Financial Economics

Financial economics is the branch of economics characterized by a "concentration on monetary activities", in which "money of one type or another is likely to appear on ''both sides'' of a trade". William F. Sharpe
"Financial Economics"
, in
Its concern is thus the interrelation of financial variables, such as share prices, interest rates and exchange rates, as opposed to those concerning the real economy.
It has two main areas of focus:Merton H. Miller, (1999). The History of Finance: An Eyewitness Account, ''Journal of Portfolio Management''. Summer 1999. asset pricing and corporate finance; the first being the perspective of providers of capital, i.e. investors, and the second of users of capital.
It thus provides the theoretical underpinning for much of finance.

The subject is concerned with "the allocation and deployment of economic resources, both spatially and across time, in an uncertain environment".See Fama and Miller (1972), ''The Theory of Finance'', in Bibliography. It therefore centers on decision making under uncertainty in the context of the financial markets, and the resultant economic and financial models and principles, and is concerned with deriving testable or policy implications from acceptable assumptions.
It thus also includes a formal study of the financial markets themselves, especially market microstructure and market regulation.
It is built on the foundations of microeconomics and decision theory.

Financial econometrics is the branch of financial economics that uses econometric techniques to parameterise the relationships identified.
Mathematical finance is related in that it will derive and extend the mathematical or numerical models suggested by financial economics.
Whereas financial economics has a primarily microeconomic focus, monetary economics is primarily macroeconomic in nature.

Underlying economics

Financial economics studies how rational investors would apply decision theory to investment management. The subject is thus built on the foundations of microeconomics and derives several key results for the application of decision making under uncertainty to the financial markets. The underlying economic logic yields the fundamental theorem of asset pricing, which gives the conditions for arbitrage-free asset pricing.
The aside formulae result directly.
The analysis here is often undertaken assuming a '' representative agent'',

essentially treating all market-participants, " agents", as identical (or, at least, that they act in such a way that the sum of their choices is equivalent to the decision of one individual).

Present value, expectation and utility

Underlying all of financial economics are the concepts of present value and expectation.

Calculating their present value $X_/r$ allows the decision maker to aggregate the cashflows (or other returns) to be produced by the asset in the future to a single value at the date in question, and to thus more readily compare two opportunities; this concept is the starting point for financial decision making.

An immediate extension is to combine probabilities with present value, leading to the expected value criterion which sets asset value as a function of the sizes of the expected payouts and the probabilities of their occurrence, $X_$ and $p_$ respectively.

This decision method, however, fails to consider risk aversion ("as any student of finance knows"). In other words, since individuals receive greater utility from an extra dollar when they are poor and less utility when comparatively rich, the approach is to therefore "adjust" the weight assigned to the various outcomes ("states") correspondingly, $Y_$. See indifference price. (Some investors may in fact be risk seeking as opposed to risk averse, but the same logic would apply).

Choice under uncertainty here may then be characterized as the maximization of expected utility. More formally, the resulting expected utility hypothesis states that, if certain axioms are satisfied, the subjective value associated with a gamble by an individual is ''that individual''s statistical expectation of the valuations of the outcomes of that gamble.

The impetus for these ideas arise from various inconsistencies observed under the expected value framework, such as the St. Petersburg paradox and the Ellsberg paradox.

Arbitrage-free pricing and equilibrium

The concepts of arbitrage-free, "rational", pricing and equilibrium are then coupled with the above to derive "classical"See Rubinstein (2006), under "Bibliography". (or "neo-classical") financial economics.

Rational pricing is the assumption that asset prices (and hence asset pricing models) will reflect the arbitrage-free price of the asset, as any deviation from this price will be "arbitraged away". 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: where market prices do not allow for profitable arbitrage, i.e. they comprise an arbitrage-free market, then these prices are also said to constitute an "arbitrage equilibrium". 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. An arbitrage equilibrium is thus a precondition for a general economic 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. "Complete" here means that there is a price for every asset in every possible state of the world, $s$, and that the complete set of possible bets on future states-of-the-world can therefore be constructed with existing assets (assuming no friction): essentially solving simultaneously for ''n'' (risk-neutral) probabilities, $q_$, given ''n'' prices. The formal derivation will proceed by arbitrage arguments.Freddy Delbaen and Walter Schachermayer. (2004)
"What is... a Free Lunch?"
(pdf). Notices of the AMS 51 (5): 526–528 For a simplified example see , where the economy has only two possible states – up and down – and where $q_$ and $q_$ (=$1-q_$) are the two corresponding probabilities, and in turn, the derived distribution, or "measure".

With this measure in place, the expected, i.e. required, return of any security (or portfolio) will then equal the riskless return, plus an "adjustment for risk", i.e. a security-specific risk premium, compensating for the extent to which its cashflows are unpredictable. All pricing models are then essentially variants of this, given specific assumptions or conditions. This approach is consistent with the above, but with the expectation based on "the market" (i.e. arbitrage-free, and, per the theorem, therefore in equilibrium) as opposed to individual preferences.

