Option hedging: dynamic and static replication of standard and barrier options, and risk management of options on more accurate sensitivities to improve edge capture ratios
Gespeichert in:
1. Verfasser: | |
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Format: | Buch |
Sprache: | English |
Veröffentlicht: |
Bern ; Stuttgart ; Wien
Haupt
2001
|
Schriftenreihe: | Bank- und finanzwirtschaftliche Forschungen
321 |
Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis |
Beschreibung: | Zugl.: Zürich, Univ., Diss., 2000 |
Beschreibung: | 306 S. Ill. : 23 cm |
ISBN: | 3258062730 |
Internformat
MARC
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100 | 1 | |a Adiliberti, Francesco |d 1970- |e Verfasser |0 (DE-588)122365216 |4 aut | |
245 | 1 | 0 | |a Option hedging |b dynamic and static replication of standard and barrier options, and risk management of options on more accurate sensitivities to improve edge capture ratios |c Francesco Adiliberti |
264 | 1 | |a Bern ; Stuttgart ; Wien |b Haupt |c 2001 | |
300 | |a 306 S. |b Ill. : 23 cm | ||
336 | |b txt |2 rdacontent | ||
337 | |b n |2 rdamedia | ||
338 | |b nc |2 rdacarrier | ||
490 | 1 | |a Bank- und finanzwirtschaftliche Forschungen |v 321 | |
500 | |a Zugl.: Zürich, Univ., Diss., 2000 | ||
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Datensatz im Suchindex
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adam_text | Table of contents (Overview)
Parti
1. Introduction 3
1.1 Outline of the dissertation 3
1.2 Objectives of the dissertation 4
1.3 Format and methodology of the dissertation 5
2. Statistical properties of foreign exchange rates and the
random walk model 7
2.1 Normal, skewed and kurtotic distributions and random walks 7
2.2 Statistical properties of foreign exchange rates 13
2.3 Tests for non linear dependence in daily foreign exchange rates 19
2.4 Brownian motion model and Ito s Lemma 24
Part II
3. Pricing standard options Analytical option pricing
models 35
3.1 Solution of the Black and Scholes partial differential equation 43
3.2 Risk neutral valuation and Martingales 46
3.3 The Black and Scholes option valuation formula 48
3.4 Analytical option valuation formula for currency options 49
3.5 Option pricing with stochastic volatility for currency options 56
3.6 Numerical methods for option valuation 72
3.7 Implied volatility functions and empirical tests 109
IX
I. Pricing barrier options 113
4.1 Definition 113
4.2 Pricing of path dependent exotic options 114
4.3 Binomial and trinomial model for the valuation of barrier options 139
4.4 Finite difference ( FD ) methods for barrier options 149
4.5 Pricing of barrier options with Monte Carlo simulations 154
4.6 First exit times 157
Part III
5. Delta hedging standard options 165
5.1 Black and Scholes dynamic option replication Delta hedging 169
5.2 Discrete option replication Discrete delta hedging 179
5.3 Delta hedging under non normal distributions 191
5.4 Delta hedging of options in the presence of transaction costs 202
5.5 Delta hedging with an imperfect volatility 215
5.6 Hedging gamma and the convexity of options 234
5.7 Hedging the vega of options 245
5.8 Hedging the time decay of options 254
5.9 Rho as a risk measure for changes in interest rates 260
6. Hedging barrier options 263
6.1 Barrier option replication 264
6.2 Static hedging of barrier options in a binomial model with options
single strikes and multiple expiries 265
6.3 Barrier option static replication in a continuous time model 271
X
6.4 Replication of the intrinsic value of the barrier option at the
barrier — parity risk 285
6.5 Vega replication mismatch of the replication portfolio 286
6.6 Static hedging of barrier options and put/call symmetry 291
6.7 Static hedging of barrier options with no intrinsic value at the
barrier 300
6.8 Static hedging of barrier options and hedging c/(vega)/c?(volatility) 307
6.9 Dynamic hedging barrier options 309
6.10 Accuracy tests of barrier option static hedging through Monte
