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Discovered in the seventies, Black-Scholes formula continues to play a central role in Mathematical Finance. We recall this formula. Let (B ,t? 0; F ,t? 0, P) - t t note a standard Brownian motion with B = 0, (F ,t? 0) being its natural ?ltra- 0 t t tion. Let E := exp B? ,t? 0 denote the exponential martingale associated t t 2 to (B ,t? 0). This martingale, also called geometric Brownian motion, is a model t to describe the evolution of prices of a risky asset. Let, for every K? 0: + ? (t) :=E (K?E ) (0.1) K t and + C (t) :=E (E?K) (0.2) K t denote respectively the price of a European put, resp. of a European call, associated with this martingale. Let N be the cumulative distribution function of a reduced Gaussian variable: x 2 y 1 ? 2 ? N (x) := e dy. (0.3) 2? ?? The celebrated Black-Scholes formula gives an explicit expression of? (t) and K C (t) in terms ofN : K ? ? log(K) t log(K) t ? (t)= KN ? + ?N ? ? (0.4) K t 2 t 2 and ? ?

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The financial market melt-down of the years 2007-2009 has posed great challenges for studies on financial economics. This financial economics text focuses on the dynamic interaction of financial markets and economic activity. The financial market to be studied here encompasses the money and bond market, credit market, stock market and foreign exchange market; economic activity includes the actions and interactions of firms, banks, households, governments and countries. The book shows how economic activity affects asset prices and the financial market, and how asset prices and financial market volatility and crises impact economic activity. The book offers extensive coverage of new and advanced topics in financial economics such as the term structure of interest rates, credit derivatives and credit risk, domestic and international portfolio theory, multi-agent and evolutionary approaches, capital asset pricing beyond consumption-based models, and dynamic portfolio decisions. Moreover a completely new section of the book is dedicated to the recent financial market meltdown of the years 2007-2009. Emphasis is placed on empirical evidence relating to episodes of financial instability and financial crises in the U.S. and in Latin American, Asian and Euro-area countries. Overall, the book explains what researchers and practitioners in the financial sector need to know about the financial-real interaction, and what practitioners and policy makers need to know about the financial market.

In recent decades, the financial markets have experienced various crises, shocks and disruptive events, driving high levels of volatility. This volatility is too strong to be fully justified simply by changes in fundamentals. This volume discusses these highly relevant issues with special focus on asset pricing and behavioral finance. Financial price assets of the 2020s appear to be driven by various attractors in addition to fundamentals, and there is no doubt that investor emotions, market sentiment, the news, and external factors such as uncertainty all play a key role. This has been clearly observed in recent years, especially during the ongoing coronavirus pandemic that has changed the common perception of the way financial markets work.

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