Quantitative analysis in financial markets : collected papers of the New York University Mathematical Finance Seminar. Volume II

This invaluable 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. Pt. I. Models and model selection -- Multivariate binomial approximations for asset prices with nonstationary variance and covariance characteristics / Marti G. Subrahmanyam, Teng-Suan Ho and Richard C. Stapleton -- Deriving closed-form solutions for Gaussian pricing models: a systematic time-domain approach / Alexander Levin -- Models for estimating the structure of interest rates from observations of yield curves / K.O. Kortanek and V.G. Medvedev -- Calibrating volatility surfaces via relative-entropy minimization / Marco Avellaneda [und weitere] -- pt. II. Option pricing and exotics -- Static hedging of exotic options / Peter Carr, Katrina Ellis and Vishal Gupta -- Closed form formulas for exotic options and their lifetime distribution / Raphael Douady -- Asian options, the sum of lognormals, and the reciprocal gamma distribution / Steven E. Posner and Moshe Arye Milevsky -- Pricing and hedging American options: a recursive integration method / Marti G. Subrahmanyam, Jing-zhi Huang and G. George Yu -- pt. III. Estimation of time series -- Piecewise convex function estimation: pilot estimators / Kurt S. Riedel -- Function estimation using data-adaptive kernel smoothers - how much smoothing? / Kurt S. Riedel and A. Sidorenko -- pt. IV. Empirical studies and options -- E-ARCH model for implied volatility term structure of FX options / Yingzi Zhu and Marco Avellaneda -- A test of efficiency for the currency option market using stochastic volatility forecasts / Dajiang Guo -- Portfolio-based risk pricing: pricing long-term put options with GJR-GARCH(1,1)/jump diffusion process / Dajiang Guo and Sergei Esipov -- pt. V. Financial economics and portfolio theory -- The existence of equilibrium in a financial market with transaction costs / Xing Jin and Frank Milne -- Portfolio generating functions / Robert Fernholz Multivariate Binomial Approximations for Asset Prices with Nonstationary Variance and Covariance Characteristics / Marti G. Subrahmanyam, Teng-Suan Ho and Richard C. Stapleton -- Deriving Closed-Form Solutions for Gaussian Pricing Models: A Systematic Time-Domain Approach / Alexander Levin -- Models for Estimating the Structure of Interest Rates from Observations of Yield Curves / K. O. Kortanek and V. G. Medvedev -- Calibrating Volatility Surface via Relative-Entropy Minimization / Marco Avellaneda, Craig Friedman and Richard Holmes / [et al.] -- Static Hedging of Exotic Options / Peter Carr, Katrina Ellis and Vishal Gupta -- Closed Form Formulas for Exotic Options and Their Lifetime Distribution / Raphael Douady -- Asian Options, the Sum of Lognormals, and the Reciprocal Gamma Distribution / Steven E. Posner and Moshe Arye Milevsky -- Pricing and Hedging American Options: A Recursive Integration Method / Marti G. Subrahmanyam, Jing-zhi Huang and G. George Yu -- Piecewise Convex Function Estimation: Pilot Estimators / Kurt S. Riedel -- Function Estimation Using Data-Adaptive Kernel Smoothers -- How Much Smoothing? / Kurt S. Riedel and A. Sidorenko -- E-ARCH Model for Implied Volatility Term Structure of FX Options / Yingzi Zhu and Marco Avellaneda -- Test of Efficiency for the Currency Option Market Using Stochastic Volatility Forecasts / Dajiang Guo -- Portfolio-Based Risk Pricing: Pricing Long-Term Put Options with GJR-GARCH(1,1)/Jump Diffusion Process / Dajiang Guo and Sergei Esipov -- Existence of Equilibrium in a Financial Market with Transaction Costs / Xing Jin and Frank Milne -- Portfolio Generating Functions / Robert Fernholz. Pt. I. Estimation and data-driven models. Transition densities for interest rate and other nonlinear diffusions / Yacine Ait-Sahalia -- Hidden Markov experts / Andreas Weigend and Shanming Shi -- When is time continuous? / Dimitris Bertsimas, Leonid Kogan and Andrew Lo -- Asset prices are Brownian motion: only in business time / Helyette Geman, Dilip Madan and Marc Yor -- Hedging under stochastic volatility / K. Ronnie Sircar -- pt. II. Model calibration and volatility smile. Determining volatility surfaces and option values from an implied volatility smile / Peter Carr and Dilip Madan -- Reconstructing the unknown local volatility function / Thomas Coleman, Yuying Li and Arun Verma -- Building a consistent pricing model from observed option prices / Jean-Paul Laurent and Dietmar Leisen -- Weighted Monte Carlo: a new technique for calibrating asset-pricing models / Marco Avellaneda [und weitere] -- pt. III. Pricing and risk management. One- and multi-factor valuation of mortgages: computational problems and shortcuts / Alexander Levin -- Simulating Bermudan interest-rate derivatives / Peter Carr and Guang Yang -- How to use self-similarities to discover similarities of path-dependent options / Alexander Lipton -- Monte Carlo within a day / Juan Cardenas [und weitere] -- Decomposition and search techniques in disjunctive programs for portfolio selection / Katherine Wyatt Introduction 6 Acknowledgements 8 The Contributors 10 CONTENTS 18 Part I Estimation and Data-Driven Models 20 Transition Densities for Interest Rate and Other Nonlinear Diffusions 20 Hidden Markov Experts 54 When is Time Continuous? 90 Asset Prices Are Brownian Motion: Only in Business Time 122 Hedging under Stochastic Volatility 166 Part II Model Calibration and Volatility Smile 182 Determining Volatility Surfaces and Option Values From an Implied Volatility Smile 182 Reconstructing the Unknown Local Volatility Function 211 Building a Consistent Pricing Model from Observed Option Prices 235 Weighted Monte Carlo: A New Technique for Calibrating Asset-Pricing Models 258 Part III Pricing and Risk Management 285 One- and Multi-Factor Valuation of Mortgages: Computational Problems and Shortcuts 285 Simulating Bermudan Interest-Rate Derivatives 314 How to Use Self-Similarities to Discover Similarities of Path-Dependent Options 336 Monte Carlo Within a Day 354 Decomposition and Search Techniques in Disjunctive Programs for Portfolio Selection 365 Annotation This invaluable book contains lectures delivered at the celebrated Seminar in Mathematical Finance at the Courant Institute. The lectures 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 This volume 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 modelling. 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 modelling, portfolio theory, price forecasting using statistical methods, and more 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 This volume contains lectures on quantitative financial analysis in financial markets, delivered at the Seminar in Mathematical Finance at the Courant Institute. The lectures deal with the emerging science of pricing and hedging derivative securities and, more generally, managing financial risk. Continuous-time modeling in finance, though introduced by Louis Bachelier's 1900 thesis on the theory of speculation, really started with Merton's seminal work in the 1970s. In practice, many problems in the valuation of the derivative assets are solved by using binomial approximations to continuous distributions.