Derivatives Algorithms Volume 1 Bones 1st edition by Thomas Hyer ISBN 9814289809 978-9814289801

1. Introduction

2. Principles

2.1 Our Code

2.1.1 auto

2.2 Functional Programming

2.3 Type and State

2.4 Physical Code Structure

2.4.1 Facts

2.5 Platform

2.6 Some Design Patterns

2.6.1 Factory Method

2.6.2 Decorator

2.6.3 Singleton

2.7 Optimization

2.7.1 Calibration

2.7.2 map

2.8 Threads

3. Types and Interfaces

3.1 The User Base

3.2 A Public Example

3.3 Interface Generation

3.4 Interface Types

3.4.1 Tables and Cells

3.5 Interface Code

3.5.1 Customization Directives

3.6 Other Containers

3.7 Environment

3.7.1 Exception Messaging

3.7.2 Fast-Path Optimization

3.7.3 Macro Hackery

3.7.4 Repository Access

3.8 Enumerated Types

4. Vector and Matrix Computations

4.1 Customizing Vectors

4.2 Algorithms

4.2.1 Join

4.3 Matrices and Square Matrices

4.3.1 Internal Layout

4.3.2 Pasting and Formatting

4.4 Matrix Multiplication

4.4.1 Inheritance and Substitutability

4.5 Decompositions (Square)

4.6 Decompositions (Symmetric)

4.7 Decompositions (Sparse)

4.7.1 Tridiagonal Matrices

4.7.2 Band Diagonal Matrices

4.7.3 SLAP Format

4.7.4 The Symmetric Case

4.8 Decompositions (Other)

5. Persistence and Memory

5.1 Storage

5.2 Extraction

5.2.1 Public Types

5.2.2 Example: Linear Interpolant

5.2.3 Reader Registry

5.3 Rebuilding

5.3.1 Some Syntactic Sugar

5.4 Code Generation

5.5 A Display Interface

5.5.1 Storage

5.5.2 Extraction

5.5.3 Refinements

5.6 Auditing

5.6.1 Bag

5.6.2 Filling Up

5.6.3 Audit Types

5.7 More on Repositories

5.7.1 Unique Objects

5.7.2 Naming

5.7.3 Matching

6. Testing Framework

6.1 Component Tests

6.1.1 Physical Structure

6.1.2 Reuse

6.2 Regression Tests

6.2.1 Repository Instrumentation

6.3 No Silver Bullet

7. Further Maths

7.1 Interpolation

7.2 Special Functions

7.2.1 The Normal Distribution

7.3 Root Solvers

7.4 Underdetermined Search

7.4.1 Function and Jacobian

7.4.2 Weights and Smoothing

7.4.3 Monitoring Progress

7.5 Quadrature

7.5.1 Gaussian Quadrature

7.5.2 Adaptive Quadrature

7.6 Distributions

7.6.1 Implied Vol

7.7 Baskets

7.7.1 Whole-Basket Moment Matching

7.7.2 Taylor Expansion of Projected Vols

7.7.3 Midpoint Variance

7.8 Random and Quasi-Random Numbers

7.8.1 Random Deviate Streams

7.8.2 Generator Implementation

7.8.3 Transforms

7.8.4 Low-Discrepancy Sequences

7.8.5 Spectral and Spining Methods

7.9 PDE Solvers

7.9.1 Cube

7.9.2 Coordinate Mapping

7.9.3 Coefficient Calculators

7.9.4 Forward Induction

7.10 American Monte Carlo

7.10.1 Recursive Partitioning

7.10.2 Biases

8. Schedules

8.1 Enumerated Switches

8.1.1 Groundwork for Extensibility

8.1.2 30E/360 ISDA, ACT/ACT ISMA

8.1.3 BUS/252

8.1.4 Other Enumerations

8.2 Holidays

8.2.1 Cities

8.2.2 Holiday Sets

8.3 Currencies

8.3.1 Internals

8.4 Increments

8.5 Legs

8.5.1 Stubs

8.5.2 Build from Parameters

8.5.3 CDS

8.5.4 Inflation Instruments

9. Indices

9.1 Naming and Parsing

9.1.1 Short Names

9.1.2 Nonstandard Indices

9.2 Fixings

9.2.1 Composites

9.3 Sorting and Hashing

9.4 Implied Vol

10. Pricing Protocols

10.0.1 Which is a Model?

10.1 Past and Future

10.2 Underlyings

10.3 Payments and Streams

10.3.1 Payment Reporting

10.3.2 Commitment to Streams

10.3.3 Destinations

10.4 Index Paths

10.4.1 Historical Paths

10.5 Defaults and Contingent Payments

10.5.1 Immediate Payments

10.5.2 Viewing Indices

10.6 Requests and Promises

10.6.1 Help for Models

10.6.2 Destinations

10.7 Bermudans and Barriers

10.8 Payouts

10.8.1 Trade State

10.8.2 Values Store

10.9 Steps

10.9.1 Valuation and Reevaluation

10.10 Use Case Review: PDE

10.11 Use Case Review: Monte Carlo and Hedge

10.11.1 Causality

10.12 Costs and Benefits

10.13 Assembling the Class Hierarchy

10.13.1 Stepper

10.13.2 Asset Values and Tokens

10.13.3 SDE

10.13.4 Model

10.13.5 Trade

10.13.6 Historical Data Access

10.13.7 Assets

10.13.8 Solvers

11. Standardized Trades

11.1 Trade Classes

11.2 Cash

11.3 Equity and FX

11.3.1 Equity Forward Payout

11.3.2 Equity Index

11.3.3 Equity Forward Data

11.3.4 FX Option

11.3.5 Forcing Backward Induction

11.4 Legs and Swaps

11.4.1 Putting it Together

11.5 Caps

11.6 Swaps and Swaptions

11.7 Bermudans

11.7.1 Two Views

11.8 Composites

11.8.1 Rescaled Trades

11.8.2 Sums and Collections

12. Curves

12.1 Risk

12.2 Libor and Funding

12.3 Build Instruments

12.3.1 Tenor

12.4 Dividend

12.5 Hazard

13. Models

13.1 Vasicek-Hull-White

13.1.1 Parametrization

13.1.2 Model Contents

13.2 Interface to Numerical Pricing

13.3 Interface to Valuation Requests

13.3.1 Index Paths

13.3.2 Efficiency

13.3.3 Back to Libor

13.4 Cox-Ingersoll-Ross

13.5 Black-Karasinski

13.5.1 Forward Induction PDE Sweep

13.6 Single Equity with Local Vol

13.6.1 Interpolated Vol

13.6.2 Derivation from Implied Vol

13.6.3 Model and SDE

13.7 A Simple Hybrid Model

13.7.1 The Case for Components

13.7.2 State Bounds Checks

14. Semianalytic Pricers

14.1 A Moment-Matching Pricer

14.2 Multimethod Objects

14.3 Method Registry

14.4 Interaction with Re-evaluator

14.5 Interaction with Composites

14.6 Pure Pricers

14.7 Trade-Dependent Calibration

14.7.1 Stabilization

15. Risk

15.1 Slides and Bumps

15.2 Mutants

15.3 Reports

15.3.1 Barewords

15.4 Portfolios

15.5 Tasks

15.6 Slide Utilities

15.7 Conclusions

16. Additional Code

16.1 Add Multiple

16.2 ArrayFunctor

16.3 Boolean

16.4 Composite

16.5 Cube

16.6 Handle

16.7 Matrix

16.8 Maybe

16.9 PWC (Piecewise Constant)

16.10 Vector

16. Acknowledgements and Further Reading

Index