Category: Financial models

Black–Scholes model
The Black–Scholes /ˌblæk ˈʃoʊlz/ or Black–Scholes–Merton model is a mathematical model for the dynamics of a financial market containing derivative investment instruments. From the parabolic partial d
Goldman Sachs asset management factor model
Goldman Sachs asset management (GSAM) factor model is one of the quantitative/ factor models used by financial analysts to assess the performance and financial condition of a company. Typically are ba
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 inte
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
Constant elasticity of variance model
In mathematical finance, the CEV or constant elasticity of variance model is a stochastic volatility model that attempts to capture stochastic volatility and the leverage effect. The model is widely u
Chepakovich valuation model
The Chepakovich valuation model is a specialized discounted cash flow valuation model, originally designed for the valuation of “growth stocks” (ordinary/common shares of companies experiencing high r
Heath–Jarrow–Morton framework
The Heath–Jarrow–Morton (HJM) framework is a general framework to model the evolution of interest rate curves – instantaneous forward rate curves in particular (as opposed to simple forward rates). Wh
Johnson binomial tree
No description available.
Capital asset pricing model
In finance, the capital asset pricing model (CAPM) is a model used to determine a theoretically appropriate required rate of return of an asset, to make decisions about adding assets to a well-diversi
Hamada's equation
In corporate finance, Hamada’s equation is an equation used as a way to separate the financial risk of a levered firm from its business risk. The equation combines the Modigliani–Miller theorem with t
Implied binomial tree
No description available.
Return on modeling effort
Return on modelling effort (ROME) is the benefit resulting from a (supplementary) effort to create and / or improve a model.
Barone-Adesi and Whaley
No description available.
Bootstrapping (finance)
In finance, bootstrapping is a method for constructing a (zero-coupon) fixed-income yield curve from the prices of a set of coupon-bearing products, e.g. bonds and swaps. A bootstrapped curve, corresp
Omega ratio
The Omega ratio is a risk-return performance measure of an investment asset, portfolio, or strategy. It was devised by Con Keating and William F. Shadwick in 2002 and is defined as the probability wei
Binomial options pricing model
In finance, the binomial options pricing model (BOPM) provides a generalizable numerical method for the valuation of options. Essentially, the model uses a "discrete-time" (lattice based) model of the
Brownian model of financial markets
The Brownian motion models for financial markets are based on the work of Robert C. Merton and Paul A. Samuelson, as extensions to the one-period market models of Harold Markowitz and William F. Sharp
Single-index model
The single-index model (SIM) is a simple asset pricing model to measure both the risk and the return of a stock. The model has been developed by William Sharpe in 1963 and is commonly used in the fina
Fama–French three-factor model
In asset pricing and portfolio management the Fama–French three-factor model is a statistical model designed in 1992 by Eugene Fama and Kenneth French to describe stock returns. Fama and French were c
Black's approximation
In finance, Black's approximation is an approximate method for computing the value of an American call option on a stock paying a single dividend. It was described by Fischer Black in 1975. The Black–
Dividend discount model
In finance and investing, the dividend discount model (DDM) is a method of valuing the price of a company's stock based on the fact that its stock is worth the sum of all of its future dividend paymen
Martingale pricing
Martingale pricing is a pricing approach based on the notions of martingale and risk neutrality. The martingale pricing approach is a cornerstone of modern quantitative finance and can be applied to a
Jarrow–Turnbull model
The Jarrow–Turnbull model is a widely used "reduced-form" credit risk model. It was published in 1995 by Robert A. Jarrow and Stuart Turnbull. Under the model, which returns the corporate's probabilit
Carr–Madan formula
In financial mathematics, the Carr–Madan formula of Peter Carr and Dilip B. Madan shows that the analytical solution of the European option price can be obtained once the explicit form of the characte
Mid-year adjustment
No description available.
Garman-Kohlhagen model
No description available.
