Financial Engineering and Computation Principles, Mathematics, Algorithms
Students and professionals intending to work in any area of finance must master not only advanced concepts and mathematical models but also learn how to implement these models computationally. This comprehensive text, first published in 2002, combines the theory and mathematics behind financial engi...
Saved in:
| Main Author: | |
|---|---|
| Format: | eBook Book |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
12.11.2001
Cambridge Univ. Press |
| Edition: | 1 |
| Subjects: | |
| ISBN: | 052178171X, 9780521781718 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- 5.6.4 Spot and Forward Rates under Simple Compounding -- 5.7 Term Structure Theories -- 5.7.1 Expectations Theory -- Unbiased Expectations Theory -- Other Versions of the Expectations Theory -- 5.7.2 Liquidity Preference Theory -- 5.7.3 Market Segmentation Theory -- 5.8 Duration and Immunization Revisited -- 5.8.1 Duration Measures -- 5.8.2 Immunization -- The Case of NO Rate Changes -- The Case of Certain Rate Movements -- Additional Reading -- NOTES -- CHAPTER SIX Fundamental Statistical Concepts -- 6.1 Basics -- 6.1.1 Generalization to Higher Dimensions -- 6.1.2 The Normal Distribution -- 6.1.3 Generation of Univariate and Bivariate Normal Distributions -- 6.1.4 The Lognormal Distribution -- 6.2 Regression -- 6.3 Correlation -- 6.4 Parameter Estimation -- 6.4.1 The Least-Squares Method -- 6.4.2 The Maximum Likelihood Estimator -- 6.4.3 The Method of Moments -- Additional Reading -- NOTES -- CHAPTER SEVEN Option Basics -- 7.1 Introduction -- 7.2 Basics -- 7.3 Exchange-Traded Options -- 7.4 Basic Option Strategies -- 7.4.1 Hedge -- 7.4.2 Spread -- 7.4.3 Combination -- NOTES -- CHAPTER EIGHT Arbitrage in Option Pricing -- 8.1 The Arbitrage Argument -- 8.2 Relative Option Prices -- 8.3 Put-Call Parity and Its Consequences -- 8.4 Early Exercise of American Options -- 8.5 Convexity of Option Prices -- 8.6 The Option Portfolio Property -- Concluding Remarks and Additional Reading -- CHAPTER NINE Option Pricing Models -- 9.1 Introduction -- 9.2 The Binomial Option Pricing Model -- 9.2.1 Options on a Non-Dividend-Paying Stock: Single Period -- 9.2.2 Risk-Neutral Valuation -- 9.2.3 Options on a Non-Dividend-Paying Stock: Multiperiod -- A Numerical Example -- 9.2.4 Numerical Algorithms for European Options -- Binomial Tree Algorithms -- An Optimal Algorithm -- The Monte Carlo Method -- The Recursive Formulation and Its Algorithms
- Cover -- Half-title -- Title -- Copyright -- Dedication -- Contents -- Preface -- Intended Audience -- Presentation -- Software -- Organization -- Acknowledgments -- Useful Abbreviations -- Acronyms -- Ticker Symbols -- CHAPTER ONE Introduction -- 1.1 Modern Finance: A Brief History -- 1.2 Financial Engineering and Computation -- 1.3 Financial Markets -- 1.4 Computer Technology -- NOTES -- CHAPTER TWO Analysis of Algorithms -- 2.1 Complexity -- 2.2 Analysis of Algorithms -- 2.3 Description of Algorithms -- 2.4 Software Implementation -- NOTE -- CHAPTER THREE Basic Financial Mathematics -- 3.1 Time Value of Money -- 3.1.1 Efficient Algorithms for Present and Future Values -- 3.1.2 Conversion between Compounding Methods -- 3.1.3 Simple Compounding -- 3.2 Annuities -- 3.3 Amortization -- 3.4 Yields -- 3.4.1 Internal Rate of Return -- 3.4.2 Net Present Value -- 3.4.3 Numerical Methods for Finding Yields -- The Bisection Method -- The Newton-Raphson Method -- 3.4.4 Solving Systems of Nonlinear Equations -- 3.5 Bonds -- 3.5.1 Valuation -- 3.5.2 Price Behaviors -- 3.5.3 Day Count Conventions -- 3.5.4 Accrued Interest -- 3.5.5 Yield for a Portfolio of Bonds -- 3.5.6 Components of Return -- Additional Reading -- NOTES -- CHAPTER FOUR Bond Price Volatility -- 4.1 Price Volatility -- 4.2 Duration -- 4.2.1 Continuous Compounding -- 4.2.2 Immunization -- 4.2.3 Macaulay Duration of Floating-Rate Instruments -- 4.2.4 Hedging -- 4.3 Convexity -- Additional Reading -- NOTE -- CHAPTER FIVE Term Structure of Interest Rates -- 5.1 Introduction -- 5.2 Spot Rates -- 5.3 Extracting Spot Rates from Yield Curves -- 5.4 Static Spread -- 5.5 Spot Rate Curve and Yield Curve -- 5.6 Forward Rates -- 5.6.1 Locking in the Forward Rate -- 5.6.2 Term Structure of Credit Spreads -- 5.6.3 Spot and Forward Rates under Continuous Compounding
- CHAPTER TWELVE Forwards, Futures, Futures Options, Swaps -- 12.1 Introduction -- 12.2 Forward Contracts -- 12.2.1 Forward Exchange Rate -- Spot and Forward Exchange Rates -- 12.2.2 Forward Price -- The Underlying Asset Pays No Income -- The Underlying Asset Pays Predictable Income -- The Underlying Asset Pays a Continuous Dividend Yield -- 12.3 Futures Contracts -- 12.3.1 Daily Cash Flows -- 12.3.2 Forward and Futures Prices -- 12.3.3 Stock Index Futures -- 12.3.4 Forward and Futures Contracts on Currencies -- 12.3.5 Futures on Commodities and the Cost of Carry -- 12.4 Futures Options and Forward Options -- 12.4.1 Pricing Relations -- 12.4.2 The Black Model -- 12.4.3 Binomial Model for Forward and Futures Options -- 12.5 Swaps -- 12.5.1 Currency Swaps -- 12.5.2 Valuation of Currency Swaps -- As a Package of Cash Market Instruments -- As a Package of Forward Contracts -- Additional Reading -- NOTES -- CHAPTER THIRTEEN Stochastic Processes and Brownian Motion -- 13.1 Stochastic Processes -- 13.2 Martingales ("Fair Games") -- 13.2.1 Martingale Pricing and Risk-Neutral Valuation -- 13.2.2 Futures Price under the Binomial Model -- 13.2.3 Martingale Pricing and the Choice of Numeraire -- 13.3 Brownian Motion -- 13.3.1 Brownian Motion as the Limit of a Random Walk -- 13.3.2 Geometric Brownian Motion -- 13.3.3 Stationarity -- 13.3.4 Variations -- 13.4 Brownian Bridge -- Additional Reading -- NOTES -- CHAPTER FOURTEEN Continuous-Time Financial Mathematics -- 14.1 Stochastic Integrals -- 14.2 Ito Processes -- 14.2.1 Discrete Approximations -- 14.2.2 Trading and the Ito Integral -- 14.2.3 Ito's Lemma -- 14.3 Applications -- 14.3.1 The Ornstein-Uhlenbeck Process -- 14.3.2 The Square-Root Process -- 14.4 Financial Applications -- 14.4.1 Transactions Costs -- 14.4.2 Stochastic Interest Rate Models -- The Merton Model -- Duration under Parallel Shifts
- 17.3 Pricing Multivariate Contingent Claims
