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 or t ...

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

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. Stochastic processes are widely used as mathematical models of systems and phenomena that appea ...

es. Investment models can be classified into single-asset and multi-asset models. They are often used for actuarial work and financial planning 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 ti ...

or asset-liability-management (ALM).

Single-asset models

Interest rate models

Interest rate models can be used to price fixed income 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—t ...

* Black–Karasinski model * Cox–Ingersoll–Ross model * Ho–Lee model * Hull–White model *

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 * Vasicek model

Multi-factor models

* Chen model * 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 investment instruments. From the parabolic partial differential equation in the model, known as the Black� ...

( geometric Brownian motion)

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