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Mathematical Models of Financial Derivatives is a textbook on the theory behind modeling derivatives using the financial engineering approach, focussing on the martingale pricing principles that are common to most derivative securities. A wide range of financial derivatives commonly traded in the equity and fixed income markets are analyzed, emphasizing on the aspects of pricing, hedging and their risk management. Starting from the renowned Black-Scholes-Merton formulation of option pricing model, readers are guided through the text on the new advances on the state-of-the-art derivative pricing models and interest rate models. Both analytic techniques and numerical methods for solving various types of derivative pricing models are emphasized. The second edition presents a substantial revision of the first edition. The continuous-time martingale pricing theory is motivated through analysis of the underlying financial economics principles within a discrete-time framework. A large collection of closed-form formulas of various forms of exotic equity and fixed income derivatives are documented. The most recent research results and methodologies are made accessible to readers through the extensive set of exercises at the end of each chapter. Yue-Kuen Kwok is Professor of Mathematics at Hong Kong University of Science and Technology. He is the author of over 80 research papers and several books, including Applied Complex Variables. He is an associate editor of Journal of Economic Dynamics and Control and Asia-Pacific Financial Markets.

financiële analyse --- stochastische analyse --- toegepaste wiskunde --- Operational research. Game theory --- financiën --- kansrekening --- Financial analysis --- Mathematics --- Finance --- Quantitative methods (economics) --- Derivative securities --- Instruments dérivés (Finances) --- Mathematical models. --- Modèles mathématiques --- EPUB-LIV-FT LIVMATHE LIVSTATI SPRINGER-B --- Public finance. --- Finance. --- Mathematics. --- Distribution (Probability theory. --- Mathematical Modeling and Industrial Mathematics. --- Public Economics. --- Quantitative Finance. --- Finance, general. --- Applications of Mathematics. --- Probability Theory and Stochastic Processes. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Math --- Science --- Funding --- Funds --- Economics --- Currency question --- Cameralistics --- Public finance --- Public finances --- AA / International- internationaal --- 333.605 --- 305.91 --- -332.6457 --- Derivative financial instruments --- Derivative financial products --- Derivative instruments --- Derivatives (Finance) --- Financial derivatives --- Securities --- Structured notes (Securities) --- Nieuwe financiële instrumenten. --- Econometrie van de financiële activa. Portfolio allocation en management. CAPM. Bubbles. --- Mathematical models --- Economics, Mathematical . --- Applied mathematics. --- Engineering mathematics. --- Probabilities. --- Mathematical economics --- Econometrics --- Models, Mathematical --- Simulation methods --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Engineering --- Engineering analysis --- Mathematical analysis --- Methodology --- Nieuwe financiële instrumenten --- Econometrie van de financiële activa. Portfolio allocation en management. CAPM. Bubbles --- -Mathematical models --- Finance, Public. --- Economics, Mathematical.

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This book summarizes recent advances in applying saddlepoint approximation methods to financial engineering. It addresses pricing exotic financial derivatives and calculating risk contributions to Value-at-Risk and Expected Shortfall in credit portfolios under various default correlation models. These standard problems involve the computation of tail probabilities and tail expectations of the corresponding underlying state variables.  The text offers in a single source most of the saddlepoint approximation results in financial engineering, with different sets of ready-to-use approximation formulas. Much of this material may otherwise only be found in original research publications. The exposition and style are made rigorous by providing formal proofs of most of the results. Starting with a presentation of the derivation of a variety of saddlepoint approximation formulas in different contexts, this book will help new researchers to learn the fine technicalities of the topic. It will also be valuable to quantitative analysts in financial institutions who strive for effective valuation of prices of exotic financial derivatives and risk positions of portfolios of risky instruments.  .

Financial engineering. --- Method of steepest descent (Numerical analysis) --- Mathematics. --- Economics, Mathematical. --- Quantitative Finance. --- Approximations, Saddlepoint --- Descent, Method of steepest (Numerical analysis) --- Method of saddle points (Numerical analysis) --- Saddle point method (Numerical analysis) --- Saddle points, Method of (Numerical analysis) --- Saddlepoint approximations --- Saddlepoint method (Numerical analysis) --- Steepest descent method (Numerical analysis) --- Approximation theory --- Asymptotic expansions --- Computational finance --- Engineering, Financial --- Finance --- Finance. --- Funding --- Funds --- Economics --- Currency question --- Economics, Mathematical . --- Mathematical economics --- Econometrics --- Mathematics --- Methodology

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This book summarizes most of the recent research results in pricing models of derivatives on discrete realized variance and VIX..

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