Options Markets : American Options, Numerical Methods and Risk Management
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Options Markets : American Options, Numerical Methods and Risk Management
Edited by George M. Constantinides and A.G. Malliaris
Table of Contents
Volume I:
Acknowledgements
Introduction George M. Constantinides and A.G. Malliaris
PART I THE CLASSICS
1. Louis Bachelier (1964), ‘Theory of Speculation’
2. Paul A. Samuelson (1965), ‘Rational Theory of Warrant Pricing’ and ‘Appendix: A Free Boundary Problem for the Heat Equation Arising from a Problem of Mathematical Economics’
3. Fischer Black and Myron Scholes (1973), ‘The Pricing of Options and Corporate Liabilities’
4. Robert C. Merton (1973), ‘Theory of Rational Option Pricing’
PART II PEDAGOGIGAL REVIEWS
5. Clifford W. Smith, Jr. (1976), ‘Option Pricing: A Review’
6. A.G. Malliaris (1983), ‘Itô’s Calculus in Financial Decision Making’
7. Robert C. Merton (1998), ‘Applications of Option-Pricing Theory: Twenty-Five Years Later’
8. Myron S. Scholes (1998), ‘Derivatives in a Dynamic Environment’
PART III THEORETICAL FOUNDATIONS AND RISK-NEUTRAL VALUATION
9. John C. Cox and Stephen A. Ross (1976), ‘The Valuation of Options for Alternative Stochastic Processes’
10. Stephen A. Ross (1976), ‘Options and Efficiency’
11. George M. Constantinides (1978), ‘Market Risk Adjustment in Project Valuation’
12. J. Michael Harrison and David M. Kreps (1979), ‘Martingales and Arbitrage in Multiperiod Securities Markets’
13. J. Michael Harrison and Stanley R. Pliska (1981), ‘Martingales and Stochastic Integrals in the Theory of Continuous Trading’
14. Freddy Delbaen and Walter Schachermayer (1994), ‘A General Version of the Fundamental Theorem of Asset Pricing’
PART IV THE BINOMIAL TREE APPROACH
15. John C. Cox, Stephen A. Ross and Mark Rubinstein (1979), ‘Option Pricing: A Simplified Approach’
16. Daniel B. Nelson and Krishna Ramaswamy (1990), ‘Simple Binomial Processes as Diffusion Approximations in Financial Models’
17. Mark Rubinstein (1994), ‘Implied Binomial Trees’
PART V STOCHASTIC VOLATILITY MODELS
18. James B. Wiggins (1987), ‘Option Values Under Stochastic Volatility: Theory and Empirical Estimates’
19. Steven L. Heston (1993), ‘A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options’
20. Marc Romano and Nizar Touzi (1997), ‘Contingent Claims and Market Completeness in a Stochastic Volatility Model’
Name Index
Volume II:
PART I OPTIONS ON FUTURES AND CURRENCIES
1. Fischer Black (1976), ‘The Pricing of Commodity Contracts’
2. Mark B. Garman and Steven W. Kohlhagen (1983), ‘Foreign Currency Option Values’
PART II INTEREST-RATE DERIVATIVES
3. Oldrich Vasicek (1977), ‘An Equilibrium Characterization of the Term Structure’
4. John C. Cox, Jonathan E. Ingersoll, Jr. and Stephen A. Ross (1985), ‘A Theory of the Term Structure of Interest Rates’
5. Darrell Duffie and Rui Kan (1996), ‘A Yield-Factor Model of Interest Rates’
6. George M. Constantinides (1992), ‘A Theory of the Nominal Term Structure of Interest Rates’
7. Farshid Jamshidian (1989), ‘An Exact Bond Option Formula’
8. Thomas S.Y. Ho and Sang-Bin Lee (1986), ‘Term Structure Movements and Pricing Interest Rate Contingent Claims’
9. Fischer Black, Emanuel Derman and William Toy (1990), ‘A One-Factor Model of Interest Rates and Its Application to Treasury Bond Options’
10. John Hull and Alan White (1990), ‘Pricing Interest-Rate-Derivative Securities’
