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Pricing Models of Volatility Products and Exotic Variance Derivatives [Hardback]

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  • Formāts: Hardback, 268 pages, height x width: 234x156 mm, weight: 526 g, 6 Tables, black and white; 9 Line drawings, black and white; 9 Illustrations, black and white
  • Sērija : Chapman and Hall/CRC Financial Mathematics Series
  • Izdošanas datums: 14-May-2022
  • Izdevniecība: Chapman & Hall/CRC
  • ISBN-10: 1032199024
  • ISBN-13: 9781032199023
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  • Cena: 145,75 €
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Pricing Models of Volatility Products and Exotic Variance DerivativesPalielināt
  • Formāts: Hardback, 268 pages, height x width: 234x156 mm, weight: 526 g, 6 Tables, black and white; 9 Line drawings, black and white; 9 Illustrations, black and white
  • Sērija : Chapman and Hall/CRC Financial Mathematics Series
  • Izdošanas datums: 14-May-2022
  • Izdevniecība: Chapman & Hall/CRC
  • ISBN-10: 1032199024
  • ISBN-13: 9781032199023
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9781032199023.html
Keywords:
Pricing Models of Volatility Products and Exotic Variance Derivatives summarizes most of the recent research results in pricing models of derivatives on discrete realized variance and VIX. The book begins with the presentation of volatility trading and uses of variance derivatives. It then moves on to discuss the robust replication strategy of variance swaps using portfolio of options, which is one of the major milestones in pricing theory of variance derivatives. The replication procedure provides the theoretical foundation of the construction of VIX. This book provides sound arguments for formulating the pricing models of variance derivatives and establishes formal proofs of various technical results. Illustrative numerical examples are included to show accuracy and effectiveness of analytic and approximation methods.

Features











Useful for practitioners and quants in the financial industry who need to make choices between various pricing models of variance derivatives





Fabulous resource for researchers interested in pricing and hedging issues of variance derivatives and VIX products





