Wiley Finance--Fourier Transform Metheds in Finance

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Fourier Transform Methods in Finance
Umberto Cherubini, Giovanni Della Lunga, Sabrina Mulinacci, Pietro Rossi
ISBN: 978-0-470-99400-9
Hardcover
256 pages
February 2010

Wiley List Price:

US $105.00

In recent years, Fourier transform methods have emerged as one of the major methodologies for the evaluation of derivative contracts, largely due to the need to strike a balance between the extension of existing pricing models beyond the traditional Black-Scholes setting and a need to evaluate prices consistently with the market quotes. Fourier Transform Methods in Finance is a practical and accessible guide to pricing financial instruments using Fourier transform. Written by an experienced team of practitioners and academics, it covers Fourier pricing methods; the dynamics of asset prices; non stationary market dynamics; arbitrage free pricing; generalized functions and the Fourier transform method. Readers will learn how to:

• compute the Hilbert transform of the pricing kernel under a Fast Fourier Transform (FFT) technique
• characterise the price dynamics on a market in terms of the characteristic function, allowing for both diffusive processes and jumps
• apply the concept of characteristic function to non-stationary processes, in particular in the presence of stochastic volatility and more generally time change techniques
• perform a change of measure on the characteristic function in order to make the price process a martingale
• recover a general representation of the pricing kernel of the economy in terms of Hilbert transform using the theory of generalised functions
• apply the pricing formula to the most famous pricing models, with stochastic volatility and jumps.

Junior and senior practitioners alike will benefit from this quick reference guide to state of the art models and market calibration techniques. Not only will it enable them to write an algorithm for option pricing using the most advanced models, calibrate a pricing model on options data, and extract the implied probability distribution in market data, they will also understand the most advanced models and techniques and discover how these techniques have been adjusted for applications in finance.

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关键词：transform Finance Fourier Metheds Financ Finance Wiley transform Metheds

Preface.
List of Symbols.

1 Fourier Pricing Methods.

1.1 Introduction.

1.2 A general representation of option prices.

1.3 The dynamics of asset prices.

1.4 A generalized function approach to Fourier pricing.

1.5 Hilbert transform.

1.6 Pricing via FFT.

1.7 Related literature.

2 The Dynamics of Asset Prices.

2.1 Introduction.

2.2 Efficient markets and Lévy processes.

2.3 Construction of Lévy markets.

2.4 Properties of Lévy processes.

3 Non-stationary Market Dynamics.

3.1 Non-stationary processes.

3.2 Time changes.

3.3 Simulation of Lévy processes.

4 Arbitrage-Free Pricing.

4.1 Introduction.

4.2 Equilibrium and arbitrage.

4.3 Arbitrage-free pricing.

4.4 Derivatives.

4.5 Lévy martingale processes.

4.6 Lévy markets.

5 Generalized Functions.

5.1 Introduction.

5.2 The vector space of test functions.

5.3 Distributions.

5.4 The calculus of distributions.

5.5 Slow growth distributions.

5.6 Function convolution.

5.7 Distributional convolution.

5.8 The convolution of distributions in S.

6 The Fourier Transform.

6.1 Introduction.

6.2 The Fourier transformation of functions.

6.3 Fourier transform and option pricing.

6.4 Fourier transform for generalized functions.

6.5 Exercises.

6.6 Fourier option pricing with generalized functions.

7 Fourier Transforms at Work.

7.1 Introduction.

7.2 The Black–Scholes model.

7.3 Finite activity models.

7.4 Infinite activity models.

7.5 Stochastic volatility.

7.6 FFT at work.

Appendices.

A Elements of probability.

A.1 Elements of measure theory.

A.2 Elements of the theory of stochastic processes.

B Elements of Complex Analysis.

B.1 Complex numbers.

B.2 Functions of complex variables.

C Complex Integration.

C.1 Definitions.

C.2 The Cauchy–Goursat theorem.

C.3 Consequences of Cauchy's theorem.

C.4 Principal value.

C.5 Laurent series.

C.6 Complex residue.

C.7 Residue theorem.

C.8 Jordan's Lemma.

D Vector Spaces and Function Spaces.

D.1 Definitions.

D.2 Inner product space.

D.3 Topological vector spaces.

D.4 Functionals and dual space.

E The Fast Fourier Transform.

E.1 Discrete Fourier transform.

E.2 Fast Fourier transform.

F The Fractional Fourier Transform.

F.1 Circular matrix.

F.2 Toepliz matrix.

F.3 Some numerical results.

G Affine Models: The Path Integral Approach.

G.1 The problem.

G.2 Solution of the Riccati equations.

Bibliogrsphy.

Index.

好东西，学习了！！！

好方法,学学

前两天刚在springer上下载了这本书，就看到有人传了上来。这本书确实是一本佳作，不过应该算是专著了。不做相关的研究，估计是不大好看懂其中的某些章节了。作者朱健卫早年在德国求学，后来一直在金融实务机构工作，研究和实务都很优秀。这本书是他的博士论文基础上的丰富而成，相信是期权定价方面很好的一本书了，很推荐大家读读看。

good, useful, thanks

这是Wiley Finance的书。好像从Springer上下不来吧，楼主对作者很了解啊。我都没看出是中国人。

小波分析会更好吗

学习了