Review
coding the numerical models in a suitable environment has not, up to this point, been particularly well covered. Until now. - Richard Norgate, Ph.D., Financial Engineering News
One of the Top Ten financial engineering titles published in 2003-2004 - Richard Norgate, Ph.D., Financial Engineering News
Book Description
Computational Finance presents a modern computational approach to mathematical finance within the Windows environment, and contains financial algorithms, mathematical proofs and computer code in C/C++. The author illustrates how numeric components can be developed which allow financial routines to be easily called by the complete range of Windows applications, such as Excel, Borland Delphi, Visual Basic and Visual C++.
These components permit software developers to call mathematical finance functions more easily than in corresponding packages. Although these packages may offer the advantage of interactive interfaces, it is not easy or computationally efficient to call them programmatically as a component of a larger system. The components are therefore well suited to software developers who want to include finance routines into a new application.
Typical readers are expected to have a knowledge of calculus, differential equations, statistics, Microsoft Excel, Visual Basic, C++ and HTML.
A CD-ROM is included which contains: working computer code, demonstration applications and also pdf versions of several research articles.
* Enables reader to incorporate advanced financial modelling techniques in Windows compatible software
* Aids the development of bespoke software solutions covering GARCH volatility modelling, derivative pricing with Partial Differential Equations, VAR, bond and stock options
* Includes CD-ROM with adaptive software
Contents of Computational Finance
PART I: Using Numerical Software Components within
Microsoft Windows
1. Introduction
2. Dynamic Link Libraries(DLLs)
2.1 Visual Basic and Excel VBA
2.2 VB.NET
2.3 C#
3. ActiveX and COM
3.1 Introduction
3.2 The COM interface IDispatch
3.3 Type libraries
3.4 Using IDispatch
3.5 ActiveX controls and the Internet
3.6 Using ActiveX components on a Web page
4. A financial derivative pricing example
4.1 Interactive user-interface
4.2 Language user-interface
4.3 Use within Delphi
5. ActiveX components and numerical optimization
5.1 Ray tracing example
5.2 Portfolio allocation example
5.3 Numerical optimization within Microsoft Excel
6. XML and transformation using XSL
6.1 Introduction
6.2 XML
6.3 XML schema
6.4 XSL
6.5 Stock market data example
7. Epilogue
7.1 Wrapping C with C++ for 00 numerics in .NET
7.2 Final remarks
PART II: Pricing Assets
8. Introduction
8.1 An introduction to options and derivatives
8.2 Brownian motion
8.3 A Brownian model of asset price movements
8.4 Ito’s lemma in one dimension
8.5 Ito’s lemma in many dimensions
9. Analytic methods and single asset European options
9.1 Introduction
9.2 Put-call parity
9.3 Vanilla options and the Black-Scholes model
9.4 Barrier options
10. Numeric methods and single asset American options
10.1 Introduction
10.2 Perpetual options
10.3 Approximations for vanilla American options
10.4 Lattice methods for vanilla options
10.5 Implied lattice methods
10.6 Grid methods for vanilla options
10.7 Pricing American options using a stochastic lattice
11. Monte Carlo simulation
11.1 Introduction
11.2 Pseudorandom and quasirandom sequences
11.3 Generation of multivariate distributions: independent variates
11.4 Generation of multivariate distributions: correlated variates
12. Multiasset European and American options
12.1 Introduction
12.2 The multiasset Black-Scholes equation
12.4 Multidimensional Monte Carlo methods
12.3 Multidimensional lattice methods
12.5 Two asset options
12.6 Three asset options
12.7 Four asset options
13. Dealing with missing data
13.1 Introduction
13.2 Iterative multiple linear regression
13.3 The EM algorithm
PART III: Financial econometrics
14. Introduction
14.1 Asset returns
14.2 Nonsynchronous trading
14.3 Bid-ask spread
14.4 Models of volatility
14.5 Stochastic autoregressive volatility, ARV
14.6 Generalized hyperbolic Levy motion
15. GARCH models
15.1 Box Jenkins models
15.3 Gaussian Linear GARCH models
15.4 The IGARCH model
15.5 The GARCH-M model
15.6 Regression-GARCH and AR-GARCH
16. Nonlinear GARCH
16.1 AGARCH-I
16.2 AGARCH-II
16.3 GJR-GARCH
17. GARCH conditional probability distributions
17.1 Gaussian distribution
17.2 Student’s t-distribution
17.3 General error distribution
18. Maximum likelihood parameter estimation
18.1 The conditional log likelihood
18.2 The covariance matrix of the parameter estimates
18.3 Numerical optimization
18.4 Scaling the data
19. Analytic derivatives of the log likelihood
19.1 The first derivatives
19.2 The second derivatives
20. GJR-GARCH Algorithms
20.1 Initial estimates and pre-observed values
20.2 Gaussian distribution
20.3 Student’s t-distribution
21. Testing GJR-GARCH software
21.1 Expected sofware capabilities
21.2 Testing GARCH software
22. GARCH process identification
22.1 Likelihood ratio test
22.2 Significance of the estimated parameters
22.3 The independence of the standardised residuals
22.4 The distribution of the standardised residuals
22.5 Modelling the S&P 500 index
22.6 Excel demonstration
22.7 Internet Explorer demonstration
23. Multivariate time series
23.1 Principal component GARCH
Appendices
A. Computer code for Part I
A.1 The ODL file for the derivative pricing control
B. Some more option pricing formulae
B.1 Binary options
B.2 Option to exchange one asset for another
B.3 Lookback options
C . Derivation of the Greeks for vanilla European options
C.1 Introduction
C.2 Gamma
C.3 Delta
C.4 Theta
C.5 Rho
C.6 Vega
D. Multiasset binomial lattices
D.1 Truncated two asset binomial lattice
D.2 Recursive two asset binomail lattice
D.3 Four asset jump probabilities
E. Derivation of the conditional mean and covariance for a multivariate normal distribution
F. Standard statistical results
F.1 The law of large numbers
F.2 The central limit theorem
F.3 The mean and variance of linear functions of random variables
F.4 Standard algorithms for the mean and variance
F.5 The Hanson and West alogorithm for the mean and variance
F.6 Jensen’s inequality
G. Derivation of barrier option integrals
G.1 The down and out call
G.2 The up and out call
H. Algorithms for an AGARCH-I process
H.1 Gaussian distribution
H.2 Student's t-distribution
I. The general error distribution
I.1 Value of for variance hi
I.2 The kurtosis
I.3 The distribution when the shape parameter, a, is very large
J. The Student's t-distribution
J.1 The kurtosis
K. Mathematical reference
K.1 Standard integrals
K.2 Gamma function
K.3 The cumulative normal distribution function
K.4 Arithmetic and geometric progressions
L. The stability of the Black-Scholes finite-di erence schemes
L.1 The general case
L.2 The log transformation and a uniform grid
Glossary of terms
Computing reading list
Mathematics and finance references
Index
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