Can be used as a university textbook in a topic course on pricing variance derivatives
Preface xi
1 Volatility Trading and Variance Derivatives
1(38)
1.1 Implied volatility and local volatility
3(3)
1.2 Volatility trading using options
6(5)
1.2.1 Taking volatility position using straddles and strangles
6(2)
1.2.2 Volatility exposure generated by delta hedging options
8(3)
1.3 Derivatives on discrete realized variance
11(7)
1.3.1 Swaps and options on realized variance and volatility
11(2)
1.3.2 Generalized variance swaps
13(2)
1.3.3 Timer options
15(2)
1.3.4 Target volatility options
17(1)
1.4 Replication of variance swaps
18(5)
1.4.1 Replication of continuous variance swaps
19(4)
1.5 Practical implementation of replication: Finite strikes and discrete monitoring
23(16)
1.5.1 Continuously sampled realized variance replicated by options of finite strikes
24(2)
1.5.2 VIX: Extracting model-free volatility from S&P 500 Index Options
26(4)
1.5.3 Replication of swaps on discrete realized variance
30(5)
Appendix
35(4)
2 Levy Processes and Stochastic Volatility Models
39(62)
2.1 Compound Poisson process
41(6)
2.1.1 Poisson process
42(1)
2.1.2 Random jump sizes
43(2)
2.1.3 Stochastic integration
45(1)
2.1.4 Jump measure and Levy measure
46(1)
2.2 Jump-diffusion models
47(7)
2.2.1 Ito's formula
48(1)
2.2.2 Asset price process: Geometric Brownian motion with compound Poisson jumps
49(3)
2.2.3 Merton's model with Gaussian jumps
52(1)
2.2.4 Kou's model with exponential jumps
53(1)
2.3 Levy processes
54(9)
2.3.1 Definition
55(1)
2.3.2 Infinite divisibility
55(1)
2.3.3 Characteristic exponent and Levy-Khintchine representation
56(2)
2.3.4 L6vy-It6 decomposition theorem
58(1)
2.3.5 CGMY model: Dampened power law as Ldvy measure
59(2)
2.3.6 Generalized Hyperbolic model
61(1)
2.3.7 Martingale condition on drift under risk neutral measure
62(1)
2.4 Time-changed Levy processes
63(10)
2.4.1 Time-change techniques: Subordinators and activity rates
63(4)
2.4.2 Variance Gamma model
67(4)
2.4.3 Normal Inverse Gaussian model
71(2)
2.4.4 Barndorff-Nielsen and Shephard model
73(1)
2.5 Stochastic volatility models with jumps
73(8)
2.5.1 Distribution formulas of instantaneous variance of CIR type
77(2)
2.5.2 Pricing of swap on continuous realized variance
79(2)
2.6 Affine jump-diffusion stochastic volatility models
81(5)
2.6.1 Joint moment generating function of the affine model
81(2)
2.6.2 Numerical valuation of complex algorithms and Heston trap
83(2)
2.6.3 Sch6bel-Zhu model
85(1)
2.7 3/2 stochastic volatility model
86(15)
2.7.1 Model formulation
88(1)
2.7.2 Partial Fourier transform of the triple joint density
88(3)
2.7.3 Partial Fourier transform of the joint density function of (X,V)
91(1)
2.7.4 Joint characteristic function of (X,I)
92(2)
Appendix
94(7)
3 VIX Derivatives under Consistent Models and Direct Models
101(32)
3.1 VIX, variance swap rate and VIX derivatives
102(5)
3.1.1 Relation between variance swap rate and VIX2 under jumps
102(3)
3.1.2 VIX derivatives
105(2)
3.2 Pricing VIX derivatives under consistent models
107(16)
3.2.1 Affine stochastic volatility models
107(8)
3.2.2 3/2-Model with Jumps in Index Value
115(3)
3.2.3 Barndorff-Nielsen and Shephard model
118(2)
3.2.4 GARCH type models
120(3)
3.3 Direct modeling of VIX
123(10)
3.3.1 Multifactor affine jump-diffusion models
125(4)
3.3.2 3/2 plus models
129(1)
Appendix
130(3)
4 Swap Products on Discrete Variance and Volatility
133(50)
4.1 Direct expectation of square of log return
134(7)
4.2 Nested expectation via partial integro-differential equation
141(12)
4.2.1 Vanilla variance swaps under the Heston stochastic volatility model
142(4)
4.2.2 Variance swaps under the 3/2-model
146(7)
4.3 Moment generating function methods
153(10)
4.3.1 Variance swap and gamma swap
154(2)
4.3.2 Corridor type swaps
156(3)
4.3.3 Numerical tests of the convergence for discretely monitored variance swaps
159(1)
4.3.4 Volatility swaps
160(3)
4.4 Variance swaps under time-changed Levy processes
163(20)
4.4.1 Multiple of log contract for pricing swaps on continuous realized variance
164(2)
4.4.2 Swaps on discrete realized variance
166(4)
4.4.3 Generalized variance swaps
170(5)
4.4.4 Convergence of fair strikes
175(2)
4.4.5 Conditions on convergence in expectation
177(4)
Appendix
181(2)
5 Options on Discrete Realized Variance
183(34)
5.1 Adjustment for discretization effect via lognormal approximation
185(6)
5.1.1 Discrete realized variance under the lognormal model
186(2)
5.1.2 Approximation formulas for moment generating function
188(3)
5.2 Normal approximation to conditional distribution of discrete realized variance
191(8)
5.2.1 Conditional normal approximation pricing scheme
192(2)
5.2.2 Simplified conditional pricing schemes
194(2)
5.2.3 Non-simulation asymptotic approximation pricing scheme
196(3)
5.3 Partially exact and bounded approximation for options on discrete realized variance
199(12)
5.3.1 Lower bound with known characteristic function
200(3)
5.3.2 Partially exact and bounded approximation
203(5)
5.3.3 Numerical calculations of partially exact and bounded approximation
208(3)
5.4 Small time asymptotic approximation
211(6)
5.4.1 Small time asymptotics under Levy models
211(2)
5.4.2 Small time asymptotics under the semimartingale models
213(1)
5.4.3 Option pricing using small time asymptotic approximation
214(3)
6 Timer Options
217(32)
6.1 Model formulation
218(3)
6.1.1 Governing partial differential equation
218(3)
6.2 Pricing perpetual timer options
221(15)
6.2.1 Conditional expectation based on Black-Scholes type formula
222(3)
6.2.2 Integral price formulas under the Heston model
225(2)
6.2.3 Perturbation approximation
227(9)
6.3 Finite maturity discrete timer options
236(13)
6.3.1 Fourier inversion integral price formula
237(3)
6.3.2 Fourier space time stepping numerical algorithm
240(5)
Appendix
245(4)
Bibliography 249(16)
Index 265
Yue Kuen Kwok is a professor in the Department of Mathematics and Financial Technology Thrust, the Hong Kong University of Science and Technology. Professor Kwoks research interests concentrate on pricing and risk management of financial derivatives and structured insurance products. He has published more than 80 research articles in major research journals in quantitative finance and actuarial sciences. In addition, he is the author of two books on quantitative finance: Mathematical Models of Financial Derivatives and Saddlepoint Approximation Methods in Financial Engineering. He has provided consulting services to financial institutions on various aspects of trading structured products and credit risk management. Professor Kwok has served on the editorial boards of Journal of Economic and Dynamics Control, Asian-Pacific Financial Markets and International Journal of Financial Engineering. He earned his PhD in applied mathematics from Brown University in 1985.

Wendong Zheng joined Credit Suisse in Hong Kong in 2018. He is currently a vice president in the Quantitative Strategies Group, covering equity and hybrid derivatives modeling and trading. Before joining Credit Suisse, he held positions at Bank of China International and Barclays Investment Bank. He has performed both academic and industrial works on pricing and trading volatility derivatives. Also, he has co-authored the book Saddlepoint Approximation Methods in Financial Engineering. Dr. Zheng holds a PhD in mathematics from the Hong Kong University of Science and Technology.