This book contains lectures delivered at the celebrated Seminar in Mathematical Finance at the Courant Institute. The lecturers and presenters of papers are prominent researchers and practitioners in the field of quantitative financial modeling. Most are faculty members at leading universities or Wall Street practitioners. The lectures deal with the emerging science of pricing and hedging derivative securities and, more generally, managing financial risk. Specific articles concern topics such as option theory, dynamic hedging, interest-rate modeling, portfolio theory, price forecasting using statistical methods, etc. Sample Chapter(s). Introduction (37 KB). Part 1.1: Closed-Form Approximations to the Transition Function (209 KB). Part 1.2: Examples (605 KB). Part 1.3: The Estimation of interest Rate Diffusions (158 KB). Part 1.4: Conclusion (203 KB). Contents: Estimation and Data-Driven Models: Transition Densities for Interest Rate and Other Nonlinear Diffusions (Y Aït-Sahalia); Hidden Markov Experts (A Weigend & S-M Shi); When is Time Continuous? (A Lo et al.); Asset Prices are Brownian Motion: Only in Business Time (H Geman et al.); Hedging Under Stochastic Volatility (K Ronnie Sircar); Model Calibration and Volatility Smile: Determining Volatility Surfaces and Option Values from an Implied Volatility Smile (P Carr & D Madan); Reconstructing the Unknown Local Volatility Function (T Coleman et al.); Building a Consistent Pricing Model from Observed Option Prices (J-P Laurent & D Leisen); Weighted Monte Carlo: A New Technique for Calibrating Asset-Pricing Models (M Avellaneda et al.); Pricing and Risk Management: One- and Multi-Factor Valuation of Mortgages: Computational Problems and Shortcuts (A Levin); Simulating Bermudan Interest-Rate Derivatives (P Carr & G Yang); How to Use Self-Similarities to Discover Similarities of Path-Dependent

Options (A Lipton); Monte Carlo Within a Day (J Cárdenas et al.); Decomposition and Search Techniques in Disjunctive Programs for Portfolio Selection (K Wyatt). Readership: Students and researchers in economics, finance and applied mathematics.