Discrete-time approximations and limit theorems: in applications to financial markets
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Boston
De Gruyter
[2022]
|
| Ausgabe: | 1. Auflage |
| Schriftenreihe: | De Gruyter Series in Probability and Stochastics
2 |
| Schlagworte: | |
| Online-Zugang: | https://www.degruyter.com/isbn/9783110652796 Inhaltsverzeichnis |
| Beschreibung: | XVI, 373 Seiten 24 cm x 17 cm |
| ISBN: | 9783110652796 311065279X |
Internformat
MARC
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| 100 | 1 | |a Mišura, Julija S. |d 1952- |e Verfasser |0 (DE-588)1050691563 |4 aut | |
| 245 | 1 | 0 | |a Discrete-time approximations and limit theorems |b in applications to financial markets |c Yuliya Mishura, Kostiantyn Ralchenko |
| 250 | |a 1. Auflage | ||
| 264 | 1 | |a Berlin ; Boston |b De Gruyter |c [2022] | |
| 300 | |a XVI, 373 Seiten |c 24 cm x 17 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a De Gruyter Series in Probability and Stochastics |v 2 | |
| 650 | 0 | 7 | |a Zeitdiskrete Approximation |0 (DE-588)4401310-3 |2 gnd |9 rswk-swf |
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| 650 | 0 | 7 | |a Finanzmathematik |0 (DE-588)4017195-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Ökonometrisches Modell |0 (DE-588)4043212-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Optionspreistheorie |0 (DE-588)4135346-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Black-Scholes-Modell |0 (DE-588)4206283-4 |2 gnd |9 rswk-swf |
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| 689 | 0 | 3 | |a Zeitdiskrete Approximation |0 (DE-588)4401310-3 |D s |
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| 689 | 0 | 5 | |a Ökonometrisches Modell |0 (DE-588)4043212-9 |D s |
| 689 | 0 | 6 | |a Optionspreistheorie |0 (DE-588)4135346-8 |D s |
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| 700 | 1 | |a Ralchenko, Kostiantyn |d 1984- |e Verfasser |0 (DE-588)1159933170 |4 aut | |
| 710 | 2 | |a Walter de Gruyter GmbH & Co. KG |0 (DE-588)10095502-2 |4 pbl | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |t Discrete-Time Approximations and Limit Theorems |b 1. Auflage |d Berlin/Boston : De Gruyter, 2021 |h Online-Ressource, 390 Seiten, 3 Illustrationen, 1 Illustrationen |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe, PDF |z 978-3-11-065424-0 |
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Datensatz im Suchindex
| _version_ | 1804182912868810752 |
|---|---|
| adam_text | CONTENTS
INTRODUCTION
-
V
ABBREVIATIONS
AND
NOTATIONS
-
XV
1
1.1
1.1.1
FINANCIAL
MARKETS.
FROM
DISCRETE
TO
CONTINUOUS
TIME
-
1
FINANCIAL
MARKETS
WITH
DISCRETE
TIME
-
2
DESCRIPTION
OF
ASSET
PRICES
AS
STOCHASTIC
PROCESSES
WITH
DISCRETE
TIME
-
2
1.1.2
1.1.3
1.1.4
1.2
DESCRIPTION
OF
INVESTORS
STRATEGIES.
SELF-FINANCING
STRATEGIES
-
4
ARBITRAGE-FREE
MULTI-PERIOD
MARKETS
-
5
CONTINGENT
CLAIMS.
COMPLETE
AND
INCOMPLETE
MARKETS
-
6
THE
SEQUENCE
OF
DISCRETE-TIME
MARKETS
AS
AN
INTERMEDIATE
STEP
IN
THE
TRANSITION
TO
CONTINUOUS
TIME
-
7
1.2.1
1.2.2
DESCRIPTION
OF
THE
SEQUENCE
OF
FINANCIAL
MARKETS
-
7
NO-ARBITRAGE
AND
COMPLETENESS
OF
THE
SEQUENCE
OF
MARKETS
WITH
DISCRETE
TIME,
CREATED
BY
INDEPENDENT
RANDOM
VARIABLES.
MULTIPLICATIVE
SCHEME
-
10
1.3
1.3.1
PRELIMINARIES
FOR
THE
FINANCIAL
MARKETS
WITH
CONTINUOUS
TIME
-
19
THE
NOTION
OF
SELF-FINANCING
STRATEGY
FOR
THE
MODELS
IN
CONTINUOUS
TIME
-
19
1.3.2
1.3.3
1.3.4
1.4
ARBITRAGE
AND
MARTINGALE
MEASURES
-
22
HEDGING
STRATEGIES
-
25
COMPLETE
MARKETS
-
26
FROM
DISCRETE
TO
CONTINUOUS
TIME.
THE
LIMIT
PROCESS
IS
A
GEOMETRIC
BROWNIAN
MOTION
-
27
1.4.1
PRE-LIMIT
SEQUENCE
OF
THE
MODELS
WITH
DISCRETE
TIME
IN
THE
MULTIPLICATIVE
SCHEME
----
27
1.4.2
1.4.3
GEOMETRIC
BROWNIAN
MOTION
----
28
FUNCTIONAL
CENTRAL
LIMIT
THEOREM
FOR
THE
FINANCIAL
MARKETS
WITH
DISCRETE
TIME
REPRESENTED
BY
THE
MULTIPLICATIVE
SCHEME
-
29
1.4.4
BLACK-SCHOLES
FORMULA
AS
THE
RESULT
OF
LIMIT
TRANSITION.