Carlo simulations 317
7. Conclusions 323
Literature 324
XI
Table of contents
Index of Figures XXI
Index of Tables XXV
Parti
1. Introduction 3
1.1 Outline of the dissertation 3
1.2 Objectives of the dissertation 4
1.3 Format and methodology of the dissertation 5
2. Statistical properties of foreign exchange rates and the
random walk model 7
2.1 Normal, skewed and kurtotic distributions and random walks 7
2.2 Statistical properties of foreign exchange rates 13
2.3 Tests for non linear dependence in daily foreign exchange rates 19
2.4 Brownian motion model and Ito s Lemma 24
2.4.1. General derivatives valuation approach 28
3. Pricing standard options Analytical option pricing
models 35
3.1 Solution of the Black and Scholes partial differential equation 43
3.2 Risk neutral valuation and Martingales 46
3.3 The Black and Scholes option valuation formula 48
3.4 Analytical option valuation formula for currency options 49
3.4.1. Option sensitivities as partial mathematical derivatives of the
option value 53
XIII
3.4.2. Currency option pricing formula when the forward is given 54
3.5 Option pricing with stochastic volatility for currency options 56
3.5.1. The Hull and White stochastic volatility model 57
3.5.2. Effects of changing the volatility 60
3.5.3. Option pricing model with stochastic volatility 62
3.5.4. Currency option pricing model with stochastic volatility 65
3.5.5. Option pricing models with stochastic volatility for currency
options 66
3.5.6. The effect of volatility risk premium and the concept of risk
adjusted volatility process
3.6 Numerical methods for option valuation 72
72
3.6.1. Lattice valuation models
3.6.1.1 Probability density function and option pricing 73
3.6.1.2 Risk neutrality, option pricing and the Black and
Scholes model 7
3.6.2. Binomial method
3.6.2.1 Binomial method 75
3.6.2.2 Binomial method and time varying volatility 81
3.6.3. The trinomial method and the backward problem 82
3.6.3.1 Backward problem 86
3.6.4. Finite difference methods (numericalprocedure) °
3.6.4.1 Explicit finite difference method ^2
3.6.4.2 Implicit difference method 99
3.6.4.3 The Crank Nicholson method 102
3.6.5. Monte Carlo simulations and related methods 1*
3.6.5.1 The anthitetic variable method l05
3.6.5.2 The control variates method 106
XIV
3.7 Implied volatility functions and empirical tests 109
3.7.1. Implied tree approach 110
3.7.2. Implied probability distribution 110
3.7.3. Summary and conclusions 111
4. Pricing barrier options 113
4.1 Definition 113
4.2 Pricing of path dependent exotic options 114
4.2.1. Barrier options 114
4.2.2. Barrier options valuation formulas with constant volatility
measure 118
4.2.2.1 Boundary and initial conditions for barrier options 119
4.2.2.2 Analytical formulas for double barrier options 135
4.2.2.3 The German/Yor model for the pricing of double
barrier options 138
4.3 Binomial and trinomial model for the valuation of barrier options 139
4.3.1. Binomial model for valuation of barrier options (basic form) 140
4.3.1.1 Enhanced binomial model for the pricing of barrier
options 143
4.3.1.2 Positioning of the nodes not lying on the barrier 144
4.3.1.3 Enhanced trinomial model positioning of the
nodes on the barrier 146
4.3.1.4 Enhanced binomial model for the pricing of barrier
options 148
4.4 Finite difference ( FD ) methods for barrier options 149
4.4.1. Finite difference method for the pricing of barrier options 152
4.5 Pricing of barrier options with Monte Carlo simulations 154
4.6 First exit times 157
XV
4.6.1. Hit probability and pricing intuition 159
4.6.2. Barrier option pricing intuition 160
5. Delta hedging standard options 165
5.1 Black and Scholes dynamic option replication Delta hedging 169
5.1.1. Delta hedging simulations with the Monte Carlo
methodology 172
5.1.2. Delta hedging simulations with the Monte Carlo method —
frequent hedging 175
5.2 Discrete option replication Discrete delta hedging 179
5.2.1. Hedging error as a random variable from a chi squared
