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Money market. Capital market --- International finance --- Derivative securities --- Hedging (Finance) --- Instruments dérivés (Finances) --- Prices. --- Prix --- Prices --- Instruments dérivés (Finances) --- Finances --- Derivative securities - Prices --- Option

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Options (Finance) --- Mathematical models --- Interest rate futures --- Securities --- Prices --- Options (Finance) - Mathematical models. --- Interest rate futures - Mathematical models. --- Securities - Prices - Mathematical models. --- Finances --- Option

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A comprehensive overview of the theory of stochastic processes and its connections to asset pricing, accompanied by some concrete applications. This book presents a self-contained, comprehensive, and yet concise and condensed overview of the theory and methods of probability, integration, stochastic processes, optimal control, and their connections to the principles of asset pricing. The book is broader in scope than other introductory-level graduate texts on the subject, requires fewer prerequisites, and covers the relevant material at greater depth, mainly without rigorous technical proofs. The book brings to an introductory level certain concepts and topics that are usually found in advanced research monographs on stochastic processes and asset pricing, and it attempts to establish greater clarity on the connections between these two fields. The book begins with measure-theoretic probability and integration, and then develops the classical tools of stochastic calculus, including stochastic calculus with jumps and Lévy processes. For asset pricing, the book begins with a brief overview of risk preferences and general equilibrium in incomplete finite endowment economies, followed by the classical asset pricing setup in continuous time. The goal is to present a coherent single overview. For example, the text introduces discrete-time martingales as a consequence of market equilibrium considerations and connects them to the stochastic discount factors before offering a general definition. It covers concrete option pricing models (including stochastic volatility, exchange options, and the exercise of American options), Merton's investment-consumption problem, and several other applications. The book includes more than 450 exercises (with detailed hints). Appendixes cover analysis and topology and computer code related to the practical applications discussed in the text.

Securities --- Stochastic processes. --- Valeurs mobilières --- Processus stochastiques --- Prices --- Mathematical models. --- Prix --- Modèles mathématiques --- Stochastic processes --- Mathematical models --- Valeurs mobilières --- Modèles mathématiques --- Cours --- Processus stochastiques. --- Modèles mathématiques. --- Securities - Prices - Mathematical models --- Modèles mathématiques.

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This mathematically elementary introduction to the theory of options pricing presents the Black-Scholes theory of options as well as introducing such topics in finance as the time value of money, mean variance analysis, optimal portfolio selection, and the capital assets pricing model. The author assumes no prior knowledge of probability and presents all the necessary preliminary material simply and clearly. He explains the concept of arbitrage with examples, and then uses the arbitrage theorem, along with an approximation of geometric Brownian motion, to obtain a simple derivation of the Black-Scholes formula. In the later chapters he presents real price data indicating that this model is not always appropriate and shows how the model can be generalized to deal with such situations. No other text presents such topics in a mathematically accurate but accessible way. It will appeal to professional traders as well as undergraduates studying the basics of finance.

Mathematical statistics --- Options (Finance) --- Prices --- Mathematics --- Investments --- Stochastic analysis --- Securities prices --- Mathematical models --- 336.714 --- -Stochastic analysis --- -Securities --- -332.60151 --- Blue sky laws --- Capitalization (Finance) --- Investment securities --- Portfolio --- Scrip --- Securities --- Securities law --- Underwriting --- Investment banking --- Analysis, Stochastic --- Mathematical analysis --- Stochastic processes --- Investing --- Investment management --- Finance --- Disinvestment --- Loans --- Saving and investment --- Speculation --- Beleggingsmaatschappijen. Collectieve beleggingsfondsen. Investeringsmaatschappijen. Investment trusts. Holdingmaatschappijen --- -Mathematical models --- Law and legislation --- Stochastic analysis. --- Mathematics. --- 336.714 Beleggingsmaatschappijen. Collectieve beleggingsfondsen. Investeringsmaatschappijen. Investment trusts. Holdingmaatschappijen --- 332.60151 --- Mathematics of investment --- Business mathematics --- Investments - Mathematics --- Options (Finance) - Mathematical models - Mathematical models --- Securities prices - Mathematical models

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Financial engineering --- Derivative securities --- Finite differences --- Differential equations, Partial --- Instruments dérivés (Finances) --- Différences finies --- Equations aux dérivées partielles --- Mathematics --- Prices --- Mathematical models --- Numerical solutions --- Prix --- Modèles mathématiques --- Solutions numériques --- Instruments dérivés (Finances) --- Différences finies --- Equations aux dérivées partielles --- Modèles mathématiques --- Solutions numériques --- Financial engineering - Mathematics --- Derivative securities - Prices - Mathematical models --- Differential equations, Partial - Numerical solutions