𝗣𝗗𝗙 | Financial economics, and the calculations of time and uncertainty derived from it, are playing an increasingly important role in. Principles of Financial Economics. Stephen F. LeRoy. University of California, Santa Barbara and. Jan Werner. University of Minnesota. @ March 10, 1 Topographic Surface Anatomy. STUDY AIMS. At the end of your study, you should be able to: Identify the key landmarks.
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PDF Drive is your search engine for PDF files. The Economics of Money, Banking, and Financial Markets (7th Ed).pdf Principles of Financial Economics. PRINCIPLES OF FINANCIAL ECONOMICS. Second Edition. This new edition provides a rigorous yet accessible graduate-level introduction to financial. PRINCIPLES OF FINANCIAL ECONOMICS. The subfield of financial economics is generally understood to be a branch of microeconomic theory and, more.
download Softcover. FAQ Policy. About this Textbook This textbook is an elementary introduction to the key topics in mathematical finance and financial economics - two realms of ideas that substantially overlap but are often treated separately from each other. Show all. Table of contents 21 chapters Table of contents 21 chapters Portfolio Selection: Introductory Comments Evstigneev, Igor V. Pages Mean-Variance Portfolio Analysis: Capital Growth Theory: Continued Evstigneev, Igor V. Show next xx.
Recommended for you. This assumption is useful in pricing fixed income securities, particularly bonds, and is fundamental to the pricing of derivative instruments. Economic equilibrium is, in general, a state in which economic forces such as supply and demand are balanced, and, in the absence of external influences these equilibrium values of economic variables will not change. General equilibrium deals with the behavior of supply, demand, and prices in a whole economy with several or many interacting markets, by seeking to prove that a set of prices exists that will result in an overall equilibrium.
This is in contrast to partial equilibrium, which only analyzes single markets. The two concepts are linked as follows: Intuitively, this may be seen by considering that where an arbitrage opportunity does exist, then prices can be expected to change, and are therefore not in equilibrium. The immediate, and formal, extension of this idea, the fundamental theorem of asset pricing , shows that where markets are as described —and are additionally implicitly and correspondingly complete —one may then make financial decisions by constructing a risk neutral probability measure corresponding to the market.
The formal derivation will proceed by arbitrage arguments. With this measure in place, the expected, i. Thus, continuing the example, to value a specific security, its forecasted cashflows in the up- and down-states are multiplied through by p and 1- p respectively, and are then discounted at the risk-free interest rate plus an appropriate premium.
With the above relationship established, the further specialized Arrow—Debreu model may be derived.
This important result suggests that, under certain economic conditions, there must be a set of prices such that aggregate supplies will equal aggregate demands for every commodity in the economy. The analysis here is often undertaken assuming a representative agent. The Arrow—Debreu model applies to economies with maximally complete markets , in which there exists a market for every time period and forward prices for every commodity at all time periods. A direct extension, then, is the concept of a state price security also called an Arrow—Debreu security , a contract that agrees to pay one unit of a numeraire a currency or a commodity if a particular state occurs "up" and "down" in the simplified example above at a particular time in the future and pays zero numeraire in all the other states.
The price of this security is the state price of this particular state of the world. For a continuous random variable indicating a continuum of possible states, the value is found by integrating over the state price density; see Stochastic discount factor.
These concepts are extended to martingale pricing and the related risk-neutral measure. State prices find immediate application as a conceptual tool " contingent claim analysis " ;  but can also be applied to valuation problems. Breeden and Litzenberger's work in  established the use of state prices in financial economics. Applying the above economic concepts, we may then derive various economic- and financial models and principles. As above, the two usual areas of focus are Asset Pricing and Corporate Finance, the first being the perspective of providers of capital, the second of users of capital.
Here, and for almost all other financial economics models, the questions addressed are typically framed in terms of "time, uncertainty, options, and information",   as will be seen below.
Applying this framework, with the above concepts, leads to the required models. This derivation begins with the assumption of "no uncertainty" and is then expanded to incorporate the other considerations. This division sometimes denoted " deterministic " and "random",  or " stochastic ". The Fisher separation theorem , asserts that the objective of a corporation will be the maximization of its present value, regardless of the preferences of its shareholders.
Related is the Modigliani—Miller theorem , which shows that, under certain conditions, the value of a firm is unaffected by how that firm is financed, and depends neither on its dividend policy nor its decision to raise capital by issuing stock or selling debt. The proof here proceeds using arbitrage arguments, and acts as a benchmark for evaluating the effects of factors outside the model that do affect value.