distribution 183
5.2.2. Quantitative relationship between delta hedge frequency and
mean captured edge volatility 184
5.2.3. Variance minimising delta values by discrete delta hedging 188
5.2.4. Replication, arbitrage and hedging error by discretely delta
hedging 189
5.3 Delta hedging under non normal distributions 191
5.3.1. Delta hedging under the Student t distribution 192
5.3.2. Delta hedging under a mix of two normal distributions 1
5.3.3. Delta hedging under a lognormal distribution (right skewed) 19/
5.3.4. Delta hedging under a reverse lognormal distribution (left
skewed) 200
5.4 Delta hedging of options in the presence of transaction costs 202
5.4.1. Local delta hedging paradigm in the presence of transaction
costs 203
5.4.1.1 Delta hedging with positive transaction costs at
fixed re balancing intervals 203
XVI
5.4.1.2 Delta hedging with transaction costs as an
adjustment to the volatility in the Black—Scholes
model 205
5.4.1.3 Variance—minimising delta and delta hedge
frequency in the presence of transaction costs 209
5.4.1.4 Delta hedging to a bandwidth in the presence of
transaction costs 210
5.4.2. Global delta hedging paradigm in the presence of transaction
costs 212
5.4.2.1 Delta hedging in the presence of transaction costs
with a utility based model 212
5.4.2.2 Proportional transaction costs 212
5.4.2.3 Fixed transaction costs 213
5.4.2.4 Proportional and fixed transaction costs 214
5.5 Delta hedging with an imperfect volatility 215
5.5.1. Delta hedging with the correct volatility as in the Black—
Scholes model 215
5.5.2. Delta hedging with imperfect volatility estimation 216
5.5.3. Delta hedging with the correct volatility and risk neutrality 221
5.5.4. Imperfect volatility forecast and the deviation from risk
neutrality 111
5.5.5. Implications of an imperfect volatility forecast for the risk
management and for the concept of risk neutrality 226
5.5.6. Different impacts on pricing and on delta hedging of an
imperfect volatility forecast and d(delta)/d(volatility) 111
5.5.7. Hedging d(delta)/d(volatility) — measure for a change in
delta for a change in volatility 231
5.6 Hedging gamma and the convexity of options 234
5.6.1. Hedging gamma with options 236
5.6.2. Hedging Black and Scholes gamma and convexity 240
XVII
5.6.3. Alternative gamma definition as GARCH— ( General Auto
Regressive Heteroskedastic ) gamma 242
5.7 Hedging the vega of options 245
5.7.1. Vega as a measure of volatility risk 245
5.7.2. Weighted and unweighted vega 248
5.7.3. Hedging vega using options on volatility 248
5.7.4. The sensitivity of vega to changes in volatility —
d(vega)/d(volatility) 249
5.7.5. Skew incorporating d(vega)/d(spot) and
d(vega)/d(volatility) 253
5.8 Hedging the time decay of options 254
5.8.1. Theta as a measure for time decay 254
5.8.2. The price of time decay risk 258
5.9 Rho as a risk measure for changes in interest rates 260
6. Hedging barrier options 263
6.1 Barrier option replication 264
6.2 Static hedging of barrier options in a binomial model with options
single strikes and multiple expiries 265
6.3 Barrier option static replication in a continuous time model 271
6.3.1. Barrier option replication algorithm for barrier options with
parity at the barrier 272
6.4 Replication of the intrinsic value of the barrier option at the
barrier — parity risk 285
6.5 Vega replication mismatch of the replication portfolio 286
6.6 Static hedging of barrier options and put/call symmetry 291
6.6.1. Put/call symmetry 291
6.6.2. Put/call symmetry for down and out call options 294
XVIII
6.6.3. Put/call symmetry for up and out call options 295
6.6.4. Put/call symmetry for double out barrier options 296
6.6.5. Put/call symmetry for partial barrier options 299
6.7 Static hedging of barrier options with no intrinsic value at the
barrier 300
6.7.1. Static hedge for down and out and up and out put options 301
6.7.2. Static hedging of down and in call and up and in put
options 302
6.7.3. Static hedging simulation of a down and in and of a