- Immunization under Parallel Shifts Revisited -- 14.4.3 Modeling Stock Prices -- Continuous-Time Limit of the Binomial Model -- Additional Reading -- NOTE -- CHAPTER FIFTEEN Continuous-Time Derivatives Pricing -- 15.1 Partial Differential Equations -- 15.2 The Black-Scholes Differential Equation -- 15.2.1 Merton's Derivation -- Continuous Adjustments -- Number of Random Sources -- Risk-Neutral Valuation -- 15.2.2 Solving the Black-Scholes Equation for European Calls -- 15.2.3 Initial and Boundary Conditions -- 15.3 Applications -- 15.3.1 Continuous Dividend Yields -- 15.3.2 Futures and Futures Options -- 15.3.3 Average-Rate and Average-Strike Options -- 15.3.4 Options on More than One Asset: Correlation Options -- 15.3.5 Exchange Options -- 15.3.6 Options on Foreign Currencies and Assets -- Foreign Equity Options -- Foreign Domestic Options -- Cross-Currency Options -- Quanto Options -- 15.3.7 Convertible Bonds with Call Provisions -- 15.4 General Derivatives Pricing -- 15.5 Stochastic Volatility -- Additional Reading -- NOTE -- CHAPTER SIXTEEN Hedging -- 16.1 Introduction -- 16.2 Hedging and Futures -- 16.2.1 Futures and Spot Prices -- 16.2.2 Hedgers, Speculators, and Arbitragers -- 16.2.3 Perfect and Imperfect Hedging -- Cross Hedge -- Hedge Ratio (Delta) -- 16.2.4 Hedging with Stock Index Futures -- 16.3 Hedging and Options -- 16.3.1 Delta Hedge -- A Numerical Example -- 16.3.2 Delta-Gamma and Vega-Related Hedges -- 16.3.3 Static Hedging -- Additional Reading -- NOTE -- CHAPTER SEVENTEEN Trees -- 17.1 Pricing Barrier Options with Combinatorial Methods -- 17.1.1 The Reflection Principle -- 17.1.2 Combinatorial Formulas for Barrier Options -- 17.1.3 Convergence of Binomial Tree Algorithms -- 17.1.4 Double-Barrier Options -- 17.2 Trinomial Tree Algorithms -- 17.2.1 Pricing Barrier Options -- 17.2.2 Remarks on Algorithm Comparison
- 9.3 The Black-Scholes Formula -- 9.3.1 Distribution of the Rate of Return -- 9.3.2 Toward the Black-Scholes Formula -- Tabulating Option Values -- 9.3.3 The Black-Scholes Model and the BOPM -- 9.4 Using the Black-Scholes Formula -- 9.4.1 Interest Rate -- 9.4.2 Estimating the Volatility from Historical Data -- 9.4.3 Implied Volatility -- 9.5 American Puts on a Non-Dividend-Paying Stock -- 9.6 Options on a Stock that Pays Dividends -- 9.6.1 European Options on a Stock that Pays a Known Dividend Yield -- 9.6.2 American Options on a Stock that Pays a Known Dividend Yield -- 9.6.3 Options on a Stock that Pays Known Dividends -- A Simplifying Assumption -- 9.6.4 Options on a Stock that Pays a Continuous Dividend Yield -- 9.7 Traversing the Tree Diagonally -- Additional Reading -- NOTES -- CHAPTER TEN Sensitivity Analysis of Options -- 10.1 Sensitivity Measures ("The Greeks") -- 10.1.1 Delta -- 10.1.2 Theta -- 10.1.3 Gamma -- 10.1.4 Vega -- 10.1.5 Rho -- 10.2 Numerical Techniques -- 10.2.1 Why Numerical Differentiation Fails -- 10.2.2 Extended Binomial Tree Algorithms -- NOTE -- CHAPTER ELEVEN Extensions of Options Theory -- 11.1 Corporate Securities -- 11.1.1 Risky Zero-Coupon Bonds and Stock -- Numerical Illustrations -- Conflicts between Stockholders and Bondholders -- Subordinated Debts -- 11.1.2 Warrants -- 11.1.3 Callable Bonds -- 11.1.4 Convertible Bonds -- Convertible Bonds with Call Provisions -- 11.2 Barrier Options -- 11.2.1 Bonds with Safety Covenants -- 11.2.2 Nonconstant Barrier -- 11.2.3 Other Types of Barrier Options -- 11.3 Interest Rate Caps and Floors -- 11.4 Stock Index Options -- 11.5 Foreign Exchange Options -- 11.5.1 The Black-Scholes Model for Forex Options -- 11.5.2 Some Pricing Relations -- 11.6 Compound Options -- 11.7 Path-Dependent Derivatives -- Additional Reading -- NOTES