Drawdown (economics)
The drawdown is the measure of the decline from a historical peak in some variable (typically the cumulative profit or total open equity of a financial trading strategy). Somewhat more formally, if is
Black model
The Black model (sometimes known as the Black-76 model) is a variant of the Black–Scholes option pricing model. Its primary applications are for pricing options on future contracts, bond options, inte
Cheyette model
In mathematical finance, the Cheyette Model is a quasi-Gaussian, quadratic volatility model of interest rates intended to overcome certain limitations of the Heath-Jarrow-Morton framework. By imposing
Black–Scholes equation
In mathematical finance, the Black–Scholes equation is a partial differential equation (PDE) governing the price evolution of a European call or European put under the Black–Scholes model. Broadly spe
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 Lattice model (finance)
Intertemporal CAPM
Within mathematical finance, the Intertemporal Capital Asset Pricing Model, or ICAPM, is an alternative to the CAPM provided by Robert Merton. It is a linear factor model with wealth as state variable
Markowitz model
In finance, the Markowitz model ─ put forward by Harry Markowitz in 1952 ─ is a portfolio optimization model; it assists in the selection of the most efficient portfolio by analyzing various possible
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 movem
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 wa
Affine term structure model
An affine term structure model is a financial model that relates zero-coupon bond prices (i.e. the discount curve) to a spot rate model. It is particularly useful for deriving the yield curve – the pr
Black–Litterman model
In finance, the Black–Litterman model is a mathematical model for portfolio allocation developed in 1990 at Goldman Sachs by Fischer Black and Robert Litterman, and published in 1992. It seeks to over
Financial modeling
Financial modeling is the task of building an abstract representation (a model) of a real world financial situation. This is a mathematical model designed to represent (a simplified version of) the pe
Bjerksund and Stensland
No description available.
Multiple factor models
In mathematical finance, multiple factor models are asset pricing models that can be used to estimate the discount rate for the valuation of financial assets. They are generally extensions of the sing
Fama–MacBeth regression
The Fama–MacBeth regression is a method used to estimate parameters for asset pricing models such as the capital asset pricing model (CAPM). The method estimates the betas and risk premia for any risk
Jamshidian's trick
Jamshidian's trick is a technique for one-factor asset price models, which re-expresses an option on a portfolio of assets as a portfolio of options. It was developed by Farshid Jamshidian in 1989. Th
Margrabe's formula
In mathematical finance, Margrabe's formula is an option pricing formula applicable to an option to exchange one risky asset for another risky asset at maturity. It was derived by William Margrabe (Ph
Mark to model
Mark-to-Model refers to the practice of pricing a position or portfolio at prices determined by financial models, in contrast to allowing the market to determine the price. Often the use of models is
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. T
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 st
Multi-curve framework
No description available.
Model audit
A model audit is the colloquial term for the tasks performed when conducting due diligence on a financial model, in order to eliminate spreadsheet error. Model audits are sometimes referred to as mode
Longstaff–Schwartz model
No description available.
Stochastic volatility jump
In mathematical finance, the stochastic volatility jump (SVJ) model is suggested by Bates. This model fits the observed implied volatility surface well. The model is a Heston process for stochastic vo
Stochastic investment model
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 poin
SABR volatility model
In mathematical finance, the SABR model is a stochastic volatility model, which attempts to capture the volatility smile in derivatives markets. The name stands for "stochastic alpha, beta, rho", refe
Financial Modelers' Manifesto
The Financial Modelers' Manifesto was a proposal for more responsibility in risk management and quantitative finance written by financial engineers Emanuel Derman and Paul Wilmott. The manifesto inclu
Arrow–Debreu model
In mathematical economics, the Arrow–Debreu model suggests that under certain economic assumptions (convex preferences, perfect competition, and demand independence) there must be a set of prices such
Kalotay–Williams–Fabozzi model
No description available.