down and out call with Monte Carlo 303
6.7.4. Static hedging of barrier options when the underlying has no
drift 305
6.7.5. Static hedging barrier options using options with the same
expiry but multiple strikes 307
6.8 Static hedging of barrier options and hedging d(vega)/d(volatility) 307
6.8.1. Hedging double barrier options and the impact on vega 308
6.9 Dynamic hedging barrier options 309
6.9.1. Dynamic hedging down and out call options 310
6.9.2. Dynamic hedging down and in call options 313
6.9.3. Dynamic hedging up and out call options 314
6.10 Accuracy tests of barrier option static hedging through Monte
Carlo simulations 317
6.10.1 .Results of static hedging simulations with daily matching 320
6. lO.LResults of static hedging simulations with monthly matching 321
6.10.3. Conclusion 321
7. Conclusions 323
Literature 324
XIX
Index of figures
Figure 1: Probability density functions of the Normal and Lognormal distributions 9
Figure 2: Normal, Cauchy distribution versus leptokurtotic USDJPY returns distribution ..12
Figure 3: Volatility clustering in USDCHF returns 15
Figure 4: Binomial tree chart Spot price distribution and call value tree 79
Figure 5: Finite difference grid with (M+1)(N+1) point 91
Figure 6: Pricing of a European call in a trinomial tree improved to a rectangular grid 95
Figure 7: Finite difference approximation method: Implicit scheme 100
Figure 8 Theoretical value of an up and out European USD/JPY call option, strike 100,
barrier 120 116
Figure 9: Theoretical value of a down and in call with rebate 125
Figure 10: Theoretical value of a down and in call with rebate and of an up and in call
option with rebate, with spot above (resp. below) the barrier 126
Figure 11: Theoretical value of an up and out call option 141
Figure 12: Effective, internal and external barrier on a binomial tree 141
Figure 13: Valuation of a barrier option on a binomial tree Spot values tree 142
Figure 14: Barrier option valuation on a basic form binomial tree Tree of option values .143
Figure 15: Enhanced barrier option pricing algorithm on a binomial tree 145
Figure 16: Barrier option pricing on an enhanced binomial tree 148
Figure 17: Trinomial tree with barriers lying on the tree nodes 171
Figure 18: Delta of a standard European call versus spot and time 171
Figure 19: Delta of a European standard call by spot and by time 174
Figure 20: Replication error for a standard European call option 175
Figure 21: Monte Carlo simulation of spot paths (50 runs) in a normal diffusion setting....177
Figure 22: Hedging error distribution by frequent delta hedging (365 delta rebalancings).. 178
Figure 23: Hedging error distribution by infrequent delta hedging (90 delta rebalancings). 180
Figure 24: Distribution of the replication error for frequent and infrequent delta hedging... 182
Figure 25: Linear relationship between the theoretical value of a 50 delta option and an
increase in implied volatility 186
Figure 26: Volatility of the option replication error by the frequency of delta re
balancings and the vegaof the option (maturity 365 days) 187
XXI
Figure 27: Normal versus Student t distribution with 5 degrees of freedom 193
Figure 28: Hedging error distribution by simulating the diffusion process with a
Student t distribution (5 degrees of freedom) 195
Figure 29: Probability density function of a normal distribution N(0,l) versus the sum
of two normal distributions N(0,0.54) and N(0,1.31) 196
Figure 30: Shifted lognormal distribution in return space (right skewed) 198
Figure 31: Hedging error distribution by simulating the diffusion process with a shifted
lognormal distribution (return space) 199
Figure 32: Shifted lognormal distribution in return space (left skewed) 200
Figure 33: Hedging error distribution by simulating the diffusion process with a shifted,
left skewed lognormal distribution (return space) 201
Figure 34: Delta hedging option replication error by hedging with a hedge volatility
