Definition of Black-Scholes option-pricing model

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

Abrams’ 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

Abrams’ 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

Abandonment option

The option of terminating an investment earlier than originally planned.

Administrative pricing rules

IRS rules used to allocate income on export sales to a foreign sales corporation.

American option

An option that may be exercised at any time up to and including the expiration date.
Related: European option

American-style option

An option contract that can be exercised at any time between the date of purchase and
the expiration date. Most exchange-traded options are American style.

Arbitrage Pricing Theory (APT)

An alternative model to the capital asset pricing model developed by
Stephen Ross and based purely on arbitrage arguments.

Arbitrage-free option-pricing models

Yield curve option-pricing models.

Asian option

option based on the average price of the asset during the life of the option.

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.

Bargain-purchase-price option

Gives the lessee the option to purchase the asset at a price below fair market
value when the lease expires.

Barrier options

Contracts with trigger points that, when crossed, automatically generate buying or selling of
other options. These are very exotic options.

Basket options

Packages that involve the exchange of more than two currencies against a base currency at
expiration. The basket option buyer purchases the right, but not the obligation, to receive designated
currencies in exchange for a base currency, either at the prevailing spot market rate or at a prearranged rate of
exchange. A basket option is generally used by multinational corporations with multicurrency cash flows
since it is generally cheaper to buy an option on a basket of currencies than to buy individual options on each
of the currencies that make up the basket.

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.

Call an option

To exercise a call option.

Call option

An option contract that gives its holder the right (but not the obligation) to purchase a specified
number of shares of the underlying stock at the given strike price, on or before the expiration date of the
contract.
Call premium
Premium in price above the par value of a bond or share of preferred stock that must be paid to
holders to redeem the bond or share of preferred stock before its scheduled maturity date.

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
plus a risk premium.

Compound option

option on an option.

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.

Covered or hedge option strategies

Strategies that involve a position in an option as well as a position in the
underlying stock, designed so that one position will help offset any unfavorable price movement in the other,
including covered call writing and protective put buying. Related: naked strategies

Currency option

An option to buy or sell a foreign currency.

Dealer options

Over-the-counter options, such as those offered by government and mortgage-backed
securities dealers.

Delivery options

The options available to the seller of an interest rate futures contract, including the quality
option, the timing option, and the wild card option. Delivery options make the buyer uncertain of which
Treasury Bond will be delivered or when it will be delivered.

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.

Doubling option

A sinking fund provision that may allow repurchase of twice the required number of bonds
at the sinking fund call price.

Down-and-in option

Barrier option that comes into existence if asset price hits a barrier.

Down-and-out option

Barrier option that expires if asset price hits a barrier.

Elasticity of an option

Percentage change in the value of an option given a 1% change in the value of the
option's underlying stock.

Embedded option

An option that is part of the structure of a bond that provides either the bondholder or
issuer the right to take some action against the other party, as opposed to a bare option, which trades
separately from any underlying security.

Equity options

Securities that give the holder the right to buy or sell a specified number of shares of stock, at
a specified price for a certain (limited) time period. Typically one option equals 100 shares of stock.

European option

option that may be exercised only at the expiration date. Related: american option.

European-style option

An option contract that can only be exercised on the expiration date.

Exercising the option

The act buying or selling the underlying asset via the option contract.

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.

Foreign currency option

An option that conveys the right to buy or sell a specified amount of foreign
currency at a specified price within a specified time period.

Futures option

An option on a futures contract. Related: options on physicals.

Garmen-Kohlhagen option pricing model

A widely used model for pricing foreign currency options.

Greenshoe option

option that allows the underwriter for a new issue to buy and resell additional shares.

Index and Option Market (IOM)

A division of the CME established in 1982 for trading stock index
products and options. Related: Chicago Mercantile Exchange (CME).

Index model

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

Index option

A call or put option based on a stock market index.

Intrinsic value of an option

The amount by which an option is in-the-money. An option which is not in-themoney
has no intrinsic value. Related: in-the-money.

Irrational call option

The implied call imbedded in the MBS. Identified as irrational because the call is
sometimes not exercised when it is in the money (interest rates are below the threshold to refinance).
Sometimes exercised when not in the money (home sold without regard to the relative level of interest rates).

Liquid yield option note (LYON)

Zero-coupon, callable, putable, convertible bond invented by Merrill

Lookback option

An option that allows the buyer to choose as the option strike price any price of the
underlying asset that has occurred during the life of the option. If a call, the buyer will choose the minimal
price, whereas if a put, the buyer will choose the maximum price. This option will always be in the money.

Liquid yield option note (LYON)

Zero-coupon, callable, putable, convertible bond invented by Merrill Lynch & Co.

Margin requirement (Options)

The amount of cash an uncovered (naked) option writer is required to
deposit and maintain to cover his daily position valuation and reasonably foreseeable intra-day price changes.

