Valuation of multidimensional American path-dependent options: a simulation approach
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| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
2002
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| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXI, 187 S. graph. Darst. |
Internformat
MARC
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| 100 | 1 | |a Scholz, Stefan |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Valuation of multidimensional American path-dependent options |b a simulation approach |c Stefan Scholz |
| 264 | 1 | |c 2002 | |
| 300 | |a XXI, 187 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 502 | |a St. Gallen, Univ., Diss., 2001 | ||
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Preface V
Table of Contents VII
List of Figures XI
List of Tables XIII
Abbreviations and Acronyms XVII
Notation XIX
1 Introduction 1
1.1 Motivation 1
1.2 Objective 3
1.3 Outline 4
2 Option Pricing 7
2.1 Financial Derivatives and Path Dependent Options 8
2.2 Stochastic Preliminaries 14
2.3 The Market Model 16
2.4 European Option Pricing 18
VIII Contents
2.4.1 Trading Strategies and Replication 19
2.4.2 Risk Neutral Valuation of European Contingent
Claims 22
2.4.3 European Option Pricing and Partial Differential Equa¬
tions 22
2.4.3.1 European Path Independent Options on a Sin¬
gle Underlying Asset 23
2.4.3.2 European Path Dependent Options on a Single
Underlying Asset 25
2.5 American Option Pricing 26
2.5.1 Risk Neutral Valuation of American Options 27
2.5.2 Exercise and Continuation Regions 29
2.5.3 American Option Pricing and Partial Differential Equa¬
tions 30
2.5.3.1 American Path Independent Options on a Sin¬
gle Underlying Asset 30
2.5.3.2 American Path Dependent Options on a Single
Underlying Asset 32
2.5.4 Classic Numerical Procedures 32
2.5.4.1 The Binomial Tree 32
2.5.4.2 The Finite Difference Method 35
2.5.5 Advanced Numerical Procedures 40
2.5.5.1 The Hull White Extension of the Binomial Tree 41
2.5.5.2 The Forward Shooting Grid Method 43
2.5.5.3 A Linear Programming Formulation of the PDE
Pricing Problem 45
Contents IX
3 Monte Carlo Method and Variance Reduction Techniques 53
3.1 Monte Carlo Method 54
3.2 Variance Reduction Techniques 55
3.2.1 Antithetic Variates 56
3.2.2 Control Variates 57
3.2.3 Moment Matching 59
3.2.4 Stratified and Latin Hypercube Sampling 62
3.2.5 Importance Sampling 65
3.2.6 Conditional Monte Carlo 66
4 Monte Carlo Methods for American Options 67
4.1 An Obvious Estimator 69
4.2 Bundling Algorithm 70
4.3 Payoff Stratification Algorithm 74
4.4 Simulated Tree Algorithm 76
4.5 Stochastic Mesh Method 82
4.6 Methods Based on Approximations of the Conditional Expectation 88
4.7 Methods Based on Approximations of the Exercise Region ... 92
4.7.1 Methods Based on Dynamic Programming 93
4.7.2 Methods Based on Simultaneous Optimization 96
4.7.2.1 Stochastic Approximation 96
4.7.2.2 The Algorithm by Garcia 100
X Contents
5 A Simulation Approach for American Path Dependent Op¬
tions 105
5.1 The Algorithm 107
5.2 Mesh and Path Generation 118
5.3 Algorithmic Description 120
5.4 Numerical Example 122
5.5 Efficiency Enhancements 134
5.5.1 Inner Controls for the Mesh Estimator 134
5.5.2 Outer Controls for the Mesh Estimator 137
5.5.3 Path Estimator Enhancements 138
5.5.4 Controls Used in the Implementation 139
5.5.5 A Note on Further Variance Reduction Techniques . . . 141
5.5.6 Solving the Least Squares Problems Associated with the
Mesh and Path Controls 142
5.6 The Implementation 145
5.7 Numerical Results 145
5.7.1 Comparison of Different Efficiency Enhancements . . . . 146
5.7.2 American Call Option 147
5.7.3 American Asian Options 149
5.7.4 American Floating Strike Lookback Put Option 160
5.7.5 American Asian Spread Call 164
5.7.6 American Swing Call 169
6 Conclusions and Outlook 175
6.1 Conclusions 175
6.2 Outlook 179
List of Figures
2.1 Illustration of classic binomial tree 34
4.1 Illustration of the bundling algorithm 70
4.2 Illustration of a simulated tree 78
4.3 Illustration of a stochastic mesh 83
4.4 Illustration of the path estimator in the context of a stochastic
mesh 86
5.1 Illustration of the number of possible values of the path variable
in a stochastic mesh 106
5.2 Illustration of the boundedness of the path variable in a stochas¬
tic mesh Ill
5.3 Numerical example of a simulated mesh 123
5.4 An example of a simulated path and its connection to the mesh
at time ^i 132
5.5 An example of a simulated path and its connection to the mesh
at time t? 134
List of Tables
5.1 Numerical example of extended mesh evaluation of transition
density 124
5.2 Numerical example of extended mesh weight function 124
5.3 Numerical example of extended mesh minimum and maximum
values of the path variable 125
5.4 Numerical example of extended mesh option price estimates at
maturity 127
5.5 Numerical example of extended mesh possible realizations of
the path variable at time t s 127
5.6 Numerical example of extended mesh continuation values at
time t2 129
5.7 Numerical example of extended mesh option values at time U. 129
5.8 Numerical example of extended mesh possible realizations of
the path variable at time t? 130
5.9 Numerical example of extended mesh continuation values at
time ty 130
5.10 Numerical example of extended mesh option values at time t . 131
5.11 Numerical example of extended mesh possible realizations of
the path variable at time t 131
5.12 Numerical example of extended mesh path evolution 132
5.13 Effect of the different efficiency enhancement techniques on the
mesh estimator 147
XIV List of Tables
