Tropics in finance: a conditional expectation approach to value Asian, basket and spread options
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
2001
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 239 S. graph. Darst. |
Internformat
MARC
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| 100 | 1 | |a Beißer, Jochen |d 1970- |e Verfasser |0 (DE-588)123183731 |4 aut | |
| 245 | 1 | 0 | |a Tropics in finance |b a conditional expectation approach to value Asian, basket and spread options |c vorgelegt von Jochen Beißer |
| 264 | 1 | |c 2001 | |
| 300 | |a XVI, 239 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 502 | |a Mainz, Univ., Diss., 2001 | ||
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Datensatz im Suchindex
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| adam_text | vi CONTENTS
Contents
Preface . iv
List of Figures viii
List of Tables xi
Glossary of Notations xiv
1 Setting the stage 1
1.1 Introduction 1
1.2 Standard Model 8
2 Closed form solutions for Two Asset Options 17
2.1 Introduction 17
2.2 Exchange Options 18
2.3 Best and Worst of Two Assets Options 24
2.4 Maximum and Minimum of Two Assets Options 27
2.5 Best and Worst of Two Assets and Cash Options 38
2.6 Best Worst Exchange Options 42
2.7 Product and Quotient Options 44
3 Asian Options 47
3.1 Introduction 47
3.2 Uses of Asian Options 52
3.3 Closed form solutions for Asian Options based on geometric average 55
3.4 Monte Carlo simulation 59
3.5 Geometric approximation approach by Vorst 63
3.6 Lognormal approximation approach by Levy 67
3.7 Edgeworth series expansion approach by TWnbull and Wakeman . 69
3.8 Reciprocal Gamma approximation approach by Milevsky and Posner 78
3.9 Conditional expectation approach by Rogers and Shi 83
3.10 Conditional expectation approach by Curran 96
3.11 Comparison of valuation results 109
4 Basket Options 119
4.1 Introduction 119
4.2 Uses of Basket Options 121
4.3 Closed form solutions for Basket Options based on geometric averagel26
4.4 Geometric approximation approach by Gentle 127
4.5 Lognormal approximation approach by Levy 128
4.6 Edgeworth series expansion approach by Huynh 129
4.7 Reciprocal Gamma approximation approach by Milevsky and Posner 131
4.8 Conditional expectation approach 132
4.9 Conditional expectation approach by Curran 142
CONTENTS vii
4.10 Comparison of valuation results 144
4.11 Comparison of approximation densities 157
4.12 Saving effect of Basket Option 164
4.13 Hedging the Basket Option 168
4.14 Asian Basket Options 173
5 Spread Options 179
5.1 Introduction 179
5.2 Uses of Spread Options 182
5.3 Normal approximation approach by Wilcox 184
5.4 Bdgeworth series expansion approach by Shimko 186
5.5 Conditional expectation approach by Pearson and Ravindran . . . 190
5.6 Conditional expectation approach 193
5.7 Comparison of valuation results 195
5.8 Conditional expectation approach for Exchange Option 210
5.9 Hedging the Spread Option 213
5.10 Best Worse Spread Options 221
6 Concluding remarks 226
References 229
viii List of Figures
List of Figures
Figure 1 Building block approach for Two Asset Options 18
Figure 2 Payoff Regions of an Exchange Option 19
Figure 3 Exchange Option value as a function of the prices of the two
underlying assets 23
Figure 4 Exchange Option value as a function of the volatility of the
second underlying asset and the correlation coefficient 24
Figure 5 Payoff Regions of a Best and a Worst of Two Assets Option 25
Figure 6 Payoff Regions of Maximum and Minimum of Two Assets
Options 28
Figure 7 Maximum of Two Assets Call Option value as a function of
the prices of the two underlying assets 38
Figure 8 Payoff Regions of a Best and a Worst of Two Assets and
Cash Option 39
Figure 9 Worst of Two Assets and Cash Option value as a function of
the prices of the two underlying assets 41
Figure 10 Worst of Two Assets and Cash Option value as a function of
the volatility of the second underlying asset and the correla¬
tion coefficient 42
Figure 11 Payoff Regions of a Best Worst Exchange Option 43
Figure 12 Payoff Regions of a Product Call Option and a Quotient Call
Option 43
Figure 13 Exchange rate and average exchange rate over a period of one
year 53
Figure 15 Asian Option value for 10000 units of foreign currency as a
function of the volatility and the time to maturity Ill
Figure 16 Payoff Regions of a Basket Call Option 120
Figure 17 Signs of the new volatilities 141
Figure 18 Basket Option value as a function of the volatility of the
second underlying asset and the correlation coefficient 146
Figure 19 Basket Option value as a function of the prices of the two
underlying assets 147
Figure 20 Monte Carlo simulated density and approximating explicit
densities for Basket Option with maturity one year 158
Figure 21 Monte Carlo simulated density and approximating explicit
densities for Basket Option with maturity one year (zoom). 159
Figure 22 Monte Carlo simulated density and approximating implicit
densities for Basket Option with maturity one year (zoom). 160