11. David Heath, Robert Jarrow and Andrew Morton (1992), ‘Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation’
12. Kristian R. Miltersen, Klaus Sandmann and Dieter Sondermann (1997), ‘Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates’
PART III EXOTICS
13. William Margrabe (1978), ‘The Value of an Option to Exchange One Asset for Another’
14. René M. Stulz (1982), ‘Options on the Minimum or the Maximum of Two Risky Assets: Analysis and Applications’
15. Robert Geske (1979), ‘The Valuation of Compound Options’
16. M. Barry Goldman, Howard B. Sosin and Mary Ann Gatto (1979), ‘Path Dependent Options: “Buy at the Low, Sell at the High”’
17. Antoine Conze and Viswanathan (1991), ‘Path Dependent Options: The Case of Lookback Options’
18. Hélyette Geman and Marc Yor (1996), ‘Pricing and Hedging Double-Barrier Options: A Probabilistic Approach’
PART IV REAL OPTIONS
19. Michael J. Brennan and Eduardo S. Schwartz (1985), ‘Evaluating Natural Resource Investments’
20. James L. Paddock, Daniel R. Siegel and James L. Smith (1988), ‘Option Valuation of Claims on Real Assets: The Case of Offshore Petroleum Leases’
21. Jonathan E. Ingersoll, Jr. and Stephen A. Ross (1992), ‘Waiting to Invest: Investment and Uncertainty’
22. George M. Constantinides (1984), ‘Optimal Stock Trading with Personal Taxes: Implications for Prices and the Abnormal January Returns’
23. Joseph T. Williams (1993), ‘Equilibrium and Options on Real Assets’
24. Steven R. Grenadier (1996), ‘The Strategic Exercise of Options: Development Cascades and Overbuilding in Real Estate Markets’
PART V EMPIRICAL EVIDENCE
25. Mark Rubinstein (1985), ‘Nonparametric Tests of Alternative Option Pricing Models Using All Reported Trades and Quotes on the 30 Most Active CBOE Option Classes from August 23, 1976 through August 31, 1978’
26. Gurdip Bakshi, Charles Cao and Zhiwu Chen (1997), ‘Empirical Performance of Alternative Option Pricing Models’
27. Bernard Dumas, Jeff Fleming and Robert E. Whaley (1998), ‘Implied Volatility Functions: Empirical Tests’
28. Yacine Aït-Sahalia and Andrew W. Lo (1998), ‘Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices’
29. Jeremy Stein (1989), ‘Overreactions in the Options Market’
Name Index
Volume III:
PART I PRICING AMERICAN OPTIONS
1. Richard Roll (1977), ‘An Analytic Valuation Formula for Unprotected American Call Options on Stocks with Known Dividends’
2. Robert Geske and H.E. Johnson (1984), ‘The American Put Option Valued Analytically’
3. Giovanni Barone-Adesi and Robert E. Whaley (1987), ‘Efficient Analytic Approximation of American Option Values’
4. A. Bensoussan (1984), ‘On the Theory of Option Pricing’
PART II NUMERICAL METHODS
5. Michael J. Brennan and Eduardo S. Schwartz (1978), ‘Finite Difference Methods and Jump Processes Arising in the Pricing of Contingent Claims: A Synthesis’
6. Sanjiv Ranjan Das (1996), ‘Discrete-Time Bond and Option Pricing for Jump-Diffusion Processes’
7. Phelim P. Boyle (1977), ‘Options: A Monte Carlo Approach’
8. Phelim Boyle, Mark Broadie and Paul Glasserman (1997), ‘Monte Carlo Methods for Security Pricing’
9. Phelim P. Boyle (1988), ‘A Lattice Framework for Option Pricing with Two State Variables’
10. Mark Broadie and Paul Glasserman (1997), ‘Pricing American-style Securities Using Simulation’
PART III TRADING AND HEDGING WITH TRANSACTION COSTS
11. Phelim P. Boyle and David Emanuel (1980), ‘Discretely Adjusted Option Hedges’