OPTION
PRICING
----
35
1.4.5
1.5
DELTA
AS
AN
EXAMPLE
OF
GREEK
FUNCTIONALS
-
39
WEAK
CONVERGENCE
OF
GREEK
SYMBOL
DELTA
FOR
PRICES
OF
EUROPEAN
OPTIONS:
FROM
DISCRETE
TIME
TO
CONTINUOUS
-
40
1.5.1
PRE-LIMIT
DELTA
AND
THE
METHOD
OF
THE
COMMON
PROBABILITY
SPACE
-
41
1.5.2
1.5.3
1.6
SOME
PRELIMINARY
RESULTS
-
41
CONVERGENCE
OF
TO
A(X,
T
-
1)
-----44
GENERAL
SCHEMES
OF
DIFFUSION
APPROXIMATION
-
50
1.6.1
GENERAL
FUNCTIONAL
LIMIT
THEOREM
FOR
DIFFUSION
APPROXIMATION
-
50
1.6.2
FUNCTIONAL
LIMIT
THEOREM
FOR
DIFFUSION
APPROXIMATION
OF
THE
SUMSAND
THE
PRODUCTS
OF
RANDOM
VARIABLES
-
53
1.7
A
RECURRENT
SCHEME
FOR
THE
DIFFUSION
APPROXIMATION
WHEN
THE
LIMIT
PROCESS
IS
A
GEOMETRIC
ORNSTEIN-UHLENBECK
PROCESS
-
58
1.7.1
GEOMETRIC
ORNSTEIN-UHLENBECK
PROCESS
AND
CONSTRUCTION
OF
DISCRETE
SCHEME
-
60
1.7.2
PRE-LIMIT
AND
LIMIT
ORNSTEIN-UHLENBECK
MARKETS
ARE
ARBITRAGE-FREE
AND
COMPLETE
-
62
1.7.3
CONVERGENCE
OF
THE
ASSET
PRICES
IN
THE
GEOMETRIC
ORNSTEIN-UHLENBECK
MODEL
-
65
1.8
FUNCTIONAL
LIMIT
THEOREMS
FOR
ADDITIVE
AND
MULTIPLICATIVE
SCHEMES
IN
THE
COX-INGERSOLL-ROSS
MODEL
-
68
1.8.1
NON-TRUNCATED
AND
TRUNCATED
COX-INGERSOLL-ROSS
PROCESSES
AND
SOME
OF
THEIR
PROPERTIES
-
69
1.8.2
DISCRETE
APPROXIMATION
SCHEMES
FOR
NON-TRUNCATED
AND
TRUNCATED
COX-INGERSOLL-ROSS
PROCESSES
-
75
1.8.3
MULTIPLICATIVE
SCHEME
FOR
THE
COX-INGERSOLL-ROSS
PROCESS
-
81
1.9
GENERAL
CONDITIONS
OF
WEAK
CONVERGENCE
OF
DISCRETE-TIME
MULTIPLICATIVE
SCHEMES
TO
ASSET
PRICES
WITH
MEMORY
-
84
1.9.1
GENERAL
CONDITIONS
OF
WEAK
CONVERGENCE
-
86
1.9.2
FRACTIONAL
BROWNIAN
MOTION
AS
A
LIMIT
PROCESS
AND
PRE-LIMIT
COEFFICIENTS
TAKEN
FROM
CHOLESKY
DECOMPOSITION
OF
ITS
COVARIANCE
FUNCTION
-
92
1.9.3
POSSIBLE
PERTURBATIONS
OF
THE
COEFFICIENTS
IN
CHOLESKY
DECOMPOSITION
-
101
1.9.4
RIEMANN-LIOUVILLE
FRACTIONAL
BROWNIAN
MOTION
AS
A
LIMIT
PROCESS
-
104
2
RATE
OF
CONVERGENCE
OF
ASSET
AND
OPTION
PRICES
-
109
2.1
THE
RATE
OF
CONVERGENCE
OF
OPTION
PRICES
WHEN
THE
LIMIT
IS
A
BLACK-SCHOLES
MODEL
-
109
2.1.1
INTRODUCTION
----
109
2.1.2
THE
RATE
OF
CONVERGENCE
IN
THE
BINOMIAL
MODEL
-
110
2.1.3
THE
RATE
OF
CONVERGENCE
OF
OPTION
PRICES
IN
THE
MODEL
WITH
UNIFORMLY
DISTRIBUTED
ASSET
JUMP
-
120
2.1.4
THE
RATE
OF
CONVERGENCE
OF
OPTION
PRICES
WHEN
A
GENERAL
MARTINGALE-TYPE
DISCRETE-TIME
SCHEME
APPROXIMATES
THE
BLACK-SCHOLES
MODEL
-
133
2.2
THE
RATE
OF
CONVERGENCE
OF
OPTION
PRICES
ON
THE
ASSET
FOLLOWING
THE
GEOMETRIC
ORNSTEIN-UHLENBECK
PROCESS
-
145
2.2.1
BRIEF
DISCUSSION
OF
THE
LIMIT
ORNSTEIN-UHLENBECK
ASSET
PRICE
PROCESS
-
146
2.2.2
DESCRIPTION
AND
PROPERTIES
OF
THE
PRE-LIMIT
DISCRETE-TIME
PRICE
PROCESSES
-
147
2.2.3
INCOMPLETENESS
OF
THE
PRE-LIMIT
MARKET
-
149
2.2.4
WEAK
CONVERGENCE
OF
ASSET
PRICE,
WITH
THE
RATE
OF
CONVERGENCE
-
151
2.2.5
THE
RATE
OF
CONVERGENCE
OF
OBJECTIVE
OPTION
PRICES
-
153
2.2.6
FROM
OBJECTIVE
MEASURE
TO
MARTINGALE
MEASURE.
THE
RATE
OF
CONVERGENCE
OF
FAIR
OPTION
PRICES
-
160
2.3
ESTIMATION
OF
THE
RATE
OF
CONVERGENCE
OF
OPTION
PRICES
BY
USING
THE
METHOD
OF
PSEUDOMOMENTS
-
166
2.3.1
RATE
OF
CONVERGENCE
IN
THE
CLT
FOR
I.