The mechanism for determining corporate value is provided by The Theory of Investment Value John Burr Williams , which proposes that the value of an asset should be calculated using "evaluation by the rule of present worth". Thus, for a common stock, the intrinsic, long-term worth is the present value of its future net cashflows, in the form of dividends.
What remains to be determined is the appropriate discount rate. Later developments show that, "rationally", i. Net present value NPV is the direct extension of these ideas typically applied to Corporate Finance decisioning introduced by Joel Dean in For other results, as well as specific models developed here, see the list of "Equity valuation" topics under Outline of finance Discounted cash flow valuation.
Bond valuation , in that cashflows coupons and return of principal are deterministic, may proceed in the same fashion. Note that in many treatments bond valuation precedes equity valuation , under which cashflows dividends are not "known" per se.
Williams and onward allow for forecasting as to these — based on historic ratios or published policy — and cashflows are then treated as essentially deterministic; see below under Corporate finance theory. These "certainty" results are all commonly employed under corporate finance; uncertainty is the focus of "asset pricing models", as follows. For "choice under uncertainty" the twin assumptions of rationality and market efficiency , as more closely defined, lead to modern portfolio theory MPT with its capital asset pricing model CAPM —an equilibrium-based result—and to the Black—Scholes—Merton theory BSM; often, simply Black—Scholes for option pricing —an arbitrage-free result.
Note that the latter derivative prices are calculated such that they are arbitrage-free with respect to the more fundamental, equilibrium determined, securities prices; see asset pricing. Briefly, and intuitively—and consistent with Arbitrage-free pricing and equilibrium above—the linkage is as follows. In doing so, traders contribute to more and more "correct", i. The EMH implicitly assumes that average expectations constitute an "optimal forecast", i. The EMH does allow that when faced with new information, some investors may overreact and some may underreact, but what is required, however, is that investors' reactions follow a normal distribution —so that the net effect on market prices cannot be reliably exploited to make an abnormal profit.
In the competitive limit, then, market prices will reflect all available information and prices can only move in response to news;  and this, of course, could be "good" or "bad", major or minor: Thus, if prices of financial assets are broadly efficient, then deviations from these equilibrium values could not last for long.
See Earnings response coefficient. On Random walks in stock prices: Under these conditions investors can then be assumed to act rationally: Here, as under the certainty-case above, the specific assumption as to pricing is that prices are calculated as the present value of expected future dividends,    as based on currently available information.
What is required though is a theory for determining the appropriate discount rate, i. Relatedly, rationality—in the sense of arbitrage-exploitation—gives rise to Black—Scholes; option values here ultimately consistent with the CAPM. In general, then, while portfolio theory studies how investors should balance risk and return when investing in many assets or securities, the CAPM is more focused, describing how, in equilibrium, markets set the prices of assets in relation to how risky they are.
The argument proceeds as follows: If one can construct an efficient frontier —i. Then, given this CML, the required return on risky securities will be independent of the investor's utility function , and solely determined by their covariance "beta" with aggregate, i.
This is because investors here can then maximize utility through leverage as opposed to pricing; see CML diagram. As can be seen in the formula aside, this result is consistent with the preceding , equaling the riskless return plus an adjustment for risk.
Sharpe , John Lintner and Jan Mossin independently. Black—Scholes provides a mathematical model of a financial market containing derivative instruments, and the resultant formula for the price of European-styled options. The model is expressed as the Black—Scholes equation, a partial differential equation describing the changing price of the option over time; it is derived assuming log-normal, geometric Brownian motion see Brownian model of financial markets.
And this price is returned by the Black—Scholes option pricing formula. The formula, and hence the price, is consistent with the equation, as the formula is the solution to the equation. Since the formula is without reference to the share's expected return, Black—Scholes entails assumes risk neutrality, consistent with the "elimination of risk" here.
Relatedly, therefore, the pricing formula may also be derived directly via risk neutral expectation. BSM - two seminal papers   - is consistent with "previous versions of the formula" of Louis Bachelier and Edward O. Thorp ;  although these were more "actuarial" in flavor, and had not established risk-neutral discounting. As mentioned, it can be shown that the two models are consistent; then, as is to be expected, "classical" financial economics is thus unified.
Both models, in turn, are ultimately consistent with the Arrow—Debreu theory, and may be derived via state-pricing,  further explaining, and if required demonstrating, this unity. As regards asset pricing , developments in equilibrium-based pricing are discussed under "Portfolio theory" below, while "Derivative pricing" relates to risk-neutral, i. As regards the use of capital, "Corporate finance theory" relates, mainly, to the application of these models.
