraire
- Implications for the Term Structure
- 9.. Volatility Explosions and the Failure of the Martingale Pricing Formula
- Introduction
- The Feller Boundary Classifications
- Volatility Explosions I
- Volatility Explosions II. Failure of the Martingale Pricing Formula
- When Martingale Pricing Fails: Generalized Pricing Formulas
- Generalized Pricing Formulas and the Transform-based Solutions
- Generalized Pricing Formulas. Example I: the 3/2 Model
- Generalized Pricing Formulas. Example II: the CEV Model
- 10.. Option Prices at Large Volatility
- Introduction
- Asymptotica for the Fundamental Transform
- 11.. Solutions to Models
- The Square Root Model
- The 3/2 Model
- Geometric Brownian Motion
- References
- Index
- Frequent Notations and Abbreviations
- About the Author
