Book contents
- Frontmatter
- Contents
- Preface
- Useful Abbreviations
- 1 Introduction
- 2 Analysis of Algorithms
- 3 Basic Financial Mathematics
- 4 Bond Price Volatility
- 5 Term Structure of Interest Rates
- 6 Fundamental Statistical Concepts
- 7 Option Basics
- 8 Arbitrage in Option Pricing
- 9 Option Pricing Models
- 10 Sensitivity Analysis of Options
- 11 Extensions of Options Theory
- 12 Forwards, Futures, Futures Options, Swaps
- 13 Stochastic Processes and Brownian Motion
- 14 Continuous-Time Financial Mathematics
- 15 Continuous-Time Derivatives Pricing
- 16 Hedging
- 17 Trees
- 18 Numerical Methods
- 19 Matrix Computation
- 20 Time Series Analysis
- 21 Interest Rate Derivative Securities
- 22 Term Structure Fitting
- 23 Introduction to Term Structure Modeling
- 24 Foundations of Term Structure Modeling
- 25 Equilibrium Term Structure Models
- 26 No-Arbitrage Term Structure Models
- 27 Fixed-Income Securities
- 28 Introduction to Mortgage-Backed Securities
- 29 Analysis of Mortgage-Backed Securities
- 30 Collateralized Mortgage Obligations
- 31 Modern Portfolio Theory
- 32 Software
- 33 Answers to Selected Exercises
- Bibliography
- Glossary of Useful Notations
- Index
2 - Analysis of Algorithms
Published online by Cambridge University Press: 19 September 2009
- Frontmatter
- Contents
- Preface
- Useful Abbreviations
- 1 Introduction
- 2 Analysis of Algorithms
- 3 Basic Financial Mathematics
- 4 Bond Price Volatility
- 5 Term Structure of Interest Rates
- 6 Fundamental Statistical Concepts
- 7 Option Basics
- 8 Arbitrage in Option Pricing
- 9 Option Pricing Models
- 10 Sensitivity Analysis of Options
- 11 Extensions of Options Theory
- 12 Forwards, Futures, Futures Options, Swaps
- 13 Stochastic Processes and Brownian Motion
- 14 Continuous-Time Financial Mathematics
- 15 Continuous-Time Derivatives Pricing
- 16 Hedging
- 17 Trees
- 18 Numerical Methods
- 19 Matrix Computation
- 20 Time Series Analysis
- 21 Interest Rate Derivative Securities
- 22 Term Structure Fitting
- 23 Introduction to Term Structure Modeling
- 24 Foundations of Term Structure Modeling
- 25 Equilibrium Term Structure Models
- 26 No-Arbitrage Term Structure Models
- 27 Fixed-Income Securities
- 28 Introduction to Mortgage-Backed Securities
- 29 Analysis of Mortgage-Backed Securities
- 30 Collateralized Mortgage Obligations
- 31 Modern Portfolio Theory
- 32 Software
- 33 Answers to Selected Exercises
- Bibliography
- Glossary of Useful Notations
- Index
Summary
In computer science there is no history of critical experiments that decide between the validity of various theories, as there are in physical sciences.
Juris Hartmanis [421]Algorithms are precise procedures that can be turned into computer programs. A classical example is Euclid's algorithm, which specifies the exact steps toward computing the greatest common divisor. Problems such as the greatest common divisor are therefore said to be computable, whereas those that do not admit algorithms are uncomputable. A computable problem may have complexity so high that no efficient algorithms exist. In this case, it is said to be intractable. The difficulty of pricing certain financial instruments may be linked to their intrinsic complexity [169].
The hardest part of software implementation is developing the algorithm [264]. Algorithms in this book are expressed in an informal style called a pseudocode. A pseudocode conveys the algorithmic ideas without getting tied up in syntax. Pseudocode programs are specified in sufficient detail as to make their coding in a programming language straightforward. This chapter outlines the conventions used in pseudocode programs.
Complexity
Precisely predicting the performance of a program is difficult. It depends on such diverse factors as the machine it runs on, the programming language it is written in, the compiler used to generate the binary code, the workload of the computer, and so on. Although the actual running time is the only valid criterion for performance [717], we need measures of complexity that are machine independent in order to have a grip on the expected performance.
- Type
- Chapter
- Information
- Financial Engineering and ComputationPrinciples, Mathematics, Algorithms, pp. 7 - 10Publisher: Cambridge University PressPrint publication year: 2001