A stochastic investment model tries to forecast how returns and

price A price is the (usually not negative) quantity of payment or compensation expected, required, or given by one party to another in return for goods or services. In some situations, especially when the product is a service rather than a ph ...

s on different assets or asset classes, (e. g. equities or bonds) vary over time. Stochastic models are not applied for making

point estimation In statistics, point estimation involves the use of sample data to calculate a single value (known as a point estimate since it identifies a point in some parameter space) which is to serve as a "best guess" or "best estimate" of an unknown popul ...

rather

interval estimation In statistics, interval estimation is the use of sample data to estimate an '' interval'' of possible values of a parameter of interest. This is in contrast to point estimation, which gives a single value. The most prevalent forms of interval es ...

and they use different

stochastic process In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables in a probability space, where the index of the family often has the interpretation of time. Sto ...

es. Investment models can be classified into single-asset and multi-asset models. They are often used for

actuarial Actuarial science is the discipline that applies mathematical and statistical methods to assess risk in insurance, pension, finance, investment and other industries and professions. Actuaries are professionals trained in this discipline. In m ...

work and

financial plan In general usage, a financial plan is a comprehensive evaluation of an individual's current pay and future financial state by using current known variables to predict future income, asset values and withdrawal plans. This often includes a budg ...

ning to allow optimization in

asset allocation Asset allocation is the implementation of an investment strategy that attempts to balance risk versus reward by adjusting the percentage of each asset in an investment portfolio according to the investor's risk tolerance, goals and investm ...

or asset-liability-management (ALM).

Single-asset models

Interest rate models

Interest rate models can be used to price

fixed income Fixed income refers to any type of investment under which the borrower or issuer is obliged to make payments of a fixed amount on a fixed schedule. For example, the borrower may have to pay interest at a fixed rate once a year and repay the pr ...

products. They are usually divided into one-factor models and multi-factor assets.

One-factor models

Black–Derman–Toy model In mathematical finance Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling in the financial field. In general, there exist two separate br ...

* Black–Karasinski model *

Cox–Ingersoll–Ross model In mathematical finance, the Cox–Ingersoll–Ross (CIR) model describes the evolution of interest rates. It is a type of "one factor model" (short-rate model) as it describes interest rate movements as driven by only one source of market risk. T ...

* Ho–Lee model *

Hull–White model In financial mathematics, the Hull–White model is a model of future interest rates. In its most generic formulation, it belongs to the class of no-arbitrage models that are able to fit today's term structure of interest rates. It is relatively st ...

Kalotay–Williams–Fabozzi 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 ...

Merton model Merton may refer to: People * Merton (surname) * Merton (given name) * Merton (YouTube), American YouTube personality Fictional characters * Merton Matowski, an alternate name for "Moose" Mason, an Archie Comics character * Richard Grey, ...

Rendleman–Bartter model The Rendleman–Bartter model (Richard J. Rendleman, Jr. and Brit J. Bartter) in finance is a short-rate model describing the evolution of interest rates. It is a "one factor model" as it describes interest rate movements as driven by only one sour ...

Vasicek model In Mathematical finance, finance, the Vasicek model is a mathematical model describing the evolution of interest rates. It is a type of one-factor short-rate model as it describes interest rate movements as driven by only one source of market risk ...

Multi-factor models

Chen model In finance, the Chen model is a mathematical model describing the evolution of interest rates. It is a type of "three-factor model" (short-rate model) as it describes interest rate movements as driven by three sources of market risk. It was the f ...

* Longstaff–Schwartz model

Term structure models

* LIBOR market model (Brace Gatarek Musiela model)

Stock price models

* Binomial model *

Black–Scholes model The Black–Scholes or Black–Scholes–Merton model is a mathematical model for the dynamics of a financial market containing Derivative (finance), derivative investment instruments. From the parabolic partial differential equation in the model, ...

(

geometric Brownian motion A geometric Brownian motion (GBM) (also known as exponential Brownian motion) is a continuous-time stochastic process in which the logarithm of the randomly varying quantity follows a Brownian motion (also called a Wiener process) with drift. It ...

)

Inflation models

Multi-asset models

* ALM.IT (GenRe) model * Cairns model * FIM-Group model * Global CAP:Link model * Ibbotson and Sinquefield model * Morgan Stanley model * Russel–Yasuda Kasai model * Smith's jump diffusion model * TSM (B & W Deloitte) model * Watson Wyatt model * Whitten & Thomas model * Wilkie investment model * Yakoubov, Teeger & Duval model