I.
D.
RANDOM
VARIABLES
BY
THE
METHOD
OF
PSEUDOMOMENTS;
RATE
OF
CONVERGENCE
OF
ASSET
PRICES
-
166
2.3.2
THE
RATE
OF
CONVERGENCE
OF
PUT
AND
CALL
OPTION
PRICES
-
172
2.4
MARKET
MODEL
WITH
STOCHASTIC
ORNSTEIN-UHLENBECK
VOLATILITY:
OPTION
PRICING
AND
DISCRETIZATION
-
174
2.4.1
DIFFUSION
MODEL
WITH
STOCHASTIC
VOLATILITY
GOVERNED
BY
THE
ORNSTEIN-UHLENBECK
PROCESS
-
177
2.4.2
DEFINITIONS
AND
AUXILIARY
RESULTS
-
178
2.4.3
ABSENCE
OF
ARBITRAGE
IN
THE
MARKET
WITH
STOCHASTIC
VOLATILITY
-
181
2.4.4
THE
CASE
OF
INDEPENDENT
WIENER
PROCESSES
-
183
2.4.5
DERIVATION
OF
AN
ANALYTIC
EXPRESSION
FOR
THE
OPTION
PRICE
-
186
2.4.6
DISCRETE
APPROXIMATION
OF
VOLATILITY
PROCESSES
-
192
2.4.7
THE
PRICE
OF
EUROPEAN
CALL
OPTIONS
----
193
2.4.8
NUMERICAL
EXAMPLES
-
196
2.4.9
APPROXIMATION
PRECISION
CHECK
FOR
THE
CASE
OF
DETERMINISTIC
VOLATILITY
----
200
2.5
OPTION
PRICING
WITH
FRACTIONALSTOCHASTIC
VOLATILITY
AND
DISCONTINUOUS
PAYOFF
FUNCTION
OF
POLYNOMIAL
GROWTH
-
202
2.5.1
PAYOFF
FUNCTION:
ADDITIONAL
ASSUMPTIONS,
AUXILIARY
PROPERTIES.
DISCUSSION
OF
ASSET
PRICE
MODEL,
ABSENCE
OF
ARBITRAGE,
MARTINGALE
MEASURES,
INCOMPLETENESS
-
204
2.5.2
MALLIAVIN
CALCULUS
WITH
APPLICATION
TO
OPTION
PRICING
-
210
2.5.3
THE
RATE
OF
CONVERGENCE
OF
APPROXIMATE
OPTION
PRICES
IN
THE
CASE
WHEN
BOTH
THE
WIENER
PROCESS
AND
FRACTIONAL
BROWNIAN
MOTIONS
ARE
DISCRETIZED
-
215
2.5.4
THE
RATE
OF
CONVERGENCE
OF
APPROXIMATE
OPTION
PRICES
IN
THE
CASE
WHEN
ONLY
FRACTIONAL
BROWNIAN
MOTION
IS
DISCRETIZED
-
223
2.5.5
OPTION
PRICE
IN
TERMS
OF
THE
DENSITY
OF
THE
INTEGRATED
STOCHASTIC
VOLATILITY
-
231
2.5.6
SIMULATIONS
-
235
3
LIMIT
THEOREMS
FOR
MARKETS
WITH
NON-RANDOM
TIME-VARYING
COEFFICIENTS
-
243
3.1
CONVERGENCE
OF
EUROPEAN
OPTION
PRICES
IN
THE
BLACK-SCHOLES
MODEL
WITH
TIME-VARYING
PARAMETERS
-
243
3.1.1
3.1.2
MODEL
----
244
EXPLICIT
FORM
OF
CALL
AND
PUT
OPTION
PRICES
WITH
TIME-VARYING
PARAMETERS
-
245
3.1.3
3.2
ROBUSTNESS
OF
ASSET
AND
EUROPEAN
OPTION
PRICES
-
250
CONVERGENCE
OF
BARRIER
OPTION
PRICES
WITH
TIME-VARYING
PARAMETERS
-
254
3.2.1
3.2.2
ROBUSTNESS
OF
THE
BARRIER
OPTION
PRICE
-
255
THE
PRICE
OF
THE
BARRIER
OPTION
AS
A
SOLUTION
TO
THE
BOUNDARY
VALUE
PROBLEM.
LIMIT
PRICING
THEOREM
-
258
3.3
THE
RATE
OF
CONVERGENCE
OF
BARRIER
OPTION
PRICES
UNDER
A
DISCRETIZATION
OF
TIME
----
260
3.3.1
DESCRIPTION
OF
THE
MODEL.