The majority of developments here relate to required return, i. Multi-factor models such as the Fama—French three-factor model and the Carhart four-factor model , propose factors other than market return as relevant in pricing.
With intertemporal portfolio choice , the investor now repeatedly optimizes her portfolio; while the inclusion of consumption in the economic sense then incorporates all sources of wealth, and not just market-based investments, into the investor's calculation of required return. Whereas the above extend the CAPM, the single-index model is a more simple model. It assumes, only, a correlation between security and market returns, without numerous other economic assumptions.
It is useful in that it simplifies the estimation of correlation between securities, significantly reducing the inputs for building the correlation matrix required for portfolio optimization. APT "gives up the notion that there is one right portfolio for everyone in the world, and As regards portfolio optimization , the Black—Litterman model departs from the original Markowitz approach of constructing portfolios via an efficient frontier.
Black—Litterman instead starts with an equilibrium assumption, and is then modified to take into account the 'views' i. Where factors additional to volatility are considered kurtosis, skew The universal portfolio algorithm Thomas M. Cover applies machine learning to asset selection, learning adaptively from historical data.
Behavioral portfolio theory recognizes that investors have varied aims and create an investment portfolio that meets a broad range of goals. Copulas have lately been applied here. As regards derivative pricing, the binomial options pricing model provides a discretized version of Black—Scholes, useful for the valuation of American styled options. Discretized models of this type are built—at least implicitly—using state-prices as above ; relatedly, a large number of researchers have used options to extract state-prices for a variety of other applications in financial economics.
Various other numeric techniques have also been developed. The theoretical framework too has been extended such that martingale pricing is now the standard approach. Drawing on these techniques, derivative models for various other underlyings and applications have also been developed, all based off the same logic using " contingent claim analysis ".
Exotic derivatives are now routinely valued. Multi-asset underlyers are handled via simulation or copula based analysis. Similarly, beginning with Oldrich Vasicek , various short rate models , as well as the HJM and BGM forward rate -based techniques, allow for an extension of these techniques to fixed income- and interest rate derivatives. The Vasicek and CIR models are equilibrium-based, while Ho—Lee and subsequent models are based on arbitrage-free pricing.
Bond valuation is relatedly extended: As above, OTC derivative pricing has relied on the BSM risk neutral pricing framework, under the assumptions of funding at the risk free rate and the ability to perfectly replicate cashflows so as to fully hedge. This, in turn, is built on the assumption of a credit-risk-free environment. Post the financial crisis of , therefore, issues such as counterparty credit risk , funding costs and costs of capital are additionally considered,  and a Credit Valuation Adjustment , or CVA—and potentially other valuation adjustments , collectively xVA —is generally added to the risk-neutral derivative value.
This is because post-crisis, OIS is considered a better proxy for the "risk-free rate". Swap pricing - and, in fact, curve construction - is further modified: Corporate finance theory has also been extended: As discussed, Monte Carlo methods in finance , introduced by David B. Relatedly, Real Options theory allows for owner—i. More traditionally, decision trees —which are complementary—have been used to evaluate projects, by incorporating in the valuation all possible events or states and consequent management decisions ;   the correct discount rate here reflecting each point's "non-diversifiable risk looking forward.
Related to this, is the treatment of forecasted cashflows in equity valuation. In more modern treatments, then, it is the expected cashflows in the mathematical sense combined into an overall value per forecast period which are discounted.
Other developments here include  agency theory , which analyses the difficulties in motivating corporate management the "agent" to act in the best interests of shareholders the "principal" , rather than in their own interests. Clean surplus accounting and the related residual income valuation provide a model that returns price as a function of earnings, expected returns, and change in book value , as opposed to dividends.
The typical application of real options is to capital budgeting type problems as described. However, they are also applied to questions of capital structure and dividend policy , and to the related design of corporate securities;  and since stockholder and bondholders have different objective functions, in the analysis of the related agency problems.
For example, convertible bonds can must be priced consistent with the state-prices of the corporate's equity. As above, there is a very close link between i the random walk hypothesis , with the associated expectation that price changes should follow a normal distribution , on the one hand, and ii market efficiency and rational expectations , on the other.
Note, however, that wide departures from these are commonly observed, and there are thus, respectively, two main sets of challenges. Empirical evidence, however, suggests that these assumptions may not hold see Kurtosis risk , Skewness risk , Long tail and that in practice, traders, analysts and risk managers frequently modify the "standard models" see Model risk.
Financial models with long-tailed distributions and volatility clustering have been introduced to overcome problems with the realism of the above "classical" financial models; while jump diffusion models allow for option pricing incorporating "jumps" in the spot price. Portfolio managers, likewise, have modified their optimization criteria and algorithms; see Portfolio theory above. Closely related is the volatility smile , where implied volatility —the volatility corresponding to the BSM price—is observed to differ as a function of strike price i.