smaller than the true volatility 219
Figure 35: Option replication error by hedging using a hedge volatility higher than the
true volatility 220
Figure 36: The sensitivity d(delta)/d(volatility) of a standard call option 223
Figure 37: The sensitivity d(delta)/d(volatility) of a standard European call by spot 232
Figure 38: The sensitivity d(delta)/d(volatility) of a standard European call option by
spot and time to expiry 232
Figure 39: Gamma of a standard European call or put option by spot and different times
to expiry 236
Figure 40: Gamma of a standard European call option by spot and by time 238
Figure 41: Gamma changes over time for a 1 year, USD call/JPY put, spot 100,
strike 100. (JPY) 246
Figure 42: Vega of a standard call by spot and by time to expiry 247
Figure 43: D(vega)/d(volatility) of a 6 months USD call/JPY put, spot 100 and
strike 100 in USD 250
Figure 44: Vega and d(vega)/d(volatility) for a 1 year 100 strike USD call/JPY put 252
Figure 45: Vega of a long 1 month USD put/JPY call, strike 112 253
Figure 46: Theta of standard European call or put options by spot and by time to expiry
(with zero interest rates) 256
Figure 47 : Theta for a standard European call option with the underlying trading at a
premium, discount or equal to spot 257
yxti
Figure 48: Theta of a standard European call over time with the forward trading at a
premium 257
Figure 49 : Theta of a standard European call over time with the forward trading at a
discount 258
Figure 50: Delta changes with respect to the passage of time for a standard European
call 259
Figure 51: Time decay effect on a standard European call option 260
Figure 52: Replication of a 5 years, up and out call, strike 60 and barrier at 120 268
Figure 53: Theoretical value of a 6 months, up and out USD call/JPY put option,
strike 100 and barrier at 120 273
Figure 54: Delta of a 6 months, up and out USD call/JPY put, strike 100 and
barrier 120 274
Figure 55: Plot of the theoretical value of the replicating portfolio for a 6 months,
up and out USD call/JPY put, strike 100, barrier 120 1 option 276
Figure 56: Theoretical value of the replicating portfolio with two options 277
Figure 57: Theoretical value of the replicating portfolio with three options 279
Figure 58: Theoretical value of the complete replicating portfolio for a 6 months,
up and out USD call/JPY put, strike 100, barrier at 120 280
Figure 59: Replication mismatch between a 6 months up and out USD call/JPY put,
strike 100, barrier 120, and the replication portfolio with matches at monthly
intervals 281
Figure 60: Graph of the replication of an up and out USD call/JPY put option, strike 100,
barrier 120 at by weekly intervals 283
Figure 61: Graph of the replication mismatch between the replication portfolio and the
barrier option 284
Figure 62: Graph of the replication mismatch between the replication portfolio and the
barrier option (3D) 284
Figure 63: Vega of the replication portfolio for a 6 months, up and out USD call/JPY
put, strike 100, barrier 120 287
Figure 64: Vega of a 6 months, up and out USD call/JPY put, strike 100 and
barrier 120 288
Figure 65: Vega mismatch between the replicating portfolio (monthly intervals) and the
up and out USD call/JPY put, strike 100, barrier 120 289
Figure 66: Vega replication mismatch between the replicating portfolio
(bi weekly intervals) and the barrier option 290
XXIII
Figure 67: Delta of a down and out call option strike 100 and barrier 95 for spot
above 95 and of an up and out call option for spot below 95 301
Figure 68: Delta of a down and in call option strike 100 and barrier 95 for spot above
95 and of an up and in call option for spot below 95 303
Figure 69: Gamma of a down and out call and of the respective standard call option 312
Figure 70: Delta of a 6 months up and out call option, strike 100, barrier 110 and
volatility 20% 315
Figure 71: Theoretical value of a 6 months up and up call, strike 100, barrier at 120 and
volatility 20% 316
XXIV
Index of Tables
