Robust Libor Modelling and Pricing of Derivative Products

ARBITRAGE-FREE MODELLING OF EFFECTIVE INTEREST RATES Elements of Arbitrage Theory and Derivative Pricing Modelling of Effective Forward Rates Pricing of Caps and Swaptions in Libor and Swap Market Models PARAMETRISATION OF THE LIBOR MARKET MODEL General Volatility Structures (Quasi) Time-Shift Homogeneous Models Parametrisation of Correlation Structures Some Possible Applications of Parametric Structures IMPLIED CALIBRATION OF A LIBOR MARKET MODEL TO CAPS AND SWAPTIONS Orientation and General Aspects Assessment of the Calibration Problem LSq Calibration and Stability Issues in Practice Regularisation via a Collateral Market Criterion Calibration of a Time-Shift Homogeneous LMM PRICING OF EXOTIC EUROPEAN STYLE PRODUCTS Exotic European Style Products Factor Dependence of Exotic Products Case Studies PRICING OF BERMUDAN STYLE LIBOR DERIVATIVES Orientation The Bermudan Pricing Problem Backward Construction of the Exercise Boundary Iterative Construction of the Optimal Stopping Time Duality; From Tight Lower Bounds to Tight Upper Bounds Monte Carlo Simulation of Upper Bounds Numerical Evaluation of Bermudan Swaptions by Different Methods Efficient Monte Carlo Construction of Upper Bounds Multiple Callable Structures PRICING LONG DATED PRODUCTS VIA LIBOR APPROXIMATIONS Introduction Different Lognormal Approximations Direct Simulation of Lognormal Approximations Efficiency Gain with Respect to SDE Simulation; an Optimal Simulation Program Practical Simulation Examples Summarisation and Final Remarks APPENDIX Glossary of Stochastic Calculus Minimum Search Procedures Additional Proofs REFERENCES INDEX