5.14 Effect of the different efficiency enhancement techniques on the
path estimator 148
5.15 Numerical results for an American call option 150
5.16 Effect of the refinement of the approximation of the path variable
on the mesh estimator in the case of an American fixed strike
Asian call with parameters taken from Hull and White [47]. . . 152
5.17 Numerical results for an American fixed strike Asian call option
with parameters taken from Hull and White [47] 154
5.18 Effect of the refinement of the approximation of the path variable
on the mesh estimator in the case of an American fixed strike
Asian call with parameters taken from Barraquand and Pudet [5]. 155
5.19 Numerical results for an American fixed strike Asian call op¬
tion with a time to maturity of 0.25 years. This and all other
parameters are taken from Barraquand and Pudet [5] 156
5.20 Numerical results for an American fixed strike Asian call op¬
tion with a time to maturity of 0.5 years. This and all other
parameters are taken from Barraquand and Pudet [5] 157
5.21 Effect of the refinement of the approximation of the path variable
on the mesh estimator in the case of an American floating strike
Asian put with parameters taken from Barraquand and Pudet [5]. 158
5.22 Numerical results for an American floating strike Asian put op¬
tion with parameters taken from Barraquand and Pudet [5]. . . 159
5.23 Effect of the refinement of the approximation of the path variable
on the mesh estimator in the case of an American fixed strike
Asian call in Hull and White s [46] stochastic volatility framework. 160
5.24 Numerical results for an American fixed strike Asian call in Hull
and White s [46] stochastic volatility framework 161
5.25 Effect of the refinement of the approximation of the path vari¬
able on the mesh estimator in the case of an American floating
strike lookback put with parameters taken from Barraquand and
Pudet [5] 162
5.26 Numerical results for an American floating strike lookback put
option with parameters taken from Barraquand and Pudet [5]. 163
List of Tables XV
5.27 Effect of the refinement of the approximation of the path variable
on the mesh estimator in the case of an American lookback put
in Hull and White s [46] stochastic volatility framework 164
5.28 Numerical results for an American floating strike lookback put
in Hull and White s [46] stochastic volatility framework 165
5.29 Effect of the refinement of the approximation of the path variable
on the mesh estimator in the case of an American Asian spread
call with parameters taken from Heenk et al. [44] 167
5.30 Numerical results for an American Asian spread call with pa¬
rameters taken from Heenk et al. [44] 168
5.31 Comparison of one and two dimensional approximation of the
path variable in the case of an American Asian spread call. . . 170
5.32 Numerical results for an American Asian spread call with one
and two dimensional approximation of the path variable 171
5.33 Effect of the refinement of the approximation of the path variable
on the mesh estimator in the case of an American swing call. . 172
5.34 Numerical results for an American swing call 173
|
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| indexdate | 2024-07-09T19:00:41Z |
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| physical | XXI, 187 S. graph. Darst. |
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| spelling | Scholz, Stefan Verfasser aut Valuation of multidimensional American path-dependent options a simulation approach Stefan Scholz 2002 XXI, 187 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier St. Gallen, Univ., Diss., 2001 Monte-Carlo-Simulation (DE-588)4240945-7 gnd rswk-swf Optionspreistheorie (DE-588)4135346-8 gnd rswk-swf Bewertung (DE-588)4006340-9 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Optionspreistheorie (DE-588)4135346-8 s Bewertung (DE-588)4006340-9 s Monte-Carlo-Simulation (DE-588)4240945-7 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009784709&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Scholz, Stefan Valuation of multidimensional American path-dependent options a simulation approach Monte-Carlo-Simulation (DE-588)4240945-7 gnd Optionspreistheorie (DE-588)4135346-8 gnd Bewertung (DE-588)4006340-9 gnd |
| subject_GND | (DE-588)4240945-7 (DE-588)4135346-8 (DE-588)4006340-9 (DE-588)4113937-9 |
| title | Valuation of multidimensional American path-dependent options a simulation approach |
| title_auth | Valuation of multidimensional American path-dependent options a simulation approach |
| title_exact_search | Valuation of multidimensional American path-dependent options a simulation approach |
| title_full | Valuation of multidimensional American path-dependent options a simulation approach Stefan Scholz |
| title_fullStr | Valuation of multidimensional American path-dependent options a simulation approach Stefan Scholz |
| title_full_unstemmed | Valuation of multidimensional American path-dependent options a simulation approach Stefan Scholz |
| title_short | Valuation of multidimensional American path-dependent options |
| title_sort | valuation of multidimensional american path dependent options a simulation approach |
| title_sub | a simulation approach |
| topic | Monte-Carlo-Simulation (DE-588)4240945-7 gnd Optionspreistheorie (DE-588)4135346-8 gnd Bewertung (DE-588)4006340-9 gnd |
| topic_facet | Monte-Carlo-Simulation Optionspreistheorie Bewertung Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009784709&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT scholzstefan valuationofmultidimensionalamericanpathdependentoptionsasimulationapproach |