A stochastic investment model tries to forecast how returns

Rate of return

In finance, rate of return , also known as return on investment , rate of profit or sometimes just return, is the ratio of money gained or lost on an investment relative to the amount of money invested. The amount of money gained or lost may be referred to as interest, profit/loss, gain/loss, or...

 and price

Price

-Definition:In ordinary usage, price is the quantity of payment or compensation given by one party to another in return for goods or services.In modern economies, prices are generally expressed in units of some form of currency...

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

Point estimation

In statistics, point estimation involves the use of sample data to calculate a single value which is to serve as a "best guess" or "best estimate" of an unknown population parameter....

 rather interval estimation

Interval estimation

In statistics, interval estimation is the use of sample data to calculate an interval of possible values of an unknown population parameter, in contrast to point estimation, which is a single number. Neyman identified interval estimation as distinct from point estimation...

 and they use different stochastic process

Stochastic process

In probability theory, a stochastic process , or sometimes random process, is the counterpart to a deterministic process...

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

Actuary

An actuary is a business professional who deals with the financial impact of risk and uncertainty. Actuaries provide expert assessments of financial security systems, with a focus on their complexity, their mathematics, and their mechanisms ....

 work and financial plan

Financial plan

In general usage, a financial plan is a series of steps which are carried out, or goals that are accomplished, which relate to an individual's or a business's financial affairs. This often includes a budget which organizes an individual's finances and sometimes includes a series of steps or...

ning to allow optimization in asset allocation

Asset allocation

Asset allocation is an investment strategy that attempts to balance risk versus reward by adjusting the percentage of each asset in an investment portfolio according to the investors risk tolerance, goals and investment time frame.-Description:...

 or asset-liability-management (ALM)

Asset liability management

In banking, asset and liability management is the practice of managing risks that arise due to mismatches between the assets and liabilities of the bank. This can also be seen in insurance....

.

Interest rate models

Interest rate models can be used to price fixed income

Fixed income

Fixed income refers to any type of investment that is not equity, which obligates the borrower/issuer to make payments on a fixed schedule, even if the number of the payments may be variable....

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

One-factor models

• Merton model
  Merton Model
  The Merton model is a model proposed by Robert C. Merton in 1974 for assessing the credit risk of a company by characterizing the company's equity as a call option on its assets...
  
  
• Vasicek model
  Vasicek model
  In finance, the Vasicek model is a mathematical model describing the evolution of interest rates. It is a type of "one-factor model" as it describes interest rate movements as driven by only one source of market risk...
  
  
• Rendleman–Bartter model
• Hull–White model
• Cox–Ingersoll–Ross model
• Ho–Lee model
• Hull–White model
• Black–Derman–Toy model
• Black–Karasinski 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....
  
  
• Kalotay–Williams–Fabozzi model

Term structure models

• LIBOR market model (Brace Gatarek Musiela model)
  LIBOR Market Model
  The LIBOR market model, also known as the BGM Model , is a financial model of interest rates...
  
  

Stock price models

• Black–Scholes model (geometric Brownian motion
  Geometric Brownian motion
  A geometric 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...
  
  )
• Binomial model

Multi-asset models

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