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".[1] 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:[2] 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".[3] [4] 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.
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| Fundamental valuation equation | |
Underlying all of financial economics are the concepts of present value and expectation.
Calculating their present value
Xsj/r
r
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,
Xs
ps
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 - i.e. "states" - correspondingly,
Ys
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 individuals 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.
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| JEL classification codes | |
| In the Journal of Economic Literature classification codes, Financial Economics is one of the 19 primary classifications, at JEL: G. It follows Monetary and International Economics and precedes Public Economics. For detailed subclassifications see . The New Palgrave Dictionary of Economics (2008, 2nd ed.) also uses the JEL codes to classify its entries in v. 8, Subject Index, including Financial Economics at pp. 863–64. The below have links to entry abstracts of The New Palgrave Online for each primary or secondary JEL category (10 or fewer per page, similar to Google searches): JEL: G0 – General JEL: G1 – General Financial Markets JEL: G2 – Financial institutions and Services JEL: G3 – Corporate finance and Governance Tertiary category entries can also be searched.[5] |
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
qs
qup
qdown
1-qup
The formal derivation will proceed by arbitrage arguments.[8] [6] 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) with the effect that the problems are then mathematically tractable.
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,
Xup
Xdown
qup
qdown
Y
r
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 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.)
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
\pis
In the above example, the state prices,
\piup
\pidown
$qup
$qdown
State prices find immediate application as a conceptual tool ("contingent claim analysis"); but can also be applied to valuation problems.[9] Given the pricing mechanism described, one can decompose the derivative value – true in fact for "every security"[2] – as a linear combination of its state-prices; i.e. back-solve for the state-prices corresponding to observed derivative prices.[9] [10] 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{m}