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Over-the-counter (OTC) markets for derivatives, collateralized debt obligations, and repurchase agreements played a significant role in the global financial crisis. Rather than being traded through a centralized institution such as a stock exchange, OTC trades are negotiated privately between market participants who may be unaware of prices that are currently available elsewhere in the market. In these relatively opaque markets, investors can be in the dark about the most attractive available terms and who might be offering them. This opaqueness exacerbated the financial crisis, as regulators and market participants were unable to quickly assess the risks and pricing of these instruments. Dark Markets offers a concise introduction to OTC markets by explaining key conceptual issues and modeling techniques, and by providing readers with a foundation for more advanced subjects in this field. Darrell Duffie covers the basic methods for modeling search and random matching in economies with many agents. He gives an overview of asset pricing in OTC markets with symmetric and asymmetric information, showing how information percolates through these markets as investors encounter each other over time. This book also features appendixes containing methodologies supporting the more theory-oriented of the chapters, making this the most self-contained introduction to OTC markets available.

Over-the-counter markets. --- Capital assets pricing model. --- Capital asset pricing model --- CAPM (Capital assets pricing model) --- Pricing model, Capital assets --- OTC markets --- Over-the-counter securities --- Unlisted securities markets --- Capital --- Finance --- Investments --- Securities --- Mathematical models --- Over-the-counter markets --- Capital assets pricing model --- E-books --- Bellman's principle. --- OTC market. --- OTC trades. --- asset pricing. --- credit risk. --- debt. --- derivatives. --- equilibrium bargaining. --- equilibrium search. --- federal funds market. --- federal loans. --- global financial crisis. --- information exchange. --- interbank market. --- intraday allocation. --- large numbers. --- market opaqueness. --- over-the-counter market. --- percolation. --- posterior beliefs. --- private information. --- random matching. --- repurchase. --- search models. --- supply shocks. --- trading. --- transparency.

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The Mathematics of Finance has been a hot topic ever since the discovery of the Black-Scholes option pricing formulas in 1973. Unfortunately, there are very few undergraduate textbooks in this area. This book is specifically written for advanced undergraduate or beginning graduate students in mathematics, finance or economics. This book concentrates on discrete derivative pricing models, culminating in a careful and complete derivation of the Black-Scholes option pricing formulas as a limiting case of the Cox-Ross-Rubinstein discrete model. This second edition is a complete rewrite of the first edition with significant changes to the topic organization, thus making the book flow much more smoothly. Several topics have been expanded such as the discussions of options, including the history of options, and pricing nonattainable alternatives. In this edition the material on probability has been condensed into fewer chapters, and the material on the capital asset pricing model has been removed. The mathematics is not watered down, but it is appropriate for the intended audience. Previous knowledge of measure theory is not needed and only a small amount of linear algebra is required. All necessary probability theory is developed throughout the book on a "need-to-know" basis. No background in finance is required, since the book contains a chapter on options.

Capital assets pricing model. --- Investments -- Mathematics. --- Options (Finance) -- Prices. --- Portfolio management -- Mathematical models. --- Investments --- Capital assets pricing model --- Portfolio management --- Options (Finance) --- Finance --- Commerce --- Business & Economics --- Accounting --- Economic Theory --- Investment & Speculation --- Mathematics --- Mathematical models --- Prices --- Business mathematics. --- Mathematical models. --- Mathematics. --- Mathematics of investment --- Arithmetic, Commercial --- Business --- Business arithmetic --- Business math --- Commercial arithmetic --- Finance. --- Economics, Mathematical. --- Probabilities. --- Quantitative Finance. --- Probability Theory and Stochastic Processes. --- Finance, general. --- Business mathematics --- Distribution (Probability theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Funding --- Funds --- Economics --- Currency question --- Economics, Mathematical . --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Mathematical economics --- Econometrics --- Methodology

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Asymptotic analysis of stochastic stock price models is the central topic of the present volume. Special examples of such models are stochastic volatility models, that have been developed as an answer to certain imperfections in a celebrated Black-Scholes model of option pricing. In a stock price model with stochastic volatility, the random behavior of the volatility is described by a stochastic process. For instance, in the Hull-White model the volatility process is a geometric Brownian motion, the Stein-Stein model uses an Ornstein-Uhlenbeck process as the stochastic volatility, and in the Heston model a Cox-Ingersoll-Ross process governs the behavior of the volatility. One of the author's main goals is to provide sharp asymptotic formulas with error estimates for distribution densities of stock prices, option pricing functions, and implied volatilities in various stochastic volatility models. The author also establishes sharp asymptotic formulas for the implied volatility at extreme strikes in general stochastic stock price models. The present volume is addressed to researchers and graduate students working in the area of financial mathematics, analysis, or probability theory. The reader is expected to be familiar with elements of classical analysis, stochastic analysis and probability theory.

Capital assets pricing model. --- Global analysis (Mathematics). --- Stocks -- Prices -- Mathematical models. --- Business & Economics --- Economic Theory --- Stock price forecasting --- Stock price indexes. --- Mathematical models. --- Averages, Stock --- Indexes, Stock --- Stock averages --- Stock indexes --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Approximation theory. --- Applied mathematics. --- Engineering mathematics. --- Economics, Mathematical. --- Probabilities. --- Quantitative Finance. --- Analysis. --- Probability Theory and Stochastic Processes. --- Approximations and Expansions. --- Applications of Mathematics. --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Economics --- Mathematical economics --- Econometrics --- Engineering --- Engineering analysis --- Mathematical analysis --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- 517.1 Mathematical analysis --- Math --- Science --- Methodology --- Price indexes --- Finance. --- Distribution (Probability theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Funding --- Funds --- Currency question --- Economics, Mathematical . --- Social sciences --- Mathematics in Business, Economics and Finance. --- Probability Theory.