Thus, continuing the example, in pricing a derivative instrument its forecasted cashflows in the up- and down-states, $X_$ and $X_$, are multiplied through by $q_$ and $q_$, and are then discounted at the risk-free interest rate; per the second equation above. In pricing a "fundamental", underlying, instrument (in equilibrium), on the other hand, a risk-appropriate premium over risk-free is required in the discounting, essentially employing the first equation with $Y$ and $r$ combined. In general, this premium may be derived by the CAPM (or extensions) as will be seen under #Uncertainty.

The difference is explained as follows: By construction, the value of the derivative will (must) grow at the risk free rate, and, by arbitrage arguments, its value must then be discounted correspondingly; in the case of an option, this is achieved by "manufacturing" the instrument as a combination of the underlying and a risk free "bond"; see (and #Uncertainty below). Where the underlying is itself being priced, such "manufacturing" is of course not possible – the instrument being "fundamental", i.e. as opposed to "derivative" – and a premium is then required for risk.

(Correspondingly, mathematical finance separates into two analytic regimes:
risk and portfolio management (generally) use physical (or actual or actuarial) probability, denoted by "P";
while derivatives pricing uses risk-neutral probability (or arbitrage-pricing probability), denoted by "Q".
In specific applications the lower case is used, as in the above equations.)

State prices

With the above relationship established, the further specialized Arrow–Debreu model may be derived.

This 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 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'' $\pi_$ of this particular state of the world; also referred to as a "Risk Neutral Density".

In the above example, the state prices, $\pi_$, $\pi_$would equate to the present values of $$q_$ and $$q_$: i.e. what one would pay today, respectively, for the up- and down-state securities; the state price vector is the vector of state prices for all states. Applied to derivative valuation, the price today would simply be math>\pi_×$X_$ + $\pi_$×$X_$ the fourth formula (see above regarding the absence of a risk premium here). For a continuous random variable indicating a continuum of possible states, the value is found by integrating over the state price "density". 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.See de Matos, as well as Bossaerts and Ødegaard, under bibliography. Given the pricing mechanism described, one can decompose the derivative value – true in fact for "every security" – as a linear combination of its state-prices; i.e. back-solve for the state-prices corresponding to observed derivative prices.

These recovered state-prices can then be used for valuation of other instruments with exposure to the underlyer, or for other decision making relating to the underlyer itself.

Using the related stochastic discount factor - also called the pricing kernel - the asset price is computed by "discounting" the future cash flow by the stochastic factor $\tilde$, and then taking the expectation;See: David K. Backus of market participants".Katalin Boer, Arie De Bruin, Uzay Kaymak (2005)
"On the Design of Artificial Stock Markets"
''Research In Management'' ERIM Report Series

These Microfoundations">'bottom-up' models "start from first principals of agent behavior",LeBaron, B. (2002)
"Building the Santa Fe artificial stock market"
'' Physica A'', 1, 20. with participants modifying their trading strategies having learned over time, and "are able to describe macro features [i.e. stylized fact">Physica (journal)">Physica A'', 1, 20. with participants modifying their trading strategies having learned over time, and "are able to describe macro features [i.e. stylized facts] Emergence#Economics, emerging from a soup of individual interacting strategies".
Agent-based models depart further from the classical approach — the representative agent, as outlined — in that they introduce heterogeneity into the environment (thereby addressing, also, the aggregation problem).

Challenges and criticism

As above, there is a very close link between (i) the random walk hypothesis, with the associated belief that price changes should follow a normal distribution, on the one hand, and (ii) market efficiency and rational expectations, on the other. Wide departures from these are commonly observed, and there are thus, respectively, two main sets of challenges.

Departures from normality

As discussed, the assumptions that market prices follow a random walk and that asset returns are normally distributed are fundamental. Empirical evidence, however, suggests that these assumptions may not hold, and that in practice, traders, analysts and risk managers frequently modify the "standard models" (see Kurtosis risk, Skewness risk, Long tail, Model risk).
In fact, Benoit Mandelbrot had discovered already in the 1960s

that changes in financial prices do not follow a normal distribution, the basis for much option pricing theory, although this observation was slow to find its way into mainstream financial economics.

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.
Risk managers, similarly, complement (or substitute) the standard value at risk models with historical simulations, mixture models, principal component analysis, extreme value theory, as well as models for volatility clustering.
For further discussion see , and .
Portfolio managers, likewise, have modified their optimization criteria and algorithms; see #Portfolio theory above.

