Asset 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)	Capital asset pricing model Consumption-based CAPM Intertemporal CAPM Single-index model Multiple factor models Fama–French three-factor model Carhart four-factor model Arbitrage pricing theory	Black–Scholes Black Garman–Kohlhagen Heston CEV SABR
Bonds, other interest rate instruments	Vasicek Rendleman–Bartter Cox–Ingersoll–Ross	Ho–Lee Hull–White Black–Derman–Toy Black–Karasinski Kalotay–Williams–Fabozzi Longstaff–Schwartz Chen Heath–Jarrow–Morton Cheyette Brace–Gatarek–Musiela LIBOR market model

For the corporate finance usage, see Valuation (finance).

In financial economics, asset pricing refers to a formal treatment and development of two main pricing principles, with the resultant models, outlined below. "Investment theory", which is near synonymous, encompasses the body of knowledge used to support the decision-making process of choosing investments.

The first principle: general equilibrium asset pricing where 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 as the prototypical result.

The second: rational pricing where (usually) derivative prices are calculated such that they are arbitrage-free with respect to more fundamental (equilibrium determined) securities prices; for an overview of the logic, see Rational pricing #Pricing derivatives. 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.

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". Correspondingly, this essentially means that one may make financial decisions, using the risk neutral probability distribution returning observed (equilibrium) prices. See Financial economics #Arbitrage-free pricing and equilibrium.

Both sets of models are extended to more complex phenomena and situations, and asset pricing then overlaps with mathematical finance. Here, corresponding to the above distinction, an important difference is that these use different probabilities: respectively, the real-world (or actuarial) probability, denoted by "P", and the risk-neutral (or arbitrage-pricing) probability, denoted by "Q". For an overview of the development of the CAPM and Black-Scholes, see Financial economics #Uncertainty; for the more advanced approaches, see #Extensions.

See also

• Value (economics)
• Fair value
• Intrinsic value
• Market price
• State prices
  • Pricing kernel
• Equilibrium price
  • market efficiency
  • economic equilibrium
  • rational expectations
  • Risk factor (finance)
• Arbitrage-free price
  • Rational pricing
    • #Arbitrage free pricing
    • #Risk neutral valuation
  • Contingent claim analysis
  • Brownian model of financial markets