12. Stephen Figlewski (1989), ‘Options Arbitrage in Imperfect Markets’
13. Hayne E. Leland (1985), ‘Option Pricing and Replication with Transactions Costs’
14. Bernard Bensaid, Jean-Philippe Lesne, Henri Pagès and José Scheinkman (1992), ‘Derivative Asset Pricing with Transaction Costs’
15. Mark H.A. Davis, Vassilios G. Panas and Thaleia Zariphopoulou (1993), ‘European Option Pricing with Transaction Costs’
16. George M. Constantinides and Thaleia Zariphopoulou (1999), ‘Bounds on Prices of Contingent Claims in an Intertemporal Economy with Proportional Transaction Costs and General Preferences’
17. Sanford J. Grossman (1988), ‘An Analysis of the Implications for Stock and Futures Price Volatility of Program Trading and Dynamic Hedging Strategies’
PART IV CREDIT RISK
18. Francis A. Longstaff and Eduardo S. Schwartz (1995), ‘A Simple Approach to Valuing Risky Fixed and Floating Rate Debt’
19. Robert A. Jarrow and Stuart M. Turnbull (1995), ‘Pricing Derivatives on Financial Securities Subject to Credit Risk’
20. Darrell Duffie and Kenneth J. Singleton (1997), ‘An Econometric Model of the Term Structure of Interest-Rate Swap Yields’
PART V VALUE AT RISK
21. Darrell Duffie and Jun Pan (1997), ‘An Overview of Value at Risk’
22. Philippe Artzner, Freddy Delbaen, Jean-Marc Eber and David Heath (1999), ‘Coherent Measures of Risk’
Name Index
The Debt Market : Valuation : The General Theory
Edited by Stephen A. Ross
Table of Contents
Volume I:
Acknowledgements
Introduction
Part I The Classical Expectations Hypothesis
1. F.A. Lutz (1941), ‘The Structure of Interest Rates’
2. J.M. Culbertson (1957), ‘The Term Structure of Interest Rates’
3. John H. Wood (1964), ‘The Expectations Hypothesis, the Yield Curve, and Monetary Policy’
4. Franco Modigliani and Richard Sutch (1966), ‘Innovations in Interest Rate Policy’
5. J. Huston McCulloch (1975), ‘An Estimate of the Liquidity Premium’
Part II Testing Rational Expectations Hypotheses
6. Robert J. Shiller (1990), ‘The Term Structure of Interest Rates’
7. John Y. Campbell and Robert J. Shiller (1991), ‘Yield Spreads and Interest Rate Movements: A Bird’s Eye View’
8. Robert F. Stambaugh (1988), ‘The Information in Forward Rates: Implications for Models of the Term Structure’
9. Eugene F. Fama (1975), ‘Short-Term Interest Rates as Predictors of Inflation’
10. Bradford Cornell (1978), ‘Monetary Policy, Inflation Forecasting and the Term Structure of Interest Rates’
11. Eugene F. Fama (1984), ‘Term Premiums in Bond Returns’
12. Tadashi Kikugawa and Kenneth J. Singleton (1994), ‘Modeling the Term Structure of Interest Rates in Japan’
Part III The Derivative Asset Approach to the Term Structure
13. Robert C. Merton (1973), ‘Theory of Rational Option Pricing’
14. John C. Cox and Stephen A. Ross (1976), ‘The Valuation of Options for Alternative Stochastic Processes’
15. Oldrich Vasicek (1977), ‘An Equilibrium Characterization of the Term Structure’
16. John C. Cox, Jonathan E. Ingersoll, Jr. and Stephen A. Ross (1981), ‘A Re-examination of Traditional Hypotheses about the Term Structure of Interest Rates’
17. John C. Cox, Jonathan E. Ingersoll, Jr. and Stephen A. Ross (1985), ‘A Theory of the Term Structure of Interest Rates’
18. John C. Cox, Jonathan E. Ingersoll, Jr. and Stephen A. Ross (1985), ‘An Intertemporal General Equilibrium Model of Asset Prices’
19. Michael J. Brennan and Eduardo S. Schwartz (1979), ‘A Continuous Time Approach to the Pricing of Bonds’
