Applies advanced analytical and geometrical methods used in physics and mathematics to the financial field. This work introduces tools and methods, including differential geometry, spectral decomposition, and supersymmetry, and applies these methods to practical problems in finance. It focuses on the calibration and dynamics of implied volatility.
Applies advanced analytical and geometrical methods used in physics and mathematics to the financial field. This work introduces tools and methods, including differential geometry, spectral decomposition, and supersymmetry, and applies these methods to practical problems in finance. It focuses on the calibration and dynamics of implied volatility.
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.
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.
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