金融における解析、幾何学とモデリング：オプション・プライシングの上級手法 Analysis, Geometry, and Modeling in Finance : Advanced Methods in Option Pricing (Chapman and Hall/crc Financial Mathematics Series)

Henry-Labordère, Pierre

Chapman & Hall/CRC（2008/09発売）

• 製本 Hardcover:ハードカバー版／ページ数 402 p.
• 言語 ENG
• 商品コード 9781420086997
• DDC分類 332.64

Full Description

Analysis, Geometry, and Modeling in Finance: Advanced Methods in Option Pricing is the first book that applies advanced analytical and geometrical methods used in physics and mathematics to the financial field. It even obtains new results when only approximate and partial solutions were previously available.

Through the problem of option pricing, the author introduces powerful tools and methods, including differential geometry, spectral decomposition, and supersymmetry, and applies these methods to practical problems in finance. He mainly focuses on the calibration and dynamics of implied volatility, which is commonly called smile. The book covers the Black-Scholes, local volatility, and stochastic volatility models, along with the Kolmogorov, Schrödinger, and Bellman-Hamilton-Jacobi equations.

Providing both theoretical and numerical results throughout, this book offers new ways of solving financial problems using techniques found in physics and mathematics.

Contents

Introduction. A Brief Course in Financial Mathematics. Smile Dynamics and Pricing of Exotic Options. Differential Geometry and Heat Kernel Expansion. Local Volatility Models and Geometry of Real Curves. Stochastic Volatility Models and Geometry of Complex Curves. Multi-Asset European Option and Flat Geometry. Stochastic Volatility Libor Market Models and Hyperbolic Geometry. Solvable Local and Stochastic Volatility Models. Schrödinger Semigroups Estimates and Implied Volatility Wings. Analysis on Wiener Space with Applications. Portfolio Optimization and Bellman-Hamilton-Jacobi Equation. Appendices. References. Index.