20. David Heath, Robert Jarrow and Andrew Morton (1992), ‘Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation’
21. Philip H. Dybvig, Jonathan E. Ingersoll, Jr. and Stephen A. Ross (1996), ‘Long Forward and Zero-Coupon Rates Can Never Fall’
Name Index
Volume II:
Part I Testing the Derivative Asset Approach
1. Stephen J. Brown and Philip H. Dybvig (1986), ‘The Empirical Implications of the Cox, Ingersoll, Ross Theory of the Term Structure of Interest Rates’
2. Robert Litterman and José Scheinkman (1991), ‘Common Factors Affecting Bond Returns’
3. Robert Litterman, José Scheinkman and Laurence Weiss (1991), ‘Volatility and the Yield Curve’
4. Michael R. Gibbons and Krishna Ramaswamy (1993), ‘A Test of the Cox, Ingersoll, and Ross Model of the Term Structure’
5. Roger H. Brown and Stephen M. Schaefer (1994), ‘The Term Structure of Real Interest Rates and the Cox, Ingersoll, and Ross Model’
Part II Implementing the Derivative Asset Approach
6. John C. Cox, Stephen A. Ross and Mark Rubinstein (1979), ‘Option Pricing: A Simplified Approach’
7. Thomas S.Y. Ho and Sang-Bin Lee (1986), ‘Term Structure Movements and Pricing Interest Rate Contingent Claims’
8. Fischer Black, Emanuel Derman and William Toy (1990), ‘A One-Factor Model of Interest Rates and Its Application to Treasury Bond Options’
9. John Hull and Alan White (1990), ‘Pricing Interest-Rate-Derivative Securities’
Part III Taxation and Clientele Effects
10. J. Huston McCulloch (1975), ‘The Tax-Adjusted Yield Curve’
11. Philip H. Dybvig and Stephen A. Ross (1986), ‘Tax Clienteles and Asset Pricing’ and ‘Discussion’
12. Walter N. Torous (1985), ‘Differential Taxation and the Equilibrium Structure of Interest Rates’
13. Stephen M. Schaefer (1982), ‘Tax-Induced Clientele Effects in the Market for British Government Securities: Placing Bounds on Security Values in an Incomplete Market’
14. Richard Roll (1984), ‘After-Tax Investment Results from Long-Term vs. Short-Term Discount Coupon Bonds’
15. George M. Constantinides and Jonathan E. Ingersoll, Jr. (1984), ‘Optimal Bond Trading with Personal Taxes’
Part IV Duration, Immunization and Hedging
16. F.M. Redington (1952), ‘Review of the Principles of Life-Office Valuations’
17. Lawrence Fisher and Roman L. Weil (1971), ‘Coping with the Risk of Interest-Rate Fluctuations: Returns to Bondholders from Naïve and Optimal Strategies’
18. G.O. Bierwag (1977), ‘Immunization, Duration, and the Term Structure of Interest Rates’
19. Jonathan E. Ingersoll, Jr., Jeffrey Skelton and Roman L. Weil (1978), ‘Duration Forty Years Later’
20. Jonathan E. Ingersoll, Jr. (1983), ‘Is Immunization Feasible? Evidence from the CRSP Data’
21. Stephen M. Schaefer (1984), ‘Immunisation and Duration: A Review of Theory, Performance and Applications’
22. John C. Cox, Jonathan E. Ingersoll, Jr. and Stephen A. Ross (1979), ‘Duration and the Measurement of Basis Risk’
Name Index
Volume III:
Part I Corporate Bonds
1. Fischer Black and Myron Scholes (1973), ‘The Pricing of Options and Corporate Liabilities’
2. Robert C. Merton (1974), ‘On the Pricing of Corporate Debt: The Risk Structure of Interest Rates’
3. Fischer Black and John C. Cox (1976), ‘Valuing Corporate Securities: Some Effects of Bond Indenture Provisions’
4. Jonathan E. Ingersoll, Jr. (1977), ‘A Contingent-Claims Valuation of Convertible Securities’
