# Asset pricing

In financial economics, asset pricing refers to a formal treatment and development of two main pricing principles, [1] outlined below, together with the resultant models. There have been many models developed for different situations, but correspondingly, these stem from general equilibrium asset pricing or rational asset pricing[2], the latter corresponding to risk neutral pricing.

Asset pricing models
Regime

Asset class
Equilibrium
pricing
Risk neutral
pricing

Equities

(and foreign exchange and commodities (and interest rates) for risk neutral pricing)

Bonds, other interest rate instruments
This article is theory focused: for the corporate finance usage see Valuation (finance); for the valuation of derivatives and interest rate / fixed income instruments see Mathematical finance.

Investment theory, which is near synonymous, encompasses the body of knowledge used to support the decision-making process of choosing investments,[3] 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.

## General Equilibrium Asset Pricing

Under General equilibrium theory prices are determined through market pricing by supply and demand. 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. 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. General equilibrium pricing is then used when evaluating diverse portfolios, creating one asset price for many assets. [4]

Calculating an investment or share value here, entails a financial forecast for the business or project in question, where the output cashflows are then discounted at the rate returned by the model selected, and then aggregated; this rate in turn reflecting the "riskiness" of these cashflows. See Financial modeling#Accounting, 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-free with respect to more fundamental (equilibrium determined) securities prices. For further discussion, see Mathematical finance #Derivatives pricing: the Q world; for an overview of the logic, see Rational pricing #Pricing derivatives. Rational pricing is also applied to fixed income instruments, such as bonds, that consist of just one asset; see Rational pricing #Fixed income securities. In general this approach does not group assets but rather creates a unique risk price for each asset.

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 a function of this behavior. See Valuation of options #Pricing models.

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 process; the other models will, for example, incorporate features such as mean reversion, or will be "volatility surface aware".

## 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". [5]

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 Financial economics #Arbitrage-free pricing and equilibrium.