THE
RATE
OF
CONVERGENCE
OF
THE
BARRIER
OPTION
FAIR
PRICE
IN
THE
DISCRETE
BINOMIAL
MARKET
TO
THE
CORRESPONDING
PRICE
IN
THE
CONTINUOUS-TIME
MARKET
-
260
3.3.2
3.4
MODELING
----
268
THE
DIFFERENTIABILITY
OF
A
BARRIER
OPTION
PRICE
AS
A
FUNCTION
OF
THE
BARRIER
----
270
4
CONVERGENCE
OF
STOCHASTIC
INTEGRALS
IN
APPLICATION
TO
FINANCIAL
MARKETS
-
279
4.1
4.2
MULTI-DIMENSIONAL
FINANCIAL
MARKET,
SELF-FINANCING
STRATEGIES
-
279
FUNCTIONAL
LIMIT
THEOREMS
FOR
THE
INTEGRALS
WITH
RESPECT
TO
SEMIMARTINGALES
-
284
4.2.1
WEAK
CONVERGENCE
OF
INTEGRALS
WITH
RESPECT
TO
PROCESSES
OF
BOUNDED
VARIATION
----
284
4.2.2
WEAK
CONVERGENCE
OF
STOCHASTIC
INTEGRALS
WITH
RESPECT
TO
MARTINGALES
-
289
4.2.3
WEAK
CONVERGENCE
OF
STOCHASTIC
INTEGRALS
WITH
RESPECT
TO
SEMIMARTINGALES
-
292
4.2.4
WEAK
CONVERGENCE
OF
INTEGRANDS
UNDER
THE
CONDITION
OF
CONVERGENCE
OF
STOCHASTIC
INTEGRALS
-
295
4.3
APPLICATION
OF
FUNCTIONAL
LIMIT
THEOREMS
FOR
STOCHASTIC
INTEGRALS
TO
FINANCIAL
INVESTMENT
-
299
4.3.1
4.3.2
4.4
WEAK
CONVERGENCE
OF
CAPITALS
OF
SELF-FINANCING
STRATEGIES
-
299
CONVERGENCE
OF
RISK
MINIMIZING
STRATEGIES
-
301
LIMIT
BEHAVIOR
OF
CAPITALS
AND
BARRIER
OPTION
PRICES
IN
THE
BLACK-SCHOLES
MODEL
WITH
STOCHASTIC
DRIFT
AND
VOLATILITY
-
307
4.4.1
4.4.2
DESCRIPTION
OF
THE
MODEL
-
308
WEAK
CONVERGENCE
OF
CAPITALS
IN
THE
GENERALIZED
BLACK-SCHOLES
MODEL
----
308
4.4.3
WEAK
CONVERGENCE
OF
EUROPEAN
BARRIER
OPTION
PRICES
IN
THE
GENERALIZED
BLACK-SCHOLES
MODEL
-
312
BIBLIOGRAPHY
-
363
A
A.L
A.
1.1
A.2
A.
2.1
A.2.2
A.3
A.
3.1
A.3.
2
A.3.
3
A.3.4
A.3.
5
A.3.6
A.3.7
A.3.8
A.3.9
A.3.
10
ESSENTIALS
OF
CALCULUS,
PROBABILITY,
AND
STOCHASTIC
PROCESSES
-
319
ESSENTIALS
OF
CALCULUS
-
319
SOME
INEQUALITIES
FOR
EXPONENTIAL
FUNCTIONS
-
319
ESSENTIALS
OF
PROBABILITY
----
320
CONDITIONAL
EXPECTATION
AND
ITS
PROPERTIES
-
320
EQUIVALENT
PROBABILITY
MEASURES
-
321
ESSENTIALS
OF
STOCHASTIC
PROCESSES
-
321
MARTINGALES,
LOCAL
MARTINGALES,
AND
SEMIMARTINGALES
-
323
WIENER
PROCESS
-
331
FRACTIONAL
BROWNIAN
MOTION
-
332
ESSENTIALS
OF
STOCHASTIC
CALCULUS
-
333
ELEMENTS
OF
MALLIAVIN
CALCULUS
----
337
CONVERGENCE
OF
STOCHASTIC
ELEMENTS
-
339
WEAK
CONVERGENCE
TO
WIENER
PROCESS
WITH
A
DRIFT
----
347
CENTRAL
LIMIT
THEOREMS
IN
THE
SCHEME
OF
SERIES
-
347
THE
RATE
OF
CONVERGENCE
IN
THE
CENTRAL
LIMIT
THEOREM
-
348
THE
RATE
OF
CONVERGENCE
TO
THE
NORMAL
LAW
IN
TERMS
OF
PSEUDOMOMENTS
-
350
A.3.
11
STOCHASTIC
DIFFERENTIAL
EQUATIONS
AND
THE
APPROXIMATIONS
OF
SOLUTIONS
----
358
A.
4
SOME
ALGEBRA
RELATED
TO
MATRICES
IN
THE
CHOLESKY
DECOMPOSITION
----
362
INDEX
-
371
|
| adam_txt |
CONTENTS
INTRODUCTION
-
V
ABBREVIATIONS
AND
NOTATIONS
-
XV
1
1.1
1.1.1
FINANCIAL
MARKETS.
FROM
DISCRETE
TO
CONTINUOUS
TIME
-
1
FINANCIAL
MARKETS
WITH
DISCRETE
TIME
-
2
DESCRIPTION
OF
ASSET
PRICES
AS
STOCHASTIC
PROCESSES
WITH
DISCRETE
TIME
-
2
1.1.2
1.1.3
1.1.4
1.2
DESCRIPTION
OF
INVESTORS
'
STRATEGIES.
SELF-FINANCING
STRATEGIES
-
4
ARBITRAGE-FREE
MULTI-PERIOD
MARKETS
-
5
CONTINGENT
CLAIMS.
COMPLETE
AND
INCOMPLETE
MARKETS
-
6
THE
SEQUENCE
OF
DISCRETE-TIME
MARKETS
AS
AN
INTERMEDIATE
STEP
IN
THE
TRANSITION
TO
CONTINUOUS
TIME
-
7
1.2.1
1.2.2
DESCRIPTION
OF
THE
SEQUENCE
OF
FINANCIAL
MARKETS
-
7
NO-ARBITRAGE
AND
COMPLETENESS
OF
THE
SEQUENCE
OF
MARKETS
WITH
DISCRETE
TIME,
CREATED
BY
INDEPENDENT
RANDOM
VARIABLES.
MULTIPLICATIVE
SCHEME
-
10
1.3
1.3.1
PRELIMINARIES
FOR
THE
FINANCIAL
MARKETS
WITH
CONTINUOUS
TIME
-
19
THE
NOTION
OF
SELF-FINANCING
STRATEGY
FOR
THE
MODELS
IN
CONTINUOUS
TIME
-
19
1.3.2
1.3.3
1.3.4
1.4
ARBITRAGE
AND
MARTINGALE
MEASURES
-
22
HEDGING
STRATEGIES
-
25
COMPLETE
MARKETS
-
26
FROM
DISCRETE
TO
CONTINUOUS
TIME.