Table 1: Hypothesis for the explanation of leptokurtosis of returns 19
Table 2: Option pricing biases for non zero and zero correlation between changes in
the spot price and changes in volatility 61
Table 3: European call pricing in a trinomial tree (Time steps N=5) 85
Table 4: European call pricing in a trinomial tree (Time steps N= 10) 86
Table 5: Explicit finite difference method for a European call 98
Table 6: Analytical formula and respective integrals specifications for a down and in
call option with rebate where H X 128
Table 7: Analytical formulas and integrals specifications for a up and in call option
with rebate where H X and H X 129
Table 8: Analytical formula and integrals specifications for a down and in put option
with rebate where H X 130
Table 9: Analytical formulas and integrals specifications for an up and in put option
with rebate where H X and H X 130
Table 10: Analytical formula and respective integrals specifications for a down and out
call option with rebate where H X 131
Table 11: Analytical formula and respective integrals specifications for a down and out
call option with rebate where H X 132
Table 12: Analytical formula and respective integrals specifications for an up and in call
option with rebate where H X 132
Table 13: Analytical formula and integrals specifications for an up and in call option
with rebate where H X 133
Table 14: Analytical formulas and integrals specifications for a down and out put option
with rebate where H X and H X 134
Table 15: Analytical formulas and respective integrals specifications for an up and out
put option with rebate where H X and H X 134
Table 16: Monte Carlo simulation for the valuation of a barrier option 154
Table 17: Delta position report for a 1 year USD call/JPY put option, spot 100,
strike 100, interest rates zero and volatility 20% p.a 173
Table 18: Simulation of delta hedging with the Monte Carlo methodology 7^
Table 19: Arbitrage strategy on an imperfect volatility estimation 229
Table 20: Adjustment of an option portfolio using the underlying 235
XXV
Table 21: Hedging of a delta position given short gamma 237
Table 22: Delta hedging using spot and put and/or put spreads 239
Table 23: Time decay effect on the delta of a standard European call option on
USD/JPY 260
Table 24: Replicating portfolio for a 6 months, up and out USD call/JPY put, strike 100
and barrier 120 275
Table 25: Replication portfolio for a 6 months, up and out USD call/JPY put, strike 100
and barrier 120 at monthly intervals (3 options) 278
Table 26: Replication portfolio for a 6 months, up and out USD call/JPY put, strike 100
and barrier 120 at monthly intervals (7 options) Trade view 280
Table 27: Values of the replication mismatch between a 6 months, up and out USD
call/JPY put, strike 100, barrier 120, and the monthly replication portfolio 282
Table 28 Trade view of the replication of an up and out USD call/JPY put option,
strike 100, barrier 120 at bi weekly intervals 283
Table 29: Mismatch between the replication portfolio and the barrier option 285
Table 30: Dynamic hedging simulation results for a down and out call 310
Table 31: Dynamic hedging simulation results for a standard European call 311
Table 32: Dynamic hedging simulation results for a down and in call 313
Table 33: Dynamic hedging simulation results for a up and out call 314
XXVI
|
any_adam_object | 1 |
author | Adiliberti, Francesco 1970- |
author_GND | (DE-588)122365216 |
author_facet | Adiliberti, Francesco 1970- |
author_role | aut |
author_sort | Adiliberti, Francesco 1970- |
author_variant | f a fa |
building | Verbundindex |
bvnumber | BV013419553 |
classification_rvk | QK 660 |
ctrlnum | (OCoLC)634436134 (DE-599)BVBBV013419553 |
discipline | Wirtschaftswissenschaften |
format | Book |
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genre | (DE-588)4113937-9 Hochschulschrift gnd-content |
genre_facet | Hochschulschrift |
id | DE-604.BV013419553 |
illustrated | Illustrated |
