A stochastic investment model tries to forecast how

returns Return may refer to: In business, economics, and finance * Return on investment (ROI), the financial gain after an expense. * Rate of return, the financial term for the profit or loss derived from an investment * Tax return, a blank document o ...

and

price A price is the (usually not negative) quantity of payment or compensation given by one party to another in return for goods or services. In some situations, the price of production has a different name. If the product is a "good" in t ...

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 popu ...

rather

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

and they use different stochastic processes. Investment models can be classified into single-asset and multi-asset models. They are often used for actuarial 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 bud ...

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 investment ...

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 pri ...

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

One-factor models

Black–Derman–Toy model In mathematical finance, the Black–Derman–Toy model (BDT) is a popular short-rate model used in the pricing of bond options, swaptions and other interest rate derivatives; see . It is a one-factor model; that is, a single stochastic factor— ...

Black–Karasinski model In financial mathematics, the Black–Karasinski model is a mathematical model of the term structure of interest rates; see short-rate model. It is a one-factor model as it describes interest rate movements as driven by a single source of randomnes ...

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 ...

Ho–Lee model In financial mathematics, the Ho–Lee model is a short-rate model widely used in the pricing of bond options, swaptions and other interest rate derivatives, and in modeling future interest rates. It was developed in 1986 by Thomas Ho and Sang Bin ...

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 str ...

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 sho ...

Merton model The Merton model, developed by Robert C. Merton in 1974, is a widely used credit risk model. Analysts and investors utilize the Merton model to understand how capable a company is at meeting financial obligations, servicing its debt, and weighing ...

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 so ...

Vasicek model In 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. The model can be ...

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 fi ...

Longstaff–Schwartz 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 sho ...

Term structure models

* LIBOR market model (Brace Gatarek Musiela model)

Stock price models

Binomial model In probability theory and statistics, the binomial distribution with parameters ''n'' and ''p'' is the discrete probability distribution of the number of successes in a sequence of ''n'' independent experiments, each asking a yes–no q ...

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

(

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. ...

)

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 The Wilkie investment model, often just called Wilkie model, is a stochastic asset model developed by A. D. Wilkie that describes the behavior of various economics factors as stochastic time series. These time series are generated by autoregressive ...

* Yakoubov, Teeger & Duval model