THE
LIMIT
PROCESS
IS
A
GEOMETRIC
BROWNIAN
MOTION
-
27
1.4.1
PRE-LIMIT
SEQUENCE
OF
THE
MODELS
WITH
DISCRETE
TIME
IN
THE
MULTIPLICATIVE
SCHEME
----
27
1.4.2
1.4.3
GEOMETRIC
BROWNIAN
MOTION
----
28
FUNCTIONAL
CENTRAL
LIMIT
THEOREM
FOR
THE
FINANCIAL
MARKETS
WITH
DISCRETE
TIME
REPRESENTED
BY
THE
MULTIPLICATIVE
SCHEME
-
29
1.4.4
BLACK-SCHOLES
FORMULA
AS
THE
RESULT
OF
LIMIT
TRANSITION.
OPTION
PRICING
----
35
1.4.5
1.5
"
DELTA
"
AS
AN
EXAMPLE
OF
GREEK
FUNCTIONALS
-
39
WEAK
CONVERGENCE
OF
GREEK
SYMBOL
"
DELTA
"
FOR
PRICES
OF
EUROPEAN
OPTIONS:
FROM
DISCRETE
TIME
TO
CONTINUOUS
-
40
1.5.1
PRE-LIMIT
"
DELTA
"
AND
THE
METHOD
OF
THE
COMMON
PROBABILITY
SPACE
-
41
1.5.2
1.5.3
1.6
SOME
PRELIMINARY
RESULTS
-
41
CONVERGENCE
OF
TO
A(X,
T
-
1)
-----44
GENERAL
SCHEMES
OF
DIFFUSION
APPROXIMATION
-
50
1.6.1
GENERAL
FUNCTIONAL
LIMIT
THEOREM
FOR
DIFFUSION
APPROXIMATION
-
50
1.6.2
FUNCTIONAL
LIMIT
THEOREM
FOR
DIFFUSION
APPROXIMATION
OF
THE
SUMSAND
THE
PRODUCTS
OF
RANDOM
VARIABLES
-
53
1.7
A
RECURRENT
SCHEME
FOR
THE
DIFFUSION
APPROXIMATION
WHEN
THE
LIMIT
PROCESS
IS
A
GEOMETRIC
ORNSTEIN-UHLENBECK
PROCESS
-
58
1.7.1
GEOMETRIC
ORNSTEIN-UHLENBECK
PROCESS
AND
CONSTRUCTION
OF
DISCRETE
SCHEME
-
60
1.7.2
PRE-LIMIT
AND
LIMIT
ORNSTEIN-UHLENBECK
MARKETS
ARE
ARBITRAGE-FREE
AND
COMPLETE
-
62
1.7.3
CONVERGENCE
OF
THE
ASSET
PRICES
IN
THE
GEOMETRIC
ORNSTEIN-UHLENBECK
MODEL
-
65
1.8
FUNCTIONAL
LIMIT
THEOREMS
FOR
ADDITIVE
AND
MULTIPLICATIVE
SCHEMES
IN
THE
COX-INGERSOLL-ROSS
MODEL
-
68
1.8.1
"
NON-TRUNCATED
"
AND
"
TRUNCATED
"
COX-INGERSOLL-ROSS
PROCESSES
AND
SOME
OF
THEIR
PROPERTIES
-
69
1.8.2
DISCRETE
APPROXIMATION
SCHEMES
FOR
"
NON-TRUNCATED
"
AND
"
TRUNCATED
"
COX-INGERSOLL-ROSS
PROCESSES
-
75
1.8.3
MULTIPLICATIVE
SCHEME
FOR
THE
COX-INGERSOLL-ROSS
PROCESS
-
81
1.9
GENERAL
CONDITIONS
OF
WEAK
CONVERGENCE
OF
DISCRETE-TIME
MULTIPLICATIVE
SCHEMES
TO
ASSET
PRICES
WITH
MEMORY
-
84
1.9.1
GENERAL
CONDITIONS
OF
WEAK
CONVERGENCE
-
86
1.9.2
FRACTIONAL
BROWNIAN
MOTION
AS
A
LIMIT
PROCESS
AND
PRE-LIMIT
COEFFICIENTS
TAKEN
FROM
CHOLESKY
DECOMPOSITION
OF
ITS
COVARIANCE
FUNCTION
-
92
1.9.3
POSSIBLE
PERTURBATIONS
OF
THE
COEFFICIENTS
IN
CHOLESKY
DECOMPOSITION
-
101
1.9.4
RIEMANN-LIOUVILLE
FRACTIONAL
BROWNIAN
MOTION
AS
A
LIMIT
PROCESS
-
104
2
RATE
OF
CONVERGENCE
OF
ASSET
AND
OPTION
PRICES
-
109
2.1
THE
RATE
OF
CONVERGENCE
OF
OPTION
PRICES
WHEN
THE
LIMIT
IS
A
BLACK-SCHOLES
MODEL
-
109
2.1.1
INTRODUCTION
----
109
2.1.2
THE
RATE
OF
CONVERGENCE
IN
THE
BINOMIAL
MODEL
-
110
2.1.3
THE
RATE
OF
CONVERGENCE
OF
OPTION
PRICES
IN
THE
MODEL
WITH
UNIFORMLY
DISTRIBUTED
ASSET
JUMP
-
120
2.1.4
THE
RATE
OF
CONVERGENCE
OF
OPTION
PRICES
WHEN
A
GENERAL
MARTINGALE-TYPE
DISCRETE-TIME
SCHEME
APPROXIMATES
THE
BLACK-SCHOLES
MODEL
-
133
2.2
THE
RATE
OF
CONVERGENCE
OF
OPTION
PRICES
ON
THE
ASSET
FOLLOWING
THE
GEOMETRIC
ORNSTEIN-UHLENBECK
PROCESS
-
145
2.2.1
BRIEF
DISCUSSION
OF
THE
LIMIT
ORNSTEIN-UHLENBECK
ASSET
PRICE
PROCESS
-
146
2.2.2
DESCRIPTION
AND
PROPERTIES
OF
THE
PRE-LIMIT
DISCRETE-TIME
PRICE
PROCESSES
-
147
2.2.3
INCOMPLETENESS
OF
THE
PRE-LIMIT
MARKET
-
149
2.2.4
WEAK
CONVERGENCE
OF
ASSET
PRICE,
WITH
THE
RATE
OF
CONVERGENCE
-
151
2.2.5
THE
RATE
OF
CONVERGENCE
OF
OBJECTIVE
OPTION
PRICES
-
153
2.2.6
FROM
OBJECTIVE
MEASURE
TO
MARTINGALE
MEASURE.