List of Figures ix
Figure 23 Monte Carlo simulated density and approximating explicit
densities for Basket Option with maturity five years 161
Figure 24 Monte Carlo simulated density and approximating explicit
densities for Basket Option with maturity five years (zoom) 162
Figure 25 Monte Carlo simulated density and Huynh s approximation
density for Basket Option with maturity five years (zoom) . 162
Figure 26 Monte Carlo simulated density and approximating implicit
densities for Basket Option with maturity five years (zoom) 163
Figure 27 Absolute hedging error of a weekly hedged Basket Option.. 172
Figure 28 500 values of the duplicating portfolio at maturity for a wee¬
kly hedged Basket Option 173
Figure 29 Payoff Regions of a Spread Call Option 179
Figure 30 Spread Option value as a function of the volatility of the
second underlying asset and the correlation coefficient 197
Figure 31 Spread Option value as a function of the prices of the two
underlying assets 197
Figure 32 Monte Carlo simulated density and Shimko s approximating
densities for j2 = 0.2 and T t = 5 204
Figure 33 Monte Carlo simulated density and Shimko s approximating
density for r2 = 0.4 and T t = 5 205
Figure 34 Monte Carlo simulated density and Shimko s approximating
density for o2 = 0.4 and T t = 1 206
Figure 35 Monte Carlo simulated density and approximating densities
for a2 = 0.4 and T t = 1 209
Figure 36 Absolute pricing error as a function of the prices of the two
underlying assets 212
Figure 37 Relative pricing error as a function of the prices of the two
underlying assets 212
Figure 38 Spread value over time 216
Figure 39 Delta values of the Spread Option over time 216
Figure 40 Delta values of the Spread Option over time 217
Figure 41 Absolute hedging error of a daily hedged Spread Option 217
Figure 42 500 values of the duplicating portfolio at maturity for a week¬
ly hedged Spread Option 218
Figure 43 500 values of the duplicating portfolio at maturity for a week¬
ly hedged Exchange Option using the new method s deltas. 220
Figure 44 500 values of the duplicating portfolio at maturity for a week¬
ly hedged Exchange Option using the closed form deltas ... 220
x List of Figures
Figure 45 Payoff Regions of a Best Worst Spread Option 221
Figure 46 Best Worst Spread Option value as a function of the prices
of the two underlying assets 224
Figure 47 Spread Option value as a function of the price of the first
underlying asset and the correlation coefficient 225
List of Tables xi
List of Tables
Table 1 Intensity of use of Plain Vanilla Options and Exotic Options
in various markets 3
Table 2 Multi Asset Options 5
Table 3 Asset Reverse Convertibles 26
Table 4 Different types of Maximum and Minimum of Two Assets
Options 28
Table 5 Two Asset Reverse Convertibles 40
Table 6 Weekly average Asian Option values in domestic currency for
10 000 units of foreign currency 110
Table 7 Relative deviation from Monte Carlo values in % 112
Table 8 Average relative deviation from Monte Carlo values in % for
different exercise prices and ;• = 4 % 112
Table 9 Lower und upper bound for value of Asian Option due to
extended conditional expectation approach 114
Table 10 Weekly average Asian Option values in domestic currency for
10 000 units of foreign currency 116
Table 11 Relative deviation from Monte Carlo values in % 117
Table 12 Average relative deviation from Monte Carlo values in % for
different exercise prices and r = 8 % 118
Table 13 US Super 7 Basket Call Option WKN 623 729 122
Table 14 European Mobile Phone Basket Call Option WKN 594 817. 122
Table 15 Basket Option value calculated using Monte Carlo method
with 1000000 simulations 145
Table 16 Standard Error of Monte Carlo Simulation with 1000000 si¬
mulations 145
Table 17 Basket Option value calculated using closed form solution for
geometric average 148
Table 18 Relative deviation in % between closed from solution value
based on geometric average and Monte Carlo value 148
Table 19 Basket Option value calculated using Gentle s geometric ap¬
proximation approach 149
Table 20 Relative deviation in % between Gentle s value and Monte
Carlo value 150
Table 21 Basket Option value calculated using Levy s Lognormal ap¬
proximation approach 150
Table 22 Relative deviation in % between Levy s value and Monte Car¬
lo value 151
xii List of Tables
Table 23 Basket Option value calculated using Huynh s Edgeworth se¬
ries expansion approach 151
Table 24 Relative deviation in % between Huynh s value and Monte
Carlo value 152
Table 25 Basket Option value calculated using Milevsky and Posner s
reciprocal gamma approximation approach 152
Table 26 Relative deviation in % between Milevsky and Posner s value
and Monte Carlo value 153
Table 27 Basket Option value calculated using conditional expectation
approach 154
Table 28 Relative deviation in % between conditional expectation ap¬
proach s value and Monte Carlo value 154
Table 29 Basket Option value calculated using Curran s conditional
