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This book examines whether continuous-time models in frictionless financial economies can be well approximated by discrete-time models. It specifically looks to answer the question: in what sense and to what extent does the famous Black-Scholes-Merton (BSM) continuous-time model of financial markets idealize more realistic discrete-time models of those markets? While it is well known that the BSM model is an idealization of discrete-time economies where the stock price process is driven by a binomial random walk, it is less known that the BSM model idealizes discrete-time economies whose stock price process is driven by more general random walks. Starting with the basic foundations of discrete-time and continuous-time models, David M. Kreps takes the reader through to this important insight with the goal of lowering the entry barrier for many mainstream financial economists, thus bringing less-technical readers to a better understanding of the connections between BSM and nearby discrete-economies.

Finance --- Securities --- Blue sky laws --- Capitalization (Finance) --- Investment securities --- Portfolio --- Scrip --- Securities law --- Underwriting --- Investments --- Investment banking --- Mathematical models. --- Valuation. --- Law and legislation --- Finance - Mathematical models --- Stocks - Prices - Mathematical models --- Discrete-time systems --- Stocks --- Quantitative methods (economics) --- Mathematical statistics --- Prices

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Money market. Capital market --- Stocks --- Efficient market theory --- Actions (Titres de société) --- Marché efficient, Hypothèse du --- Prices --- Mathematical models. --- Prix --- Modèles mathématiques --- Mathematical models --- 336.76 --- -Stocks --- -Efficient market theory --- -332.6322 --- Common shares --- Common stocks --- Equities --- Equity capital --- Equity financing --- Shares of stock --- Stock issues --- Stock offerings --- Stock trading --- Trading, Stock --- Securities --- Bonds --- Corporations --- Going public (Securities) --- Stock repurchasing --- Stockholders --- Market theory, Efficient --- Capital market --- Stock exchanges --- Beurswezen. Geldmarkt. Valutamarkt. Binnenlandse geldmarkt. Valutamarkt --- -Mathematical models --- 336.76 Beurswezen. Geldmarkt. Valutamarkt. Binnenlandse geldmarkt. Valutamarkt --- Actions (Titres de société) --- Marché efficient, Hypothèse du --- Modèles mathématiques --- 332.6322 --- Prices&delete& --- Finance. --- Stocks - Prices - Mathematical models --- Efficient market theory - Mathematical models

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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.

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For over half a century, financial experts have regarded the movements of markets as a random walk--unpredictable meanderings akin to a drunkard's unsteady gait--and this hypothesis has become a cornerstone of modern financial economics and many investment strategies. Here Andrew W. Lo and A. Craig MacKinlay put the Random Walk Hypothesis to the test. In this volume, which elegantly integrates their most important articles, Lo and MacKinlay find that markets are not completely random after all, and that predictable components do exist in recent stock and bond returns. Their book provides a state-of-the-art account of the techniques for detecting predictabilities and evaluating their statistical and economic significance, and offers a tantalizing glimpse into the financial technologies of the future. The articles track the exciting course of Lo and MacKinlay's research on the predictability of stock prices from their early work on rejecting random walks in short-horizon returns to their analysis of long-term memory in stock market prices. A particular highlight is their now-famous inquiry into the pitfalls of "data-snooping biases" that have arisen from the widespread use of the same historical databases for discovering anomalies and developing seemingly profitable investment strategies. This book invites scholars to reconsider the Random Walk Hypothesis, and, by carefully documenting the presence of predictable components in the stock market, also directs investment professionals toward superior long-term investment returns through disciplined active investment management.

Stocks --- Random walks (Mathematics) --- Prices --- Mathematical models --- Financial organisation --- Additive process (Probability theory) --- Random walk process (Mathematics) --- Walks, Random (Mathematics) --- Stochastic processes --- Mathematical models. --- 305.91 --- 333.613 --- 333.645 --- 339.42 --- AA / International- internationaal --- 336.76 --- 336.76 Beurswezen. Geldmarkt. Valutamarkt. Binnenlandse geldmarkt. Valutamarkt --- Beurswezen. Geldmarkt. Valutamarkt. Binnenlandse geldmarkt. Valutamarkt --- Common shares --- Common stocks --- Equities --- Equity capital --- Equity financing --- Shares of stock --- Stock issues --- Stock offerings --- Stock trading --- Trading, Stock --- Securities --- Bonds --- Corporations --- Going public (Securities) --- Stock repurchasing --- Stockholders --- Prices&delete& --- Econometrie van de financiële activa. Portfolio allocation en management. CAPM. Bubbles --- Activiteiten van de nationale en internationale markten. Beursnoteringen van aandelen en obligaties --- Speculatie op de beurs --- Financiële analyse --- Beleggen. --- Stocks - Prices - Mathematical models