Advanced modelling in finance using Excel and VBA:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Chichester [u.a.]
Wiley
2007
|
| Edition: | Reprint. |
| Series: | Wiley finance series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | X, 263 S. graph. Darst. 1 CD-ROM (12 cm) |
| ISBN: | 0471499226 9780471499220 |
Staff View
MARC
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| 100 | 1 | |a Jackson, Mary |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Advanced modelling in finance using Excel and VBA |c Mary Jackson and Mike Staunton |
| 250 | |a Reprint. | ||
| 264 | 1 | |a Chichester [u.a.] |b Wiley |c 2007 | |
| 300 | |a X, 263 S. |b graph. Darst. |e 1 CD-ROM (12 cm) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Wiley finance series | |
| 650 | 4 | |a Portfolio Selection - EXCEL - VisualBASIC für Applikationen | |
| 650 | 4 | |a Wertpapieranalyse - EXCEL - VisualBASIC für Applikationen | |
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| 650 | 0 | 7 | |a Finanzmathematik |0 (DE-588)4017195-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a VisualBASIC für Applikationen |0 (DE-588)4341325-0 |2 gnd |9 rswk-swf |
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| 856 | 4 | 2 | |m Digitalisierung UB Passau |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016351197&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 856 | 4 | 2 | |m Digitalisierung UB Passau |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016351197&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |3 Klappentext |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-016351197 | |
Record in the Search Index
| _version_ | 1808228700533030912 |
|---|---|
| adam_text |
This book will appeal to both graduate students and practitioners. Students will
value the Excel spreadsheets allowing them to develop their knowledge of modelling
in finance, using a step-by-step approach accompanied by explanations using
elementary mathematical statistics and probability. Practitioners will value the
VBA functions as a source of up-to-date and efficient programs that can be easily
used from Excel.
_f¿:
Standard material covered includes:
U
•
portfolio theory and efficient frontiers
•
the Capital Asset Pricing Model, beta and variance-covariance matrices
•
performance measurement
* , *
•
the Black-Scholes option pricing formula If/:
ГЬ
9
binomial trees for options on equities and bonds
® Monte Carlo simulation
•
bond yield-to-maturity, duration and convexity
Φ
term structure models from Vasicek and Cox, Ingersoll and Ross
Advanced topics covered include: af>
*
«
Value-at-Risk
•
style analysis
•
an improved binomial tree
(Leisen & Reimer)
•
quasi Monte Carlo simulation
•
volatility smiles
{
® Black, Derman
&
Toy
treesï
® normal interest rate trees
Л
The book is accompanied by a CD-ROM containing the spreadsheets, VBA functions
and macros used throughout the work.
*
f
Contents
Preface
xi
Acknowledgements
xii
1
Introduction
1
1.1
Finance insights
1
1.2
Asset price assumptions
2
1.3
Mathematical and statistical problems
2
1.4
Numerical methods
2
1.5
Excel solutions
3
1.6
Topics covered
3
1.7
Related Excel workbooks
5
1.8
Comments and suggestions
5
Part One Advanced Modelling in Excel
7
2
Advanced Excel functions and procedures
9
9
10
12
12
14
15
16
18
19
20
20
22
23
26
27
28
31
2.1
Accessing functions in Excel
2.2
Mathematical functions
2.3
Statistical functions
2.3.1
Using the frequency function
2.3.2
Using the quartile function
2.3.3
Using Excel's normal functions
2.4
Lookup functions
2.5
Other functions
2.6
Auditing tools
2.7
Data Tables
2.7.1
Setting up Data Tables with one input
2.7.2
Setting up Data Tables with two inputs
2.8
XY charts
2.9
Access to Data Analysis and Solver
2.10
Using range names
2.11
Regression
2.12
Goal Seek
2.13
Matrix algebra
and related functions
33
2.13.1
Introduction to matrices
33
2.13.2
Transposing a matrix
33