expectation approach 155
Table 30 Relative deviation in % between Curran s value and Mont°
Carlo value 155
Table 31 Average relative deviation in % between approximation va¬
lues and Monte Carlo values with respect to time to maturity
and moneyness 156
Table 32 G 7 index linked guaranteed investment certificate weigh¬
tings 164
Table 33 Correlation structure 165
Table 34 Valuation results for 100 option contracts 165
Table 35 Old and new volatilities Oi and ffj, respectively, in % 167
Table 36 New exercise prices A , with old exercise prices being
K = K,; = 1 167
Table 37 Value of basket of options and savings effect of Basket Option 168
Table 38 Stock characteristics 177
Table 39 Correlation structure 177
Table 40 Valuation results for Asian Basket Option with arithmetic
arithmetic averaging 178
Table 41 Spread Option value calculated using Pearson s conditional
expectation approach 196
Table 42 Spread Option value calculated using Wilcox s normal appro¬
ximation approach 198
Table 43 Relative deviation in % between Wilcox s value and Pearson s
value 199
Table 44 Spread Option value calculated using Shimko s Edgeworth
series expansion approach (without correction term) 200
List of Tables xiii
Table 45 Relative deviation in % between Shimko s values (without
correction term) and Pearson s value 201
Table 46 Spread Option value calculated using Shimko s Edgeworth
series expansion approach (with correction term) 202
Table 47 Relative deviation in % between Shimko s value (with correc¬
tion term) and Pearson s value 203
Table 48 Spread Option value calculated using the conditional expec¬
tation approach 207
Table 49 Relative deviation in % between the conditional expectation
approach s value and Pearson s value 208
Table 50 Average relative deviations in % between approximation va¬
lues and Pearson s values with respect to time to maturity
and moneyness 210
Table 51 Relative deviation in % between new methods value and
closed form solution value for Exchange Option 211
Table 52 Relative deviation in % between Wilcox s A! and Pearson s
Ai for Spread Option 214
Table 53 Relative deviation in % between new method s Aj and Pear¬
son s Ai for Spread Option 215
Table 54 Relative deviation in % between new method s Ai and closed
form solution Ai for Exchange Option 219
|
| any_adam_object | 1 |
| author | Beißer, Jochen 1970- |
| author_GND | (DE-588)123183731 |
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| building | Verbundindex |
| bvnumber | BV014672601 |
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| indexdate | 2024-07-09T19:04:54Z |
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| language | English |
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| physical | XVI, 239 S. graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
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| spelling | Beißer, Jochen 1970- Verfasser (DE-588)123183731 aut Tropics in finance a conditional expectation approach to value Asian, basket and spread options vorgelegt von Jochen Beißer 2001 XVI, 239 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mainz, Univ., Diss., 2001 Spread (DE-588)4265331-9 gnd rswk-swf Optionshandel (DE-588)4126185-9 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Optionshandel (DE-588)4126185-9 s Spread (DE-588)4265331-9 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009954189&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Beißer, Jochen 1970- Tropics in finance a conditional expectation approach to value Asian, basket and spread options Spread (DE-588)4265331-9 gnd Optionshandel (DE-588)4126185-9 gnd |
| subject_GND | (DE-588)4265331-9 (DE-588)4126185-9 (DE-588)4113937-9 |
| title | Tropics in finance a conditional expectation approach to value Asian, basket and spread options |
| title_auth | Tropics in finance a conditional expectation approach to value Asian, basket and spread options |
| title_exact_search | Tropics in finance a conditional expectation approach to value Asian, basket and spread options |
| title_full | Tropics in finance a conditional expectation approach to value Asian, basket and spread options vorgelegt von Jochen Beißer |
| title_fullStr | Tropics in finance a conditional expectation approach to value Asian, basket and spread options vorgelegt von Jochen Beißer |
| title_full_unstemmed | Tropics in finance a conditional expectation approach to value Asian, basket and spread options vorgelegt von Jochen Beißer |
| title_short | Tropics in finance |
| title_sort | tropics in finance a conditional expectation approach to value asian basket and spread options |
| title_sub | a conditional expectation approach to value Asian, basket and spread options |
| topic | Spread (DE-588)4265331-9 gnd Optionshandel (DE-588)4126185-9 gnd |
| topic_facet | Spread Optionshandel Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009954189&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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