Arbitrage pricing theory
In finance, arbitrage pricing theory (APT) is a multi-factor model for asset pricing which relates various macro-economic (systematic) risk variables to the pricing of financial assets. Proposed by ec
Carhart four-factor model
In portfolio management, the Carhart four-factor model is an extra factor addition in the Fama–French three-factor model, proposed by Mark Carhart. The Fama-French model, developed in the 1990, argued
Datar–Mathews method for real option valuation
The Datar–Mathews Method (DM Method) is a method for real options valuation. The method provides an easy way to determine the real option value of a project simply by using the average of positive out
Expected shortfall
Expected shortfall (ES) is a risk measure—a concept used in the field of financial risk measurement to evaluate the market risk or credit risk of a portfolio. The "expected shortfall at q% level" is t
Lattice model (finance)
In finance, a lattice model is a technique applied to the valuation of derivatives, where a discrete time model is required. For equity options, a typical example would be pricing an American option,
Model risk
In finance, model risk is the risk of loss resulting from using insufficiently accurate models to make decisions, originally and frequently in the context of valuing financial securities. However, mod
Vanna–Volga pricing
The Vanna–Volga method is a mathematical tool used in finance. It is a technique for pricing first-generation exotic options in foreign exchange market (FX) derivatives.
Treynor–Black model
In Finance the Treynor–Black model is a mathematical model for security selection published by Fischer Black and Jack Treynor in 1973. The model assumes an investor who considers that most securities
No description available.
Smith–Wilson method
The Smith–Wilson method is a method for extrapolating forward rates. It is recommended by EIOPA to extrapolate interest rates. It was introduced in 2000 by A. Smith and T. Wilson for .
Adjusted present value
Adjusted present value (APV) is a valuation method introduced in 1974 by Stewart Myers. The idea is to value the project as if it were all equity financed ("unleveraged"), and to then add the present
No description available.
Trinomial tree
The trinomial tree is a lattice-based computational model used in financial mathematics to price options. It was developed by Phelim Boyle in 1986. It is an extension of the binomial options pricing m
Edgeworth binomial tree
No description available.
Brace-Gatarek-Musiela model
No description available.
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
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
Project finance model
A project finance model is a specialized financial model, the purpose of which is to assess the economic feasibility of the project in question. The model's output can also be used in structuring, or
Asset pricing
In financial economics, asset pricing refers to a formal treatment and development of two main pricing principles, outlined below, together with the resultant models. There have been many models devel
LIBOR market model
The LIBOR market model, also known as the BGM Model (Brace Gatarek Musiela Model, in reference to the names of some of the inventors) is a financial model of interest rates. It is used for pricing int
Korn–Kreer–Lenssen model
The Korn–Kreer–Lenssen model (KKL model) is a discrete trinomial model proposed in 1998 by Ralf Korn, Markus Kreer and Mark Lenssen to model illiquid securities and to value financial derivatives on t
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
Fuzzy pay-off method for real option valuation
The fuzzy pay-off method for real option valuation (FPOM or pay-off method) is a method for valuing real options, developed by Mikael Collan, Robert Fullér, and József Mezei; and published in 2009. It
Financial models with long-tailed distributions and volatility clustering
Financial models with long-tailed distributions and volatility clustering have been introduced to overcome problems with the realism of classical financial models. These classical models of financial
Heston model
In finance, the Heston model, named after Steven L. Heston, is a mathematical model that describes the evolution of the volatility of an underlying asset. It is a stochastic volatility model: such a m
Implied trinomial tree
No description available.
Chan–Karolyi–Longstaff–Sanders process
In mathematics, the Chan–Karolyi–Longstaff–Sanders process (abbreviated as CKLS process) is a stochastic process with applications to finance. In particular it has been used to model the term structur
In finance, the T-model is a formula that states the returns earned by holders of a company's stock in terms of accounting variables obtainable from its financial statements. The T-model connects fund
PSA prepayment model
The PSA Prepayment Model is a prepayment scale developed by the Public Securities Association in 1985 for analyzing American mortgage-backed securities. The PSA model assumes increasing prepayment rat
Bachelier model
The Bachelier model is a model of an asset price under brownian motion presented by Louis Bachelier on his PhD thesis The Theory of Speculation (Théorie de la spéculation, published 1900). It is also
Consumption-based capital asset pricing model
The consumption-based capital asset pricing model (CCAPM) is a model of the determination of expected (i.e. required) return on an investment. The foundations of this concept were laid by the research