2.13.3
Adding matrices
34
2.13.4
Multiplying matrices
34
2.13.5
Matrix inversion
35
2.13.6
Solving systems of simultaneous linear equations
36
2.13.7
Summary of Excel'
s
matrix functions
37
Summary
37
3
Introduction to VBA
39
3.1
Advantages of mastering VBA
39
3.2
Object-oriented aspects of VBA
40
3.3
Starting to write VBA macros
42
3.3.1
Some simple examples of VBA subroutines
42
3.3.2
MsgBox for interaction
43
3.3.3
The writing environment
44
3.3.4
Entering code and executing macros
44
3.3.5
Recording keystrokes and editing code
45
3.4
Elements of programming
47
3.4.1
Variables and data types
48
3.4.2
VBA array variables
48
3.4.3
Control structures
50
3.4.4
Control of repeating procedures
51
3.4.5
Using Excel functions and VBA functions in code
52
3.4.6
General points on programming
53
3.5
Communicating between macros and the spreadsheet
53
3.6
Subroutine examples
56
3.6.1
Charts
56
3.6.2
Normal probability plot
59
3.6.3
Generating the efficient frontier with Solver
61
Summary
65
References
65
Appendix
ЗА
The Visual Basic Editor
65
Stepping through a macro and using other
debug tools
68
Appendix 3B Recording keystrokes in 'relative references' mode
69
4
Writing VBA user-defined functions
73
4.1
A simple sales commission function
73
4.2
Creating CommissionCSales) in the spreadsheet
74
4.3
Two functions with multiple inputs for valuing options
75
4.4
Manipulating arrays in VBA
78
4.5
Expected value and variance functions with array inputs
79
4.6
Portfolio variance function with array inputs
81
4.7
Functions with array output
84
4.8
Using Excel and VBA functions in user-defined functions
85
4.8.1
Using
VBA
functions in user-defined functions
85
4.8.2
Add-ins
86
4.9
Pros and cons of developing VBA functions
86
Summary
87
Appendix 4A Functions illustrating array handling
88
Appendix 4B Binomial tree option valuation functions
89
Exercises on writing functions
94
Solution notes for exercises on functions
95
Part Two Equities
99
5
Introduction to equities
101
6
Portfolio optimisation
103
6.1
Portfolio mean and variance
103
6.2
Risk-return representation of portfolios
105
6.3
Using Solver to find efficient points
106
6.4
Generating the efficient frontier (Huang and Litzenberger's
approach)
109
6.5
Constrained frontier portfolios 111
6.6
Combining risk-free and risky assets
113
6.7
Problem One-combining a risk-free asset with a risky asset
114
6.8
Problem Two-combining two risky assets
115
6.9
Problem Three-combining a risk-free asset with a risky portfolio
117
6.10
User-defined functions in
Modulei
119
6.11
Functions for the three generic portfolio problems in
Modulei
120
6.12
Macros in ModuleM
121
Summary
123
References
123
7
Asset pricing
125
7.1
The single-index model
125
7.2
Estimating beta coefficients
126
7.3
The capital asset pricing model
129
7.4
Variance-covariance matrices
130
7.5
Value-at-Risk
131
7.6
Horizon wealth
134
7.7
Moments of related distributions such as normal and
lognormal 136
7.8
User-defined functions in
Modulei
136
Summary
138
References
138
8
Performance measurement and attribution
139
8.1
Conventional performance measurement
140
8.2
Active-passive management
141
8.3
Introduction to style analysis
144
8.4 Simple style
analysis
145
8.5
Rolling-period
style
analysis
146
8.6
Confidence intervals for style weights
148
8.7
User-defined functions in
Modulei
151
8.8
Macros in ModuleM
151
Summary
152
References
153
Part Three Options on Equities
155
9
Introduction to options on equities
157
9.1
The genesis of the Black-Scholes formula
158
9.2
The Black-Scholes formula
158
9.3
Hedge portfolios
159
9.4
Risk-neutral valuation
161
9.5
A simple one-step binomial tree with risk-neutral valuation
162
9.6
Put-call parity
163
9.7
Dividends
163
9.8
American features
164
9.9
Numerical methods
164
9.10
Volatility and non-normal share returns
165
Summary
165
References
166
10
Binomial trees
167
10.1
Introduction to binomial trees
167
10.2
