Financial Terms Black-Scholes model

Definition of Black-Scholes model

Black-Scholes model

The first complete mathematical model for pricing
options, developed by Fischer black and Myron scholes. It examines market
price, strike price, volatility, time to expiration, and interest rates. It is limited
to only certain kinds of options.

Related Terms:

Black-Scholes option-pricing model

A model for pricing call options based on arbitrage arguments that uses
the stock price, the exercise price, the risk-free interest rate, the time to expiration, and the standard deviation
of the stock return.

economic components model

Abramsâ€™ model for calculating DLOM based on the interaction of discounts from four economic components.
This model consists of four components: the measure of the economic impact of the delay-to-sale, monopsony power to buyers, and incremental transactions costs to both buyers and sellers.

Gordon model

present value of a perpetuity with growth.
The end-ofyear Gordon model formula is: 1/(r - g)
and the midyear formula is: SQRT(1 + r)/(r - g).

log size model

Abramsâ€™ model to calculate discount rates as a function of the logarithm of the value of the firm.

QMDM (quantitative marketability discount model)

model for calculating DLOM for minority interests r the discount rate

Arbitrage-free option-pricing models

Yield curve option-pricing models.

Asset pricing model

A model for determining the required rate of return on an asset.

Asset pricing model

A model, such as the Capital Asset Pricing model (CAPM), that determines the required
rate of return on a particular asset.

Binomial option pricing model

An option pricing model in which the underlying asset can take on only two
possible, discrete values in the next time period for each value that it can take on in the preceding time period.

Black market

An illegal market.

Capital asset pricing model (CAPM)

An economic theory that describes the relationship between risk and
expected return, and serves as a model for the pricing of risky securities. The CAPM asserts that the only risk
that is priced by rational investors is systematic risk, because that risk cannot be eliminated by diversification.
The CAPM says that the expected return of a security or a portfolio is equal to the rate on a risk-free security

Constant-growth model

Also called the Gordon-Shapiro model, an application of the dividend discount
model which assumes (1) a fixed growth rate for future dividends and (2) a single discount rate.

Deterministic models

Liability-matching models that assume that the liability payments and the asset cash
flows are known with certainty. Related: Compare stochastic models

Discounted dividend model (DDM)

A formula to estimate the intrinsic value of a firm by figuring the
present value of all expected future dividends.

Dividend discount model (DDM)

A model for valuing the common stock of a company, based on the
present value of the expected cash flows.

Dividend growth model

A model wherein dividends are assumed to be at a constant rate in perpetuity.

Extrapolative statistical models

models that apply a formula to historical data and project results for a
future period. Such models include the simple linear trend model, the simple exponential model, and the
simple autoregressive model.

Factor model

A way of decomposing the factors that influence a security's rate of return into common and
firm-specific influences.

Garmen-Kohlhagen option pricing model

A widely used model for pricing foreign currency options.

Index model

A model of stock returns using a market index such as the S&P 500 to represent common or
systematic risk factors.

Market model

This relationship is sometimes called the single-index model. The market model says that the
return on a security depends on the return on the market portfolio and the extent of the security's
responsiveness as measured, by beta. In addition, the return will also depend on conditions that are unique to
the firm. Graphically, the market model can be depicted as a line fitted to a plot of asset returns against
returns on the market portfolio.

Modeling

The process of creating a depiction of reality, such as a graph, picture, or mathematical
representation.

Pie model of capital structure

A model of the debt/equity ratio of the firms, graphically depicted in slices of
a pie that represent the value of the firm in the capital markets.

Single factor model

A model of security returns that acknowledges only one common factor.
See: factor model.

Single index model

A model of stock returns that decomposes influences on returns into a systematic factor,
as measured by the return on the broad market index, and firm specific factors.

Simple linear trend model

An extrapolative statistical model that asserts that earnings have a base level and
grow at a constant amount each period.

Single-index model

Related: market model

Stochastic models

Liability-matching models that assume that the liability payments and the asset cash flows
are uncertain. Related: Deterministic models.

Two-factor model

black's zero-beta version of the capital asset pricing model.

Two-state option pricing model

An option pricing model in which the underlying asset can take on only two
possible (discrete) values in the next time period for each value it can take on in the preceding time period.
Also called the binomial option pricing model.

Value-at-Risk model (VAR)

Procedure for estimating the probability of portfolio losses exceeding some
specified proportion based on a statistical analysis of historical market price trends, correlations, and volatilities.

Yield curve option-pricing models

models that can incorporate different volatility assumptions along the
yield curve, such as the black-Derman-Toy model. Also called arbitrage-free option-pricing models.

Capital Asset Pricing Model (CAPM)

A model for estimating equilibrium rates of return and values of
assets in financial markets; uses beta as a measure of asset risk
relative to market risk

a model that involves
(1) few physical assets,
(2) little management hierarchy, and
(3) a direct pipeline to customers

Binomial model

A method of pricing options or other equity derivatives in
which the probability over time of each possible price follows a binomial
distribution. The basic assumption is that prices can move to only two values
(one higher and one lower) over any short time period.

Markowitz model

A model for selecting an optimum investment portfolio,
devised by H. M. Markowitz. It uses a discrete-time, continuous-outcome
approach for modeling investment problems, often called the mean-variance

capital asset pricing model (CAPM)

Theory of the relationship between risk and return which states that the expected risk
premium on any security equals its beta times the market risk premium.

constant-growth dividend discount model

Version of the dividend discount model in which dividends grow at a constant rate.

dividend discount model

Computation of todayâ€™s stock price which states that share value equals the present value of all expected future dividends.

Making a profit.

percentage of sales models

Planning model in which sales forecasts are the driving variables and most other variables are
proportional to sales.

Implied volatility

The expected volatility in a stock's return derived from its option price, maturity date,
exercise price, and riskless rate of return, using an option-pricing model such as black/scholes.

Implied volatility

For an option, the variance that makes a call option price
equal to the market price. Given the option price, strike price, and other
factors, the black-scholes model computes implied volatility.