indexdate | 2024-07-09T18:45:34Z |
institution | BVB |
isbn | 3258062730 |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009157557 |
oclc_num | 634436134 |
open_access_boolean | |
owner | DE-739 |
owner_facet | DE-739 |
physical | 306 S. Ill. : 23 cm |
publishDate | 2001 |
publishDateSearch | 2001 |
publishDateSort | 2001 |
publisher | Haupt |
record_format | marc |
series | Bank- und finanzwirtschaftliche Forschungen |
series2 | Bank- und finanzwirtschaftliche Forschungen |
spelling | Adiliberti, Francesco 1970- Verfasser (DE-588)122365216 aut Option hedging dynamic and static replication of standard and barrier options, and risk management of options on more accurate sensitivities to improve edge capture ratios Francesco Adiliberti Bern ; Stuttgart ; Wien Haupt 2001 306 S. Ill. : 23 cm txt rdacontent n rdamedia nc rdacarrier Bank- und finanzwirtschaftliche Forschungen 321 Zugl.: Zürich, Univ., Diss., 2000 Optionspreistheorie (DE-588)4135346-8 gnd rswk-swf Optionsgeschäft (DE-588)4043670-6 gnd rswk-swf Hedging (DE-588)4123357-8 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Hedging (DE-588)4123357-8 s Optionsgeschäft (DE-588)4043670-6 s DE-604 Optionspreistheorie (DE-588)4135346-8 s Bank- und finanzwirtschaftliche Forschungen 321 (DE-604)BV023546687 321 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009157557&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
spellingShingle | Adiliberti, Francesco 1970- Option hedging dynamic and static replication of standard and barrier options, and risk management of options on more accurate sensitivities to improve edge capture ratios Bank- und finanzwirtschaftliche Forschungen Optionspreistheorie (DE-588)4135346-8 gnd Optionsgeschäft (DE-588)4043670-6 gnd Hedging (DE-588)4123357-8 gnd |
subject_GND | (DE-588)4135346-8 (DE-588)4043670-6 (DE-588)4123357-8 (DE-588)4113937-9 |
title | Option hedging dynamic and static replication of standard and barrier options, and risk management of options on more accurate sensitivities to improve edge capture ratios |
title_auth | Option hedging dynamic and static replication of standard and barrier options, and risk management of options on more accurate sensitivities to improve edge capture ratios |
title_exact_search | Option hedging dynamic and static replication of standard and barrier options, and risk management of options on more accurate sensitivities to improve edge capture ratios |
title_full | Option hedging dynamic and static replication of standard and barrier options, and risk management of options on more accurate sensitivities to improve edge capture ratios Francesco Adiliberti |
title_fullStr | Option hedging dynamic and static replication of standard and barrier options, and risk management of options on more accurate sensitivities to improve edge capture ratios Francesco Adiliberti |
title_full_unstemmed | Option hedging dynamic and static replication of standard and barrier options, and risk management of options on more accurate sensitivities to improve edge capture ratios Francesco Adiliberti |
title_short | Option hedging |
title_sort | option hedging dynamic and static replication of standard and barrier options and risk management of options on more accurate sensitivities to improve edge capture ratios |
title_sub | dynamic and static replication of standard and barrier options, and risk management of options on more accurate sensitivities to improve edge capture ratios |
topic | Optionspreistheorie (DE-588)4135346-8 gnd Optionsgeschäft (DE-588)4043670-6 gnd Hedging (DE-588)4123357-8 gnd |
topic_facet | Optionspreistheorie Optionsgeschäft Hedging Hochschulschrift |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009157557&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
volume_link | (DE-604)BV023546687 |
work_keys_str_mv | AT adilibertifrancesco optionhedgingdynamicandstaticreplicationofstandardandbarrieroptionsandriskmanagementofoptionsonmoreaccuratesensitivitiestoimproveedgecaptureratios |