5. Michael J. Brennan and Eduardo S. Schwartz (1977), ‘Savings Bonds, Retractable Bonds and Callable Bonds’
6. Clifford W. Smith, Jr. and Jerold B. Warner (1979), ‘On Financial Contracting: An Analysis of Bond Covenants’
7. René M. Stulz and Herb Johnson (1985), ‘An Analysis of Secured Debt’
8. Edward I. Altman (1989), ‘Measuring Corporate Bond Mortality and Performance’
9. Robert Litterman and Thomas Iben (1991), ‘Corporate Bond Valuation and the Term Structure of Credit Spreads’
10. Kenneth B. Dunn and Kenneth M. Eades (1989), ‘Voluntary Conversion of Convertible Securities and the Optimal Call Strategy’
11. Douglas W. Diamond (1993), ‘Seniority and Maturity of Debt Contracts’
Part II Mortgages and Other Fixed Income Instruments
12. Scott M. Pinkus, Susan Mara Hunter and Richard Roll (1987), ‘An Introduction to the Mortgage Market and Mortgage Analysis’
13. Douglas T. Breeden (1991), ‘Risk, Return, and Hedging of Fixed-Rate Mortgages’
14. Scott F. Richard and Richard Roll (1989), ‘Prepayments on Fixed-Rate Mortgage-Backed Securities’
15. Eduardo S. Schwartz and Walter N. Torous (1989), ‘Valuing Stripped Mortgage-Backed Securities’
16. Sheridan Titman and Walter Torous (1989), ‘Valuing Commercial Mortgages: An Empirical Investigation of the Contingent-Claims Approach to Pricing Risky Debt’
17. John C. Cox, Jonathan E. Ingersoll, Jr. and Stephen A. Ross (1980), ‘An Analysis of Variable Rate Loan Contracts’
18. Krishna Ramaswamy and Suresh M. Sundaresan (1986), ‘The Valuation of Floating-Rate Instruments: Theory and Evidence’
19. Richard Roll (1996), ‘U.S. Treasury Inflation-Indexed Bonds: The Design of a New Security’
Name Index
Option Pricing, Interest Rates and Risk Management (Handbooks in Mathematical Finance)
Edited by Elyes Jouini, Jaksa Cvitanic, Marek Musiela
Table of Contents
Introduction
Part I. Option Pricing: Theory and Practice:
1. Arbitrage theory Yu. M. Kabanov
2. Market models with frictions: arbitrage and pricing issues E. Jouini and C. Napp
3. American options: symmetry properties J. Detemple
4. Purely discontinuous asset price processes D. Madan
5. Latent variable models for stochastic discount factors R. Garcia and I. Renault
6. Monte Carlo methods for security pricing P. Boyle, M. Broadie and P. Glasserman
Part II. Interest Rate Modeling:
7. A geometric view of interest rate theory T. Bjork
8. Towards a central interest rate model A. Brace, T. Dun and G. Barton
9. Infinite dimensional diffusions, Kolmogorov equations and interest rate models B. Goldys and M. Musiela
10. Libor market model with semimartingales F. Jamshidian
11. Modeling of forward Libor and swap rates M. Rutkowski
Part III. Risk Management and Hedging:
12. Credit risk modeling, intensity based approach T. Bielecki and M. Rutkowski
13. Towards a theory of volatility trading P. Carr and D. Madan
14. Shortfall risk in long-term hedging with short-term futures contracts P. Glasserman
15. Numerical comparison and local risk-minimisation and mean-variance hedging D. Heath, E. Platen and M. Schweizer
16. A guided tour through quadratic hedging approaches M. Schweizer
Part IV. Utility Maximization:
17. Theory of portfolio optimization in markets with frictions J. Cvitanic
18. Bayesian adaptive portfolio optimization I. Karatzas and X. Zhao.
Table of Contents
New Directions in Mathematical Finance
Table of Contents
BASIC THEORY OF DERIVATIVES.
Table of Contents
Financial Derivatives: A Brief Introduction.