A simplified binomial tree
168
10.3
The Jarrow and Rudd binomial tree
170
10.4
The Cox, Ross and Rubinstein tree
173
10.5
Binomial approximations and Black-Scholes formula
175
10.6
Convergence of CRR binomial trees
176
10.7
The
Leisen
and
Reimer
tree
177
10.8
Comparison of CRR and LR trees
178
10.9
American options and the CRR American tree
180
10.10
User-defined functions in ModuleO and
Modulei
182
Summary
183
References
184
11
The Black-Scholes formula
185
11.1
The Black-Scholes formula
185
11.2
Black-Scholes formula in the spreadsheet
186
11.3
Options on currencies and commodities
187
11.4
Calculating the option's 'greek' parameters
189
11.5
Hedge portfolios
190
11.6
Formal derivation of the Black-Scholes formula
192
11.7
User-defined functions in
Modulei
194
Summary
195
References
196
12
Other numerical methods for European options
197
12.1
Introduction to Monte Carlo simulation
197
12.2
Simulation with antithetic variables
199
12.3
Simulation with quasi-random sampling
200
12.4
Comparing simulation methods
202
12.5
Calculating greeks in Monte Carlo simulation
203
12.6
Numerical integration
203
12.7
User-defined functions in
Modulei
205
Summary
207
References
207
13
Non-normal distributions and implied volatility
209
13.1
Black-Scholes using alternative distributional assumptions
209
13.2
Implied volatility
211
13.3
Adapting for skewness and kurtosis
212
13.4
The volatility smile
215
13.5
User-defined functions in
Modulei
217
Summary
219
References
220
221
223
224
225
226
227
228
230
230
230
15
Interest rate models
231
15.1
Vasicek'
s
term structure model
231
15.2
Valuing European options on zero-coupon bonds, Vasicek's model
234
15.3
Valuing European options on coupon bonds, Vasicek's model
235
15.4
CIR
term structure model
236
15.5
Valuing European options on zero-coupon bonds,
CIR
model
237
15.6
Valuing European options on coupon bonds,
CIR
model
238
15.7
User-defined functions in
Modulei
239
Summary
240
References
241
Part Four
Options on Bonds
14
Introduction to valuing options on
bonds
14.1
The term structure of interest
rates
14.2
Cash flows for coupon bonds
and yield to maturity
14.3
Binomial trees
14.4
Black's bond option valuation
ι
formula
14.5
Duration and convexity
14.6
Notation
Summary
References
Contents
16
Matching the term structure
243
16.1
Trees with lognormally distributed interest rates
243
16.2
Trees with normal interest rates
246
16.3
The Black, Derman and Toy tree
247
16.4
Valuing bond options using BDT trees
248
16.5
User-defined functions in
Modulei
250
Summary
252
References
252
Appendix Other VBA functions
253
Forecasting
253
ARMA
modelling
254
Splines
256
Eigenvalues and eigenvectors
257
References
258
Index
259 |
| adam_txt |
This book will appeal to both graduate students and practitioners. Students will
value the Excel spreadsheets allowing them to develop their knowledge of modelling
in finance, using a step-by-step approach accompanied by explanations using
elementary mathematical statistics and probability. Practitioners will value the
VBA functions as a source of up-to-date and efficient programs that can be easily
used from Excel.
_f¿:
Standard material covered includes:
U
•
portfolio theory and efficient frontiers
•
the Capital Asset Pricing Model, beta and variance-covariance matrices
•
performance measurement
* , *
•
the Black-Scholes option pricing formula If/:
ГЬ
9
binomial trees for options on equities and bonds
® Monte Carlo simulation
•
bond yield-to-maturity, duration and convexity
Φ
term structure models from Vasicek and Cox, Ingersoll and Ross
Advanced topics covered include: af>
*
«
Value-at-Risk
•
style analysis
•
an improved binomial tree
(Leisen & Reimer)
•
quasi Monte Carlo simulation
•
volatility smiles
{
® Black, Derman
&
Toy
treesï
® normal interest rate trees
Л
The book is accompanied by a CD-ROM containing the spreadsheets, VBA functions
and macros used throughout the work.