THE
RATE
OF
CONVERGENCE
OF
FAIR
OPTION
PRICES
-
160
2.3
ESTIMATION
OF
THE
RATE
OF
CONVERGENCE
OF
OPTION
PRICES
BY
USING
THE
METHOD
OF
PSEUDOMOMENTS
-
166
2.3.1
RATE
OF
CONVERGENCE
IN
THE
CLT
FOR
I.
I.
D.
RANDOM
VARIABLES
BY
THE
METHOD
OF
PSEUDOMOMENTS;
RATE
OF
CONVERGENCE
OF
ASSET
PRICES
-
166
2.3.2
THE
RATE
OF
CONVERGENCE
OF
PUT
AND
CALL
OPTION
PRICES
-
172
2.4
MARKET
MODEL
WITH
STOCHASTIC
ORNSTEIN-UHLENBECK
VOLATILITY:
OPTION
PRICING
AND
DISCRETIZATION
-
174
2.4.1
DIFFUSION
MODEL
WITH
STOCHASTIC
VOLATILITY
GOVERNED
BY
THE
ORNSTEIN-UHLENBECK
PROCESS
-
177
2.4.2
DEFINITIONS
AND
AUXILIARY
RESULTS
-
178
2.4.3
ABSENCE
OF
ARBITRAGE
IN
THE
MARKET
WITH
STOCHASTIC
VOLATILITY
-
181
2.4.4
THE
CASE
OF
INDEPENDENT
WIENER
PROCESSES
-
183
2.4.5
DERIVATION
OF
AN
ANALYTIC
EXPRESSION
FOR
THE
OPTION
PRICE
-
186
2.4.6
DISCRETE
APPROXIMATION
OF
VOLATILITY
PROCESSES
-
192
2.4.7
THE
PRICE
OF
EUROPEAN
CALL
OPTIONS
----
193
2.4.8
NUMERICAL
EXAMPLES
-
196
2.4.9
APPROXIMATION
PRECISION
CHECK
FOR
THE
CASE
OF
DETERMINISTIC
VOLATILITY
----
200
2.5
OPTION
PRICING
WITH
FRACTIONALSTOCHASTIC
VOLATILITY
AND
DISCONTINUOUS
PAYOFF
FUNCTION
OF
POLYNOMIAL
GROWTH
-
202
2.5.1
PAYOFF
FUNCTION:
ADDITIONAL
ASSUMPTIONS,
AUXILIARY
PROPERTIES.
DISCUSSION
OF
ASSET
PRICE
MODEL,
ABSENCE
OF
ARBITRAGE,
MARTINGALE
MEASURES,
INCOMPLETENESS
-
204
2.5.2
MALLIAVIN
CALCULUS
WITH
APPLICATION
TO
OPTION
PRICING
-
210
2.5.3
THE
RATE
OF
CONVERGENCE
OF
APPROXIMATE
OPTION
PRICES
IN
THE
CASE
WHEN
BOTH
THE
WIENER
PROCESS
AND
FRACTIONAL
BROWNIAN
MOTIONS
ARE
DISCRETIZED
-
215
2.5.4
THE
RATE
OF
CONVERGENCE
OF
APPROXIMATE
OPTION
PRICES
IN
THE
CASE
WHEN
ONLY
FRACTIONAL
BROWNIAN
MOTION
IS
DISCRETIZED
-
223
2.5.5
OPTION
PRICE
IN
TERMS
OF
THE
DENSITY
OF
THE
INTEGRATED
STOCHASTIC
VOLATILITY
-
231
2.5.6
SIMULATIONS
-
235
3
LIMIT
THEOREMS
FOR
MARKETS
WITH
NON-RANDOM
TIME-VARYING
COEFFICIENTS
-
243
3.1
CONVERGENCE
OF
EUROPEAN
OPTION
PRICES
IN
THE
BLACK-SCHOLES
MODEL
WITH
TIME-VARYING
PARAMETERS
-
243
3.1.1
3.1.2
MODEL
----
244
EXPLICIT
FORM
OF
CALL
AND
PUT
OPTION
PRICES
WITH
TIME-VARYING
PARAMETERS
-
245
3.1.3
3.2
ROBUSTNESS
OF
ASSET
AND
EUROPEAN
OPTION
PRICES
-
250
CONVERGENCE
OF
BARRIER
OPTION
PRICES
WITH
TIME-VARYING
PARAMETERS
-
254
3.2.1
3.2.2
ROBUSTNESS
OF
THE
BARRIER
OPTION
PRICE
-
255
THE
PRICE
OF
THE
BARRIER
OPTION
AS
A
SOLUTION
TO
THE
BOUNDARY
VALUE
PROBLEM.