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.

Multi-option financing facility

A syndicated confirmed credit line with attached options.

Naked option strategies

An unhedged strategy making exclusive use of one of the following: Long call
strategy (buying call options ), short call strategy (selling or writing call options), Long put strategy (buying
put options ), and short put strategy (selling or writing put options). By themselves, these positions are called
naked strategies because they do not involve an offsetting or risk-reducing position in another option or the
underlying security.
Related: covered option strategies.

Option

Gives the buyer the right, but not the obligation, to buy or sell an asset at a set price on or before a
given date. Investors, not companies, issue options. Investors who purchase call options bet the stock will be
worth more than the price set by the option (the strike price), plus the price they paid for the option itself.
Buyers of put options bet the stock's price will go down below the price set by the option. An option is part of
a class of securities called derivatives, so named because these securities derive their value from the worth of
an underlying investment.

Option elasticity

The percentage increase in an option's value given a 1% change in the value of the
underlying security.

Option not to deliver

In the mortgage pipeline, an additional hedge placed in tandem with the forward or
substitute sale.

Option premium

The option price.

Option price

Also called the option premium, the price paid by the buyer of the options contract for the right
to buy or sell a security at a specified price in the future.

Option seller

Also called the option writer , the party who grants a right to trade a security at a given price in
the future.

Option writer

option seller.

Option-adjusted spread (OAS)

1) The spread over an issuer's spot rate curve, developed as a measure of
the yield spread that can be used to convert dollar differences between theoretical value and market price.
2) The cost of the implied call embedded in a MBS, defined as additional basis-yield spread. When added to the
base yield spread of an MBS without an operative call produces the option-adjusted spread.

Options contract

A contract that, in exchange for the option price, gives the option buyer the right, but not
the obligation, to buy (or sell) a financial asset at the exercise price from (or to) the option seller within a
specified time period, or on a specified date (expiration date).

Options contract multiple

A constant, set at $100, which when multiplied by the cash index value gives the
dollar value of the stock index underlying an option. That is, dollar value of the underlying stock index = cash
index value x $100 (the options contract multiple).

Options on physicals

Interest rate options written on fixed-income securities, as opposed to those written on
interest rate futures contracts.

Out-of-the-money option

A call option is out-of-the-money if the strike price is greater than the market price
of the underlying security. A put option is out-of-the-money if the strike price is less than the market price of
the underlying security.

Path dependent option

An option whose value depends on the sequence of prices of the underlying asset
rather than just the final price of the asset.

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.

Postponement option

The option of postponing a project without eliminating the possibility of undertaking it.

Pricing efficiency

Also called external efficiency, a market characteristic where prices at all times fully
reflect all available information that is relevant to the valuation of securities.

Put an option

To exercise a put option.

Put option

This security gives investors the right to sell (or put) fixed number of shares at a fixed price within
a given time frame. An investor, for example, might wish to have the right to sell shares of a stock at a certain
price by a certain time in order to protect, or hedge, an existing investment.

Quality option

Also called the swap option, the seller's choice of deliverables in Treasury Bond and Treasury
note futures contract. Related: cheapest to deliver issue

Regulatory pricing risk

Risk that arises when regulators restrict the premium rates that insurance companies
can charge.

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

Split-fee option

An option on an option. The buyer generally executes the split fee with first an initial fee,
with a window period at the end of which upon payment of a second fee the original terms of the option may
be extended to a later predetermined final notification date.

Stochastic models

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

Stock index option

An option in which the underlying is a common stock index.

Stock option

An option in which the underlying is the common stock of a corporation.

Tax deferral option

The feature of the U.S. Internal Revenue Code that the capital gains tax on an asset is
payable only when the gain is realized by selling the asset.

Tax-timing option

The option to sell an asset and claim a loss for tax purposes or not to sell the asset and
defer the capital gains tax.

Time value of an option

The portion of an option's premium that is based on the amount of time remaining
until the expiration date of the option contract, and that the underlying components that determine the value of
the option may change during that time. Time value is generally equal to the difference between the premium
and the intrinsic value. Related: in-the-money.

Timing option

For a Treasury Bond or note futures contract, the seller's choice of when in the delivery month to deliver.

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.

Underpricing

Issue of securities below their market value.

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.

Virtual currency option

A new option contract introduced by the PHLX in 1994 that is settled in US$ rather
than in the underlying currency. These options are also called 3-Ds (dollar denominated delivery).

Wild card option

The right of the seller of a Treasury Bond futures contract to give notice of intent to deliver
at or before 8:00 p.m. Chicago time after the closing of the exchange (3:15 p.m. Chicago time) when the
futures settlement price has been fixed. Related: Timing option.

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.

Cost-plus pricing

A method of pricing in which a mark-up is added to the total product/service cost.

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