*
f
Contents
Preface
xi
Acknowledgements
xii
1
Introduction
1
1.1
Finance insights
1
1.2
Asset price assumptions
2
1.3
Mathematical and statistical problems
2
1.4
Numerical methods
2
1.5
Excel solutions
3
1.6
Topics covered
3
1.7
Related Excel workbooks
5
1.8
Comments and suggestions
5
Part One Advanced Modelling in Excel
7
2
Advanced Excel functions and procedures
9
9
10
12
12
14
15
16
18
19
20
20
22
23
26
27
28
31
2.1
Accessing functions in Excel
2.2
Mathematical functions
2.3
Statistical functions
2.3.1
Using the frequency function
2.3.2
Using the quartile function
2.3.3
Using Excel's normal functions
2.4
Lookup functions
2.5
Other functions
2.6
Auditing tools
2.7
Data Tables
2.7.1
Setting up Data Tables with one input
2.7.2
Setting up Data Tables with two inputs
2.8
XY charts
2.9
Access to Data Analysis and Solver
2.10
Using range names
2.11
Regression
2.12
Goal Seek
2.13
Matrix algebra
and related functions
33
2.13.1
Introduction to matrices
33
2.13.2
Transposing a matrix
33
2.13.3
Adding matrices
34
2.13.4
Multiplying matrices
34
2.13.5
Matrix inversion
35
2.13.6
Solving systems of simultaneous linear equations
36
2.13.7
Summary of Excel'
s
matrix functions
37
Summary
37
3
Introduction to VBA
39
3.1
Advantages of mastering VBA
39
3.2
Object-oriented aspects of VBA
40
3.3
Starting to write VBA macros
42
3.3.1
Some simple examples of VBA subroutines
42
3.3.2
MsgBox for interaction
43
3.3.3
The writing environment
44
3.3.4
Entering code and executing macros
44
3.3.5
Recording keystrokes and editing code
45
3.4
Elements of programming
47
3.4.1
Variables and data types
48
3.4.2
VBA array variables
48
3.4.3
Control structures
50
3.4.4
Control of repeating procedures
51
3.4.5
Using Excel functions and VBA functions in code
52
3.4.6
General points on programming
53
3.5
Communicating between macros and the spreadsheet
53
3.6
Subroutine examples
56
3.6.1
Charts
56
3.6.2
Normal probability plot
59
3.6.3
Generating the efficient frontier with Solver
61
Summary
65
References
65
Appendix
ЗА
The Visual Basic Editor
65
Stepping through a macro and using other
debug tools
68
Appendix 3B Recording keystrokes in 'relative references' mode
69
4
Writing VBA user-defined functions
73
4.1
A simple sales commission function
73
4.2
Creating CommissionCSales) in the spreadsheet
74
4.3
Two functions with multiple inputs for valuing options
75
4.4
Manipulating arrays in VBA
78
4.5
Expected value and variance functions with array inputs
79
4.6
Portfolio variance function with array inputs
81
4.7
Functions with array output
84
4.8
Using Excel and VBA functions in user-defined functions
85
4.8.1
Using
VBA
functions in user-defined functions
85
4.8.2
Add-ins
86
4.9
Pros and cons of developing VBA functions
86
Summary
87
Appendix 4A Functions illustrating array handling
88
Appendix 4B Binomial tree option valuation functions
89
Exercises on writing functions
94
Solution notes for exercises on functions
95
Part Two Equities
99
5
Introduction to equities
101
6
Portfolio optimisation
103
6.1
Portfolio mean and variance
103
6.2
Risk-return representation of portfolios
105
6.3
Using Solver to find efficient points
106
6.4
Generating the efficient frontier (Huang and Litzenberger's
approach)
109
6.5
Constrained frontier portfolios 111
6.6
Combining risk-free and risky assets
113
6.7
Problem One-combining a risk-free asset with a risky asset
114
6.8
Problem Two-combining two risky assets
115
6.9
Problem Three-combining a risk-free asset with a risky portfolio
117
6.10
User-defined functions in
Modulei
119
6.11
Functions for the three generic portfolio problems in
Modulei
120
6.12
Macros in ModuleM
121
Summary
123
References
123
7
Asset pricing
125
7.1
The single-index model