LIMIT
PRICING
THEOREM
-
258
3.3
THE
RATE
OF
CONVERGENCE
OF
BARRIER
OPTION
PRICES
UNDER
A
DISCRETIZATION
OF
TIME
----
260
3.3.1
DESCRIPTION
OF
THE
MODEL.
THE
RATE
OF
CONVERGENCE
OF
THE
BARRIER
OPTION
FAIR
PRICE
IN
THE
DISCRETE
BINOMIAL
MARKET
TO
THE
CORRESPONDING
PRICE
IN
THE
CONTINUOUS-TIME
MARKET
-
260
3.3.2
3.4
MODELING
----
268
THE
DIFFERENTIABILITY
OF
A
BARRIER
OPTION
PRICE
AS
A
FUNCTION
OF
THE
BARRIER
----
270
4
CONVERGENCE
OF
STOCHASTIC
INTEGRALS
IN
APPLICATION
TO
FINANCIAL
MARKETS
-
279
4.1
4.2
MULTI-DIMENSIONAL
FINANCIAL
MARKET,
SELF-FINANCING
STRATEGIES
-
279
FUNCTIONAL
LIMIT
THEOREMS
FOR
THE
INTEGRALS
WITH
RESPECT
TO
SEMIMARTINGALES
-
284
4.2.1
WEAK
CONVERGENCE
OF
INTEGRALS
WITH
RESPECT
TO
PROCESSES
OF
BOUNDED
VARIATION
----
284
4.2.2
WEAK
CONVERGENCE
OF
STOCHASTIC
INTEGRALS
WITH
RESPECT
TO
MARTINGALES
-
289
4.2.3
WEAK
CONVERGENCE
OF
STOCHASTIC
INTEGRALS
WITH
RESPECT
TO
SEMIMARTINGALES
-
292
4.2.4
WEAK
CONVERGENCE
OF
INTEGRANDS
UNDER
THE
CONDITION
OF
CONVERGENCE
OF
STOCHASTIC
INTEGRALS
-
295
4.3
APPLICATION
OF
FUNCTIONAL
LIMIT
THEOREMS
FOR
STOCHASTIC
INTEGRALS
TO
FINANCIAL
INVESTMENT
-
299
4.3.1
4.3.2
4.4
WEAK
CONVERGENCE
OF
CAPITALS
OF
SELF-FINANCING
STRATEGIES
-
299
CONVERGENCE
OF
RISK
MINIMIZING
STRATEGIES
-
301
LIMIT
BEHAVIOR
OF
CAPITALS
AND
BARRIER
OPTION
PRICES
IN
THE
BLACK-SCHOLES
MODEL
WITH
STOCHASTIC
DRIFT
AND
VOLATILITY
-
307
4.4.1
4.4.2
DESCRIPTION
OF
THE
MODEL
-
308
WEAK
CONVERGENCE
OF
CAPITALS
IN
THE
GENERALIZED
BLACK-SCHOLES
MODEL
----
308
4.4.3
WEAK
CONVERGENCE
OF
EUROPEAN
BARRIER
OPTION
PRICES
IN
THE
GENERALIZED
BLACK-SCHOLES
MODEL
-
312
BIBLIOGRAPHY
-
363
A
A.L
A.
1.1
A.2
A.
2.1
A.2.2
A.3
A.
3.1
A.3.
2
A.3.
3
A.3.4
A.3.
5
A.3.6
A.3.7
A.3.8
A.3.9
A.3.
10
ESSENTIALS
OF
CALCULUS,
PROBABILITY,
AND
STOCHASTIC
PROCESSES
-
319
ESSENTIALS
OF
CALCULUS
-
319
SOME
INEQUALITIES
FOR
EXPONENTIAL
FUNCTIONS
-
319
ESSENTIALS
OF
PROBABILITY
----
320
CONDITIONAL
EXPECTATION
AND
ITS
PROPERTIES
-
320
EQUIVALENT
PROBABILITY
MEASURES
-
321
ESSENTIALS
OF
STOCHASTIC
PROCESSES
-
321
MARTINGALES,
LOCAL
MARTINGALES,
AND
SEMIMARTINGALES
-
323
WIENER
PROCESS
-
331
FRACTIONAL
BROWNIAN
MOTION
-
332
ESSENTIALS
OF
STOCHASTIC
CALCULUS
-
333
ELEMENTS
OF
MALLIAVIN
CALCULUS
----
337
CONVERGENCE
OF
STOCHASTIC
ELEMENTS
-
339
WEAK
CONVERGENCE
TO
WIENER
PROCESS
WITH
A
DRIFT
----
347
CENTRAL
LIMIT
THEOREMS
IN
THE
SCHEME
OF
SERIES
-
347
THE
RATE
OF
CONVERGENCE
IN
THE
CENTRAL
LIMIT
THEOREM
-
348
THE
RATE
OF
CONVERGENCE
TO
THE
NORMAL
LAW
IN
TERMS
OF
PSEUDOMOMENTS
-
350
A.3.
11
STOCHASTIC
DIFFERENTIAL
EQUATIONS
AND
THE
APPROXIMATIONS
OF
SOLUTIONS
----
358
A.
