In
financial economics
Financial economics, also known as finance, 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"Financia ...
, asset pricing refers to a formal treatment and development of two main
pricing principles, outlined below, together with the resultant models.
There have been many models developed for different situations, but correspondingly, these stem from either
general equilibrium asset pricing or
rational asset pricing, the latter corresponding to risk neutral pricing.
Investment theory, which is near synonymous, encompasses the body of knowledge used to support the
decision-making process of choosing
investment
Investment is the dedication of money to purchase of an asset to attain an increase in value over a period of time. Investment requires a sacrifice of some present asset, such as time, money, or effort.
In finance, the purpose of investing is ...
s,
and the asset pricing models are then applied in determining the
asset-specific required rate of return on the investment in question, or in pricing derivatives on these, for trading or
hedging.
(See also .)
General Equilibrium Asset Pricing
Under
General equilibrium theory prices are determined through
market pricing by
supply and demand
In microeconomics, supply and demand is an economic model of price determination in a Market (economics), market. It postulates that, Ceteris paribus, holding all else equal, in a perfect competition, competitive market, the unit price for a ...
. Here asset prices jointly satisfy the requirement that the quantities of each asset supplied and the quantities demanded must be equal at that price - so called
market clearing
In economics, market clearing is the process by which, in an economic market, the supply of whatever is traded is equated to the demand so that there is no excess supply or demand. The new classical economics assumes that in any given market, as ...
. These models are born out of
modern portfolio theory, with the
capital asset pricing model (CAPM) as the prototypical result. Prices here are determined with reference to macroeconomic variables - for the CAPM, the "overall market"; for the
CCAPM, overall wealth - such that individual preferences are subsumed.
These models aim at modeling the statistically derived probability distribution of the market prices of "all" securities at a given future investment horizon; they are thus of "large dimension". See
§ Risk and portfolio management: the P world under
Mathematical finance
Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling of financial markets.
In general, there exist two separate branches of finance that require ...
.
General equilibrium pricing is then used when evaluating diverse portfolios, creating one asset price for many assets.
Calculating an investment or share value here, entails:
(i) a
financial forecast for the business or project in question;
(ii) where the
output cashflows are then
discounted at the rate returned by the model selected; this rate in turn reflecting the "riskiness" - i.e. the
idiosyncratic, or
undiversifiable risk - of these cashflows;
(iii) these present values are then aggregated, returning the value in question.
See: , and
Valuation using discounted cash flows.
(Note that an alternate, although less common approach, is to apply a "fundamental valuation" method, such as the
T-model, which instead relies on accounting information, attempting to model return based on the company's expected financial performance.)
Rational Pricing
Under
Rational pricing, (usually)
derivative prices are calculated such that they are
arbitrage
In economics and finance, arbitrage (, ) is the practice of taking advantage of a difference in prices in two or more markets; striking a combination of matching deals to capitalise on the difference, the profit being the difference between t ...
-free with respect to
more fundamental (equilibrium determined) securities prices;
for an overview of the logic see .
In general this approach does not group assets but rather creates a unique risk price for each asset; these models are then of "low dimension".
For further discussion, see
§ Derivatives pricing: the Q world under Mathematical finance.
Calculating option prices (or their
"Greeks") combines:
(i) a model of the underlying price behavior, or "
process" - ie the asset pricing model selected;
and
(ii) a
mathematical method which returns the premium (or sensitivity) as the
expected value
In probability theory, the expected value (also called expectation, expectancy, mathematical expectation, mean, average, or first moment) is a generalization of the weighted average. Informally, the expected value is the arithmetic mean of a ...
of option payoffs over the range of prices of the underlying.
See .
The classical model here is
Black–Scholes which describes the dynamics of a market including derivatives (with its
option pricing formula); leading more generally to
Martingale pricing, as well as the aside models. Black–Scholes assumes a
log-normal
In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normal distribution, normally distributed. Thus, if the random variable is log-normally distributed, ...
process; the other models will, for example, incorporate features such as
mean reversion, or will be "
volatility surface aware", applying
local volatility or
stochastic volatility.
Rational pricing is also applied to fixed income instruments such as bonds (that consist of just one asset), as well as to interest rate modeling in general, where
yield curves must be arbitrage free
with respect to the prices of individual instruments.
See ,
Bootstrapping (finance),
Multi-curve framework
In finance, an interest rate swap (IRS) is an interest rate derivative (IRD). It involves exchange of interest rates between two parties. In particular it is a "linear" IRD and one of the most liquid, benchmark products. It has associations wi ...
.
As regards options on these instruments, and other
interest rate derivatives, see
short-rate model
A short-rate model, in the context of interest rate derivatives, is a mathematical model that describes the future evolution of interest rates by describing the future evolution of the short rate, usually written r_t \,.
The short rate
Under a s ...
and
Heath–Jarrow–Morton framework for discussion as to how the various models listed above are applied.
Interrelationship
These principles are interrelated through the
Fundamental theorem of asset pricing.
Here, "in the absence of arbitrage, the market imposes a probability distribution, called a risk-neutral or equilibrium measure, on the set of possible market scenarios, and... this probability measure determines market prices via discounted expectation".
[Steven Lalley]
The Fundamental Theorem of Asset Pricing
(course notes). University of Chicago
The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park neighborhood. The University of Chicago is consistently ranked among the b ...
.
Correspondingly, this essentially means that one may make financial decisions, using the risk neutral probability distribution consistent with (i.e. solved for) observed equilibrium prices. See .
Related articles
*
List of financial economics articles
The following outline is provided as an overview of and topical guide to finance:
Finance – addresses the ways in which individuals and organizations raise and allocate monetary resources over time, taking into account the risks entailed ...
*
References
Financial economics
Asset
Pricing
Financial models
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