125
7.2
Estimating beta coefficients
126
7.3
The capital asset pricing model
129
7.4
Variance-covariance matrices
130
7.5
Value-at-Risk
131
7.6
Horizon wealth
134
7.7
Moments of related distributions such as normal and
lognormal 136
7.8
User-defined functions in
Modulei
136
Summary
138
References
138
8
Performance measurement and attribution
139
8.1
Conventional performance measurement
140
8.2
Active-passive management
141
8.3
Introduction to style analysis
144
8.4 Simple style
analysis
145
8.5
Rolling-period
style
analysis
146
8.6
Confidence intervals for style weights
148
8.7
User-defined functions in
Modulei
151
8.8
Macros in ModuleM
151
Summary
152
References
153
Part Three Options on Equities
155
9
Introduction to options on equities
157
9.1
The genesis of the Black-Scholes formula
158
9.2
The Black-Scholes formula
158
9.3
Hedge portfolios
159
9.4
Risk-neutral valuation
161
9.5
A simple one-step binomial tree with risk-neutral valuation
162
9.6
Put-call parity
163
9.7
Dividends
163
9.8
American features
164
9.9
Numerical methods
164
9.10
Volatility and non-normal share returns
165
Summary
165
References
166
10
Binomial trees
167
10.1
Introduction to binomial trees
167
10.2
A simplified binomial tree
168
10.3
The Jarrow and Rudd binomial tree
170
10.4
The Cox, Ross and Rubinstein tree
173
10.5
Binomial approximations and Black-Scholes formula
175
10.6
Convergence of CRR binomial trees
176
10.7
The
Leisen
and
Reimer
tree
177
10.8
Comparison of CRR and LR trees
178
10.9
American options and the CRR American tree
180
10.10
User-defined functions in ModuleO and
Modulei
182
Summary
183
References
184
11
The Black-Scholes formula
185
11.1
The Black-Scholes formula
185
11.2
Black-Scholes formula in the spreadsheet
186
11.3
Options on currencies and commodities
187
11.4
Calculating the option's 'greek' parameters
189
11.5
Hedge portfolios
190
11.6
Formal derivation of the Black-Scholes formula
192
11.7
User-defined functions in
Modulei
194
Summary
195
References
196
12
Other numerical methods for European options
197
12.1
Introduction to Monte Carlo simulation
197
12.2
Simulation with antithetic variables
199
12.3
Simulation with quasi-random sampling
200
12.4
Comparing simulation methods
202
12.5
Calculating greeks in Monte Carlo simulation
203
12.6
Numerical integration
203
12.7
User-defined functions in
Modulei
205
Summary
207
References
207
13
Non-normal distributions and implied volatility
209
13.1
Black-Scholes using alternative distributional assumptions
209
13.2
Implied volatility
211
13.3
Adapting for skewness and kurtosis
212
13.4
The volatility smile
215
13.5
User-defined functions in
Modulei
217
Summary
219
References
220
221
223
224
225
226
227
228
230
230
230
15
Interest rate models
231
15.1
Vasicek'
s
term structure model
231
15.2
Valuing European options on zero-coupon bonds, Vasicek's model
234
15.3
Valuing European options on coupon bonds, Vasicek's model
235
15.4
CIR
term structure model
236
15.5
Valuing European options on zero-coupon bonds,
CIR
model
237
15.6
Valuing European options on coupon bonds,
CIR
model
238
15.7
User-defined functions in
Modulei
239
Summary
240
References
241
Part Four
Options on Bonds
14
Introduction to valuing options on
bonds
14.1
The term structure of interest
rates
14.2
Cash flows for coupon bonds
and yield to maturity
14.3
Binomial trees
14.4
Black's bond option valuation
ι
formula
14.5
Duration and convexity
14.6
Notation
Summary
References
Contents
16
Matching the term structure
243
16.1
Trees with lognormally distributed interest rates
243
16.2
Trees with normal interest rates
246
16.3
The Black, Derman and Toy tree
247
16.4
Valuing bond options using BDT trees
248
16.5
