A stochastic investment model tries to forecast how returns 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 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 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 prin ...

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

One-factor models

* Black–Derman–Toy model *

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 randomness ...

* Cox–Ingersoll–Ross model * Ho–Lee model * Hull–White model * Kalotay–Williams–Fabozzi model *

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 u ...

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 ( 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