Book Description
This book provides an advanced treatment of option pricing for traders,
About the Author
Alan Lewis has been active in option valuation and financial research
Table of Contents
Preface
1. Introduction and Summary of Results
2. The Fundamental Transform
3. The Volatility of Volatility Series Expansion
4. Mixing Solutions and Applications
5. The Smile
6. The Term Structure of Implied Volatility
7. Utility-based Equilibrium Models
8. Duality and Changes of Numeraire
9. Volatility Explosions and the
10. Option Prices at Large Volatility
11. Solutions to Models
References
Table of Contents
Foreword
PART ONE : FOUNDATIONS
Volatility: Fundamental Concepts and
PART TWO : DEALING WITH SMILES
Pricing Options in the Presence of Smiles
PART THREE : INTEREST RATES
The Role of Mean Reversion in Interest-Rate Models
The Interactive Guide to Fixed Income
The Interactive Guide to Derivatives Application
The Interactive Guide to Swaps
The Interactive Guide to Technical Analysis
The Interactive Guide to Options
The Interactive Guide to Equites
The Interactive Guide to Foreign Exchange
The Professional Handbook of Financial Risk Management
Forecasting Volatility in the Financial Markets
Managing Operational Risk in Financial Markets
Fixed Income and Interest Rate Derivative Analysis
CFROI Valuation (Cash Flow Return on Investment) : A Total System Approach to Valuing the Firm
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First Edition was published 1987 in Wiley
Series in Probability and Mathematical Statistics
Table of Contents
BROWNIAN MOTION
Basics About Brownian Motion
SOME CLASSICAL THEORY
Basic Measure Theory
MARKOV PROCESSES
Transition Functions and Resolvents
Derivatives in Financial Markets with Stochastic Volatility
Theory of Financial Risks : From Statistical Physics to Risk Management
Value at Risk : The New Benchmark for Managing Financial Risk
Measuring Market Risk with Value-at-Risk
Risk : The New Management Imperative in Finance
Puzzles of Finance: Six Practical Problems and Their Remarkable Solutions
The International Handbook of Convertible Securities : A Global Guide to Convertible Market
Handbook of Hybrid Instruments : Convertible Bonds, Preferred Shares, Lyons, Elks, Decs and Other Mandatory Convertible Notes (with CD-ROM)
Interest Rate Modelling : A Source Book Chicago
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Part 1: Background.
Chapter 1: Overview of the Types and Features of Fixed Income Securities.
Chapter 2: Risks Associated with Investing in Fixed Income Securities.
Chapter 3: A Review of the Time Value of Money.
Chapter 4: Bond Pricing and Return Measures.
Chapter 5: Measuring Interest Rate Risk.
Chapter 6: The Sturcture of Interest Rates.
Chapter 7: Bond Market Indexes.
Part 2: Government and Private Debt Obligations.
Chapter 8: U.S. Treasury and Agency Securities.
Chapter 9: Municipal Bonds.
Chapter 10: Private Money Market Instruments.
Chapter 11: Corporate Bonds.
Chapter 12: Medium-Term Notes.
Chapter 13: Inflation-Indexed Bonds (Tips).
Chapter 14: Floating-Rate Securities.
Chapter 15: Nonconvertible Preferred Stock.
Chapter 16: International Bond Markets and Instruments.
Chapter 17: Brady Bonds.
Chapter 18: Stable Value Investments.
Part 3: Credit Analysis.
Chapter 19: Credit Analysis for Corporate Bonds.
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Products and Markets.
Derivatives.
The Random Behavior of Assets.
Elementary Stochastic Calculus.
The Black-Scholes Model.
Partial Differential Equations.
The Black-Scholes Formulae and the 'Greeks'.
Simple Generalizations of the Black-Scholes World.
Early Exercise and American Options.
Probability Density Functions and First Exit Times.
Multi-asset Options.
The Binomial Model.
PATH DEPENDENCY.
An Introduction to Exotic and Path-dependent Options.
Barrier Options.
Strongly Path-dependent Options.
Asian Options.
Lookback Options.
Miscellaneous Exotics.
EXTENDING BLACK-SCHOLES.
Defects in the Black-Scholes Model.
Discrete Hedging.
Transaction Costs.
Volatility Smiles and Surfaces.
Stochastic Volatility.
Uncertain Parameters.
Empirical Analysis of Volatility.
Jump Diffusion.
Crash Modeling.
Speculating with Options.
The Feedback Effect of Hedging in Illiquid Markets.
Static Hedging.
INTEREST RATES AND PRODUCTS.
Fixed-income Products and Analysis: Yield, Duration and Convexity.
Swaps.
One-factor Interest Rate Modeling.
Yield Curve Fitting.
Interest Rate Derivatives.
Convertible Bonds.
Two-factor Interest Rate Modeling.