User-defined functions in
Modulei
250
Summary
252
References
252
Appendix Other VBA functions
253
Forecasting
253
ARMA
modelling
254
Splines
256
Eigenvalues and eigenvectors
257
References
258
Index
259 |
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| author | Jackson, Mary Staunton, Mike |
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| discipline | Informatik Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Informatik Mathematik Wirtschaftswissenschaften |
| edition | Reprint. |
| format | Book |
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| illustrated | Illustrated |
| index_date | 2024-07-02T19:56:40Z |
| indexdate | 2024-08-24T01:01:09Z |
| institution | BVB |
| isbn | 0471499226 9780471499220 |
| language | English |
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| publisher | Wiley |
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| spelling | Jackson, Mary Verfasser aut Advanced modelling in finance using Excel and VBA Mary Jackson and Mike Staunton Reprint. Chichester [u.a.] Wiley 2007 X, 263 S. graph. Darst. 1 CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier Wiley finance series Portfolio Selection - EXCEL - VisualBASIC für Applikationen Wertpapieranalyse - EXCEL - VisualBASIC für Applikationen EXCEL (DE-588)4138932-3 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 gnd rswk-swf VisualBASIC für Applikationen (DE-588)4341325-0 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 s Mathematisches Modell (DE-588)4114528-8 s EXCEL (DE-588)4138932-3 s DE-604 VisualBASIC für Applikationen (DE-588)4341325-0 s Staunton, Mike Verfasser aut Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016351197&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016351197&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Jackson, Mary Staunton, Mike Advanced modelling in finance using Excel and VBA Portfolio Selection - EXCEL - VisualBASIC für Applikationen Wertpapieranalyse - EXCEL - VisualBASIC für Applikationen EXCEL (DE-588)4138932-3 gnd Mathematisches Modell (DE-588)4114528-8 gnd Finanzmathematik (DE-588)4017195-4 gnd VisualBASIC für Applikationen (DE-588)4341325-0 gnd |
| subject_GND | (DE-588)4138932-3 (DE-588)4114528-8 (DE-588)4017195-4 (DE-588)4341325-0 |
| title | Advanced modelling in finance using Excel and VBA |
| title_auth | Advanced modelling in finance using Excel and VBA |
| title_exact_search | Advanced modelling in finance using Excel and VBA |
| title_exact_search_txtP | Advanced modelling in finance using Excel and VBA |
| title_full | Advanced modelling in finance using Excel and VBA Mary Jackson and Mike Staunton |
| title_fullStr | Advanced modelling in finance using Excel and VBA Mary Jackson and Mike Staunton |
| title_full_unstemmed | Advanced modelling in finance using Excel and VBA Mary Jackson and Mike Staunton |
| title_short | Advanced modelling in finance using Excel and VBA |
| title_sort | advanced modelling in finance using excel and vba |
| topic | Portfolio Selection - EXCEL - VisualBASIC für Applikationen Wertpapieranalyse - EXCEL - VisualBASIC für Applikationen EXCEL (DE-588)4138932-3 gnd Mathematisches Modell (DE-588)4114528-8 gnd Finanzmathematik (DE-588)4017195-4 gnd VisualBASIC für Applikationen (DE-588)4341325-0 gnd |
| topic_facet | Portfolio Selection - EXCEL - VisualBASIC für Applikationen Wertpapieranalyse - EXCEL - VisualBASIC für Applikationen EXCEL Mathematisches Modell Finanzmathematik VisualBASIC für Applikationen |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016351197&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016351197&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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