4
SOME
ALGEBRA
RELATED
TO
MATRICES
IN
THE
CHOLESKY
DECOMPOSITION
----
362
INDEX
-
371 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Mišura, Julija S. 1952- Ralchenko, Kostiantyn 1984- |
| author_GND | (DE-588)1050691563 (DE-588)1159933170 |
| author_facet | Mišura, Julija S. 1952- Ralchenko, Kostiantyn 1984- |
| author_role | aut aut |
| author_sort | Mišura, Julija S. 1952- |
| author_variant | j s m js jsm k r kr |
| building | Verbundindex |
| bvnumber | BV047568334 |
| classification_rvk | SK 980 |
| ctrlnum | (OCoLC)1286860305 (DE-599)DNB1237509866 |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 1. Auflage |
| format | Book |
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| id | DE-604.BV047568334 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T18:29:32Z |
| indexdate | 2024-07-10T09:15:06Z |
| institution | BVB |
| institution_GND | (DE-588)10095502-2 |
| isbn | 9783110652796 311065279X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032954007 |
| oclc_num | 1286860305 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-634 |
| owner_facet | DE-19 DE-BY-UBM DE-634 |
| physical | XVI, 373 Seiten 24 cm x 17 cm |
| publishDate | 2022 |
| publishDateSearch | 2022 |
| publishDateSort | 2022 |
| publisher | De Gruyter |
| record_format | marc |
| series | De Gruyter Series in Probability and Stochastics |
| series2 | De Gruyter Series in Probability and Stochastics |
| spelling | Mišura, Julija S. 1952- Verfasser (DE-588)1050691563 aut Discrete-time approximations and limit theorems in applications to financial markets Yuliya Mishura, Kostiantyn Ralchenko 1. Auflage Berlin ; Boston De Gruyter [2022] XVI, 373 Seiten 24 cm x 17 cm txt rdacontent n rdamedia nc rdacarrier De Gruyter Series in Probability and Stochastics 2 Zeitdiskrete Approximation (DE-588)4401310-3 gnd rswk-swf Kreditmarkt (DE-588)4073788-3 gnd rswk-swf Grenzwertsatz (DE-588)4158163-5 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Ökonometrisches Modell (DE-588)4043212-9 gnd rswk-swf Optionspreistheorie (DE-588)4135346-8 gnd rswk-swf Black-Scholes-Modell (DE-588)4206283-4 gnd rswk-swf Black-Scholes-Modell Grenzwertsatz Kreditmarkt Kreditmarkt (DE-588)4073788-3 s Finanzmathematik (DE-588)4017195-4 s Black-Scholes-Modell (DE-588)4206283-4 s Zeitdiskrete Approximation (DE-588)4401310-3 s Grenzwertsatz (DE-588)4158163-5 s Ökonometrisches Modell (DE-588)4043212-9 s Optionspreistheorie (DE-588)4135346-8 s DE-604 Ralchenko, Kostiantyn 1984- Verfasser (DE-588)1159933170 aut Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe Discrete-Time Approximations and Limit Theorems 1. Auflage Berlin/Boston : De Gruyter, 2021 Online-Ressource, 390 Seiten, 3 Illustrationen, 1 Illustrationen Erscheint auch als Online-Ausgabe, PDF 978-3-11-065424-0 Erscheint auch als Online-Ausgabe, EPUB 978-3-11-065299-4 De Gruyter Series in Probability and Stochastics 2 (DE-604)BV044781973 2 X:MVB https://www.degruyter.com/isbn/9783110652796 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032954007&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p vlb 20210723 DE-101 https://d-nb.info/provenance/plan#vlb |
| spellingShingle | Mišura, Julija S. 1952- Ralchenko, Kostiantyn 1984- Discrete-time approximations and limit theorems in applications to financial markets De Gruyter Series in Probability and Stochastics Zeitdiskrete Approximation (DE-588)4401310-3 gnd Kreditmarkt (DE-588)4073788-3 gnd Grenzwertsatz (DE-588)4158163-5 gnd Finanzmathematik (DE-588)4017195-4 gnd Ökonometrisches Modell (DE-588)4043212-9 gnd Optionspreistheorie (DE-588)4135346-8 gnd Black-Scholes-Modell (DE-588)4206283-4 gnd |
| subject_GND | (DE-588)4401310-3 (DE-588)4073788-3 (DE-588)4158163-5 (DE-588)4017195-4 (DE-588)4043212-9 (DE-588)4135346-8 (DE-588)4206283-4 |
| title | Discrete-time approximations and limit theorems in applications to financial markets |
| title_auth | Discrete-time approximations and limit theorems in applications to financial markets |
| title_exact_search | Discrete-time approximations and limit theorems in applications to financial markets |
| title_exact_search_txtP | Discrete-time approximations and limit theorems in applications to financial markets |
| title_full | Discrete-time approximations and limit theorems in applications to financial markets Yuliya Mishura, Kostiantyn Ralchenko |
| title_fullStr | Discrete-time approximations and limit theorems in applications to financial markets Yuliya Mishura, Kostiantyn Ralchenko |
| title_full_unstemmed | Discrete-time approximations and limit theorems in applications to financial markets Yuliya Mishura, Kostiantyn Ralchenko |
| title_short | Discrete-time approximations and limit theorems |
| title_sort | discrete time approximations and limit theorems in applications to financial markets |
| title_sub | in applications to financial markets |
| topic | Zeitdiskrete Approximation (DE-588)4401310-3 gnd Kreditmarkt (DE-588)4073788-3 gnd Grenzwertsatz (DE-588)4158163-5 gnd Finanzmathematik (DE-588)4017195-4 gnd Ökonometrisches Modell (DE-588)4043212-9 gnd Optionspreistheorie (DE-588)4135346-8 gnd Black-Scholes-Modell (DE-588)4206283-4 gnd |
| topic_facet | Zeitdiskrete Approximation Kreditmarkt Grenzwertsatz Finanzmathematik Ökonometrisches Modell Optionspreistheorie Black-Scholes-Modell |
| url | https://www.degruyter.com/isbn/9783110652796 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032954007&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV044781973 |
| work_keys_str_mv | AT misurajulijas discretetimeapproximationsandlimittheoremsinapplicationstofinancialmarkets AT ralchenkokostiantyn discretetimeapproximationsandlimittheoremsinapplicationstofinancialmarkets AT walterdegruytergmbhcokg discretetimeapproximationsandlimittheoremsinapplicationstofinancialmarkets |