Empirical Behavior of the Spot Interest Rate.
Heath, Jarrow and Morton.
Interest-rate Modeling Without Probabilities.
RISK MEASUREMENT AND MANAGEMENT.
Portfolio Management.
Value at Risk.
Credit Risk.
Credit Derivatives.
RiskMetrics, CreditMetrics and CrashMetrics.
NUMERICAL METHODS.
Finite-difference Methods for One-factor Models.
Further Finite-difference Methods for One-factor Models.
Finite-difference Methods for Two-factor Models.
Monte Carlo Simulation and Related Methods.
Finite-difference Programs.
Epilog.
Bibliography.
Index.
by Salih N. Neftci / Hardcover - 540 pages / Published April 2000
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A Primer on Arbitrage Theorem.
Calculus in Deterministic and Stochastic Environments.
Pricing Derivatives: Models and Notation.
Tools in Probability Theory.
Martingales and Martingale Representations.
Differentiation in Stochastic Environments.
The Wiener Process and Rare Events in Financial Markets.
Integration in Stochastic Environments: The Ito Integral.
Ito's Lemma.
The Dynamics of Derivative Prices: Stochastic Differential Equations.
Pricing Derivative Products: Partial Differential Equations.
The Black-Scholes PDE: An Application.
Pricing Derivative Products: Equivalent Martingale Measures.
Equivalent Martingale Measures: Applications.
New Results and Tools for Interest Sensitive Securities.
Arbitrage Theorem in a New Setting: Normalization and Random Interest
Rates.
Modeling Term Structure and Related Concepts.
Classical and HJM Approaches to Fixed Income.
Classical PDE Analysis for Interest Rate Derivatives.
Relating Conditional Expectations to PDEs.
Stopping Times and American-Type Securities.
Bibliography.
Index.
An
Introduction to the Mathematics of Financial Derivatives, First Edition
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Option
Valuation under Stochastic Volatility : with Mathematica Code
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money managers, and researchers. Providing largely original research not
available elsewhere, it covers the latest generation of option models where
both the stock price and its volatility follow diffusion processes. These
new models help explain important features of real-world option pricing,
including the "volatility smile" pattern. The book includes Mathematica
code and 37 illustrations.
for over 20 years. He served as the Director of Research, Chief Investment
Officer, and President of the mutual fund family for a money manager specializing
in derivative securities. He has published articles in many of the leading
financial journals including: The Journal of Business, The Journal of Finance,
The Financial Analysts Journal, and Mathematical Finance. He received a
Ph.D. in physics from the University of California at Berkeley and a B.S.
from Caltech.
Historical Volatility of the S&P 500 Index
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
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
Assumptions
General Steps in the expansion
The Two Series for a Parameterized Model
App. 3.1 Details of the Volatility of Volatility
Expansion
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
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
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
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
Put-Call Duality
Introduction to the Change of Numeraire
Mathematics of the Change of Numeraire
Implications for the Term Structure
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
Introduction
Asymptotica for the Fundamental Transform
The Square Root Model
The 3/2 Model
Geometric Brownian Motion
Index
Frequent Notations and Abbreviations
About the Author
Volatility
and Correlation in the Pricing of Equity, FX and Interest-Rate Options
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Acknowledgements
Case Studies
Definitions
Introduction and Plan of the Chapter
Fundamental Concepts and Definitions
Hedging Forward Contracts Using Spot Quantities
Hedging Options: Volatilities of Spot and Forward
Processes
Definitions
A Series of Options on Futures Contracts
Hedging an Option with a Forward-Setting Strike
Switching from the Real World to the Pricing
Measure
Variance and Mean Reversion in the Real and the
Risk-Adjusted Worlds
Introduction and Plan of the Chapter
Hedging a Plain-Vanilla Option in the
