Definition of Stochastic models

Stochastic models

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

Deterministic models

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

Arbitrage-free option-pricing models

Yield curve option-pricing models.

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.

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.

Stochastic

Involving or containing a random variable or variables; involving
chance or probability.

percentage of sales models

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

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

The simultaneous buying and selling of a security at two different prices in two different markets,
resulting in profits without risk. Perfectly efficient markets present no arbitrage opportunities. Perfectly
efficient markets seldom exist.

Arbitrage Pricing Theory (APT)

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

Arbitrageurs

People who search for and exploit arbitrage opportunities.

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-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.

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.

Covered interest arbitrage

A portfolio manager invests dollars in an instrument denominated in a foreign
currency and hedges his resulting foreign exchange risk by selling the proceeds of the investment forward for
dollars.

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 arbitrage

Taking advantage of divergences in exchange rates in different money markets by
buying a currency in one market and selling it in another market.

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.

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.

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.

Free cash flows

Cash not required for operations or for reinvestment. Often defined as earnings before
interest (often obtained from operating income line on the income statement) less capital expenditures less the
change in working capital.

Free float

An exchange rate system characterized by the absence of government intervention. Also known as
clean float.

Free on board

Implies that distributive services like transport and handling performed on goods up to the
customs frontier of the economy from which the goods are classed as merchandise.

Free reserves

Excess reserves minus member bank borrowings at the Fed.

Free rider

A follower who avoids the cost and expense of finding the best course of action and by simply
mimicking the behavior of a leader who made these investments.

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 arbitrage

An investment/trading strategy that exploits divergences between actual and theoretical
futures prices.

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.

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.

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.

Risk arbitrage

Speculation on perceived mispriced securities, usually in connection with merger and
acquisition deals. Mike Donatelli, John Demasi, Frank Cohane, and Scott Lewis are all hardcore arbs. They
had a huge BT/MCI position in the summer of 1997, and came out smelling like roses.

Risk controlled arbitrage

A self-funding, self-hedged series of transactions that generally utilize mortgage
securities as the primary assets.

Riskless arbitrage

The simultaneous purchase and sale of the same asset to yield a profit.

Riskless or risk-free asset

An asset whose future return is known today with certainty. The risk free asset is
commonly defined as short-term obligations of the U.S. government.

Risk-free asset

An asset whose future return is known today with certainty.

Risk-free rate

The rate earned on a riskless asset.

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.

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.

Structured arbitrage transaction

A self-funding, self-hedged series of transactions that usually utilize
mortgage securities as the primary assets.

Tax free acquisition

A merger or consolidation in which 1) the acquirer's tax basis in each asset whose
ownership is transferred in the transaction is generally the same as the acquiree's, and 2) each seller who
receives only stock does not have to pay any tax on the gain he realizes until the shares are sold.

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.

Triangular arbitrage

Striking offsetting deals among three markets simultaneously to obtain an arbitrage profit.

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.

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.

Target rate of return pricing

A method of pricing that estimates the desired return on investment to be achieved from the
fixed and working capital investment and includes that return in the price of a product/service.

free cash flow

Generally speaking, this term refers to cash flow from
profit (cash flow from operating activities, to use the more formal term).
The underlying idea is that a business is free to do what it wants with its
cash flow from profit. However, a business usually has many ongoing
commitments and demands on this cash flow, so it may not actually be
free to decide what do with this source of cash. Warning: This term is
not officially defined anywhere and different persons use the term to
mean different things. Pay particular attention to how an author or
speaker is using the term.

Call Option

A contract that gives the holder the right to buy an asset for a
specified price on or before a given expiration (maturity) date

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