Closely related is the volatility smile, where, as above, implied volatility – the volatility corresponding to the BSM price – is observed to ''differ'' as a function of strike price (i.e. moneyness), true only if the price-change distribution is non-normal, unlike that assumed by BSM.
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.
These empirical phenomena negate the assumption of constant volatility – and log-normality – upon which Black–Scholes is built.
Within institutions, the function of Black-Scholes is now, largely, to ''communicate'' prices via implied volatilities, much like bond prices are communicated via YTM; see .

In consequence traders ( and risk managers) now, instead, use "smile-consistent" models, firstly, when valuing derivatives not directly mapped to the surface, facilitating the pricing of other, i.e. non-quoted, strike/maturity combinations, or of non-European derivatives, and generally for hedging purposes.
The two main approaches are local volatility and stochastic volatility.
The first returns the volatility which is "local" to each spot-time point of the finite difference- or simulation-based valuation; i.e. as opposed to implied volatility, which holds overall. 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. Models here are first calibrated to observed prices, and are then applied to the valuation or hedging in question; the most common are Heston, SABR and CEV. 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, but less commonly, used for pricing; these are built on state-prices recovered from the surface. Edgeworth binomial trees allow for a specified (i.e. non-Gaussian) skew and kurtosis in the spot price; priced here, options with differing strikes will return differing implied volatilities, and the tree can be calibrated to the smile as required.
Similarly purposed (and derived) closed-form models were also developed.

As discussed, additional to assuming log-normality in returns, "classical" BSM-type models also (implicitly) assume the existence of a credit-risk-free environment, where one can perfectly replicate cashflows so as to fully hedge, and then discount at "the" risk-free-rate.
And therefore, post crisis, the various x-value adjustments must be employed, effectively correcting the risk-neutral value for counterparty- and funding-related risk.
These xVA are ''additional'' to any smile or surface effect. This is valid as the surface is built on price data relating to fully collateralized positions, and there is therefore no " double counting" of credit risk (etc.) when appending xVA. (Were this not the case, then each counterparty would have its own surface...)

As mentioned at top, mathematical finance (and particularly financial engineering) is more concerned with mathematical consistency (and market realities) than compatibility with economic theory, and the above "extreme event" approaches, smile-consistent modeling, and valuation adjustments should then be seen in this light. Recognizing this, James Rickards, amongst other critics of financial economics, suggests that, instead, the theory needs revisiting almost entirely:
:"The current system, based on the idea that risk is distributed in the shape of a bell curve, is flawed... The problem is hat economists and practitioners never abandon the bell curve. They are like medieval astronomers who believe the sun revolves around the earth and are furiously tweaking their geo-centric math in the face of contrary evidence. They will never get this right; they need their Copernicus."

Departures from rationality

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.

For related criticisms re corporate finance theory vs its practice see: .

Consistent with, and complementary to these findings, various persistent market anomalies have been documented, these being price or return distortions – e.g. size premiums – which appear to contradict the efficient-market hypothesis; calendar effects are the best known group here. 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". For further context see Random walk hypothesis § A non-random walk hypothesis, and sidebar for specific instances.

More generally, and particularly following the financial crisis of 2007–2008, 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 has thus been financial crises,

and the failure of (financial) economics to model (and predict) these.

A related problem is systemic risk: where companies hold securities in each other then this interconnectedness may entail a "valuation chain" – and the performance of one company, or security, here will impact all, a phenomenon not easily modeled, regardless of whether the individual models are correct. See: Systemic risk § Inadequacy of classic valuation models; Cascades in financial networks; Flight-to-quality.

Areas of research attempting to explain (or at least model) these phenomena, and crises, include noise trading, market microstructure (as above), and Heterogeneous agent models. The latter is extended to agent-based computational models, as mentioned; here For a survey see: LeBaron, Blake (2006)
"Agent-based Computational Finance"''Handbook of Computational Economics''
Elsevier 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 buy 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. See also Hyman Minsky's "financial instability hypothesis", as well as George Soros' application of "reflexivity".

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, i.e. attain "alpha". William F. Sharpe (1991)
"The Arithmetic of Active Management"
. ''Financial Analysts Journal'' Vol. 47, No. 1, January/February The practical implication, therefore, is that passive investing (e.g. via low-cost index funds) should, on average, serve better than any other active strategy. William F. Sharpe (2002)
''Indexed Investing: A Prosaic Way to Beat the Average Investor''
. Presention: Monterey Institute of International Studies. Retrieved May 20, 2010.
Relatedly, 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.

See also

* :Finance theories
* :Financial models
* Deutsche Bank Prize in Financial Economics
*
* Fischer Black Prize
* List of financial economics articles
* List of financial economists
*
* Master of Financial Economics
* Monetary economics
* Outline of economics
* Outline of corporate finance
* Outline of finance

Historical notes

References

Bibliography

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External links

{{Financial risk

Actuarial science