Presence of Constant Volatility
Hedging a Plain-Vanilla Option in the Presence
of Time-Dependent Volatility
First View
Second View
Third View
Hedging a Plain-Vanilla Option When the Real-World
Process is Mean Reverting
Hedging a Plain-Vanilla Option With Finite Re-Hedging
Intervals
Instantaneous and Terminal Correlations
Introduction
The Stochastic Evolution of Imperfectly Correlated
Variables
The Role of Terminal Correlation in the Joint
Evolution of Stochastic Variables
Case 1: European Option, One Underlying Asset
Case 2: Path-Dependent Option, One Asset
Case 3: Path-Dependent Option, Two Assets
Generalising the Results
Introduction
Hedging With a Compensated Process: Plain-Vanilla
and Binary Options
Smile Tale 1: `Sticky' Smiles
Smile Tale 2: `Floating' Smiles
Stylised Empirical Facts About Smiles
Equities
Interest Rates
Foreign Exchange Rates
General Features of the Smile-Modelling Approaches
Fully Stochastic Volatility Models
Complete-Markets Jump--Diffusion Models
Random-Amplitude Jump--Diffusion Models
Stochastic Volatility Functionally Dependent
on the Underlying (Restricted-Stochastic-Volatility) Models
Risk Derivatives for Plain-Vanilla Options in
the Presence of Smiles
Tree Methodologies for Smiley Option Prices
Introduction
General Considerations on Stochastic-Volatility
Models
The Dupire, Rubinstein and Derman and Kani Approaches
Green's Function (Arrow--Debreu Prices) in the
DK Construction
The Derman and Kani Tree Construction
Numerical Aspects of the Implementation of the
DK Construction
Implementation Results
Efficient Extraction of the Future Local Volatility
from Plain-Vanilla Option Prices
Introduction
The Computational Framework
Computational Results
The Link Between Implied and Local Volatility
Surfaces
Symmetric (`FX') Smiles
Asymmetric (`Equity') Smile Surface
Monotonic (`Interest-Rate') Smile Surface
Gaining an Intuitive Understanding
No-Arbitrage Conditions on the Implied Volatility
Smile Surface
A Worked-Out Example: Pricing Continous Double
Barriers in the Presence of Smiles
Analysis of the Cost of Unwinding and Related
Considerations About Option Pricing in the Presence of Smiles
Appendix 6.1: Proof that Closed-Form Solutions
for Smiley Option Prices via Direct Modelling of the Density
Introduction
Estimating the Risk-Neutral Density Function
Derivation of Analytic Formulae
Results and Applications
Conclusions and Range of Possible Applications
Appendix 7.1 Obtaining the Density of the Underlying
from Quoted Option Prices
Explaining Smiles by Means of Mixed Jump---Diffusion
Processes
Introduction
The Financial Model: Smile Tale 2 Revisited
Analytic Description of Mixed Jump--Diffusion
Processes
A General Framework for Option Pricing in Complete
or Incomplete Markets
Finding the Optimal Hedge
Numerical Implementation of the Britten-Jones-Neuberger
Methodology
Computational Results
Discussion of the Results and Possible
Developments
Introduction: Why Mean Reversion Matters in the
Case of Interest-Rate Models
The BDT Mean-Reversion Paradox
The Unconditional Variance of the Short Rate
in BDT---The Discrete Case
The Unconditional Variance of the Short Rate
in BDT---The Continuous-Time Equivalent
Mean Reversion in Short-Rate Lattices: The Equi-Probable
Binomial Versus the Bushy-Tree Approach
Extension to More General Interest-Rate Models:
The `True' Role of Mean Reversion
Appendix 9.1: Evaluation of the Variance of the
Logarithm of the Instantaneous Short Rate
Optimal Calibration of the Brace--Gatarek--Musiela
Model
Introduction and Statement of the Problem
Constructing the Most General BGM (Market)
Model
A Worked-Out Example: Caplets and a Two-Period
Swaption
A Worked-Out Example: Serial Options
Reducing the Dimensionality of the BGM Model
Numerical Results
Fitting the Correlation Surface with a Three-Factor
Model
Fitting the Correlation Surface with a Four-Factor
Model
Conclusions
Specifying the Instantaneous Volatility of Forward
Rates
The Link Between Instantaneous Volatility and
the Future Term Structure of Volatilities
A Functional Form for the Instantaneous Volatility
Function
Fitting the Instantaneous Volatility Function:
Imposing Time-Homogeneity of the Term Structure of Volatilities
Fitting the Instantaneous Volatility Function:
Information from the Swaption Market
Conclusions
References
Index
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