The term structure of volatility describes how implied volatility differs for related options with different maturities. An implied volatility surface is then a three-dimensional surface plot of volatility smile and term structure. In consequence traders and risk managers use "smile-consistent" models, firstly, when valuing derivatives not directly mapped to the surface, facilitating the pricing of other, i.
The two main approaches are local volatility and stochastic volatility. In this way calculated prices — and numeric structures — are market-consistent in an arbitrage-free sense. The second approach assumes that the volatility of the underlying price is a stochastic process rather than a constant. This approach addresses certain problems identified with hedging under local volatility. Related to local volatility are the lattice -based implied-binomial and -trinomial trees — essentially a discretization of the approach — which are similarly used for pricing; these are built on state-prices recovered from the surface.
Edgeworth binomial trees allow for a specified i. As above, additional to log-normality in returns, BSM—and, typically, other derivative models—assume d the ability to perfectly replicate cashflows so as to fully hedge, and hence to discount at the risk-free rate. Post crisis, then, various x-value adjustments are made to the risk-neutral derivative value. Note that these are additional to any smile or surface effect: Also, were this not the case, then each counterparty would have its own surface As seen, a common assumption is that financial decision makers act rationally; see Homo economicus.
Recently, however, researchers in experimental economics and experimental finance have challenged this assumption empirically. These assumptions are also challenged theoretically , by behavioral finance , a discipline primarily concerned with the limits to rationality of economic agents. Related to these are various of the economic puzzles , concerning phenomena similarly contradicting the theory. The equity premium puzzle , as one example, arises in that the difference between the observed returns on stocks as compared to government bonds is consistently higher than the risk premium rational equity investors should demand, an " abnormal return ".
More generally, and particularly following the financial crisis of — , financial economics and mathematical finance have been subjected to deeper criticism; notable here is Nassim Nicholas Taleb , who claims that the prices of financial assets cannot be characterized by the simple models currently in use, rendering much of current practice at best irrelevant, and, at worst, dangerously misleading; see Black swan theory , Taleb distribution.
A topic of general interest studied in recent years has thus been financial crises ,  and the failure of financial economics to model these. A related problem is systemic risk: Areas of research attempting to explain or at least model these phenomena, and crises, include  noise trading , market microstructure , and Heterogeneous agent models. The latter is extended to agent-based computational economics , where price is treated as an emergent phenomenon , resulting from the interaction of the various market participants agents.
The noisy market hypothesis argues that prices can be influenced by speculators and momentum traders , as well as by insiders and institutions that often download and sell stocks for reasons unrelated to fundamental value ; see Noise economic. The adaptive market hypothesis is an attempt to reconcile the efficient market hypothesis with behavioral economics, by applying the principles of evolution to financial interactions.
An information cascade , alternatively, shows market participants engaging in the same acts as others " herd behavior " , despite contradictions with their private information. Copula-based modelling has similarly been applied.
On the obverse, however, various studies have shown that despite these departures from efficiency, asset prices do typically exhibit a random walk and that one cannot therefore consistently outperform market averages "alpha". See also John C. Note also that institutionally inherent limits to arbitrage —as opposed to factors directly contradictory to the theory—are sometimes proposed as an explanation for these departures from efficiency.
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See under "External links". Lewin Notices of the AMS 51 5: Culp and John H. A History. Peter Field, ed. Risk Books, Doyne, Geanakoplos John Chance Journal of Business. Eugene F. Random Walks in Stock Market Prices. Journal of Economic Perspectives. A Historical Overview". McGraw-Hill Inc. Journal of Political Economy. Bell Journal of Economics and Management Science.
Industrial Management Review. The Derivatives Discounting Dilemma". Journal of Investment Management. Scenario Analysis, Decision Trees and Simulations". In Strategic Risk Taking: A Framework for Risk Management. Prentice Hall. Management Science. Magee, John F. Harvard Business Review. July Financial Analysts Journal. Ch 13 in Ivo Welch Corporate Finance: Methods and Models in Applied Corporate Finance.
FT Press. Garbade Pricing Corporate Securities as Contingent Claims. MIT Press. Journal of Applied Corporate Finance. The Professional Risk Managers' Handbook: Wilmott Magazine Sep: Jackson, Mary; Mike Staunton Advanced modelling in finance using Excel and VBA. New Jersey: Reinhart and Kenneth S. Rogoff , This Time Is Different: Eight Centuries of Financial Folly , Princeton.