10.1 Glossary of keywords

Accrual period

Time interval between the payment of bond coupons or swap settlements.

American exercise style

Contract that can be exercised at any time during its life.

Arbitrage

Trading strategy taking advantage of the price difference of two or more securities to make an immediate (risk free) profit.

Arbitrageur

Person who uses arbitrage as a trading strategy to make immediate (risk free) profits.

Asset

Something of value, a property owned by a person or a company.

Bear

Animal used as a symbol when the market prices are falling in an economic downturn.

Bid price

The price a potential buyer is willing to pay for a security.

Boundary conditions (natural / essential)

Conditions (usually justified by no-arbitrage arguments) that are imposed on the boundary of the domain where the solution of a differential equation is sought. Natural conditions are usually imposed through a surface term after partial integration; essential conditions are imposed explicitly in the linear system by replacing an equation by the condition.

Broker

Individual who buys and sells goods for other persons.

Bull

Animal used as a symbol when the market prices are rising in an economic upturn.

Call option

Security giving its holder the right and no obligation to buy an underlying asset.

Cap

Collection of caplets maturing at different times.

Caplet

Interest rate option providing for an upper limit on the interest rate; a caplet entitles the holder to the difference between the spot rate and the strike if this is positive, or zero otherwise.

Capital

Amount of money that is invested or used to start a business.

Capital gain

Amount of cash raised by the original owners who sell shares in the initial public offering (IPO) of a company.

Capital asset pricing model (CAPM)

Linear fit measuring the relative performance of a portfolio in comparison with a market index average.

Capitalism

Economic system in which a country's business and industry is controlled and run for profit by private owners.

Clearing margin

A margin deposit by a member of a clearing house (e.g. a broker) that guarantees the performance of all the parties in a financial transaction.

Collar

Interest rate option combining a cap and a floor used as an insurance to guarantee that the interest rates remain within a certain interval.

Commission

Part of a cost that is proportional to the total value of a trade.

Contingent claims

A demand that can be made only if one or more specified outcomes occur.

Coupon

Predetermined amount of cash payed as an interest during the life of a bond.

Covered

A written option is covered if the writer also has an opposing market position on a share-for-share basis in the underlying security.

Delivery date

The date when a forward or futures contract ends with an amount of cash payed in exchange for the underlying asset.

Delivery price

Amount of cash in a forward contract that will be payed on the maturity date in exchange of the underlying asset.

Derivative

Financial instrument whose value is derived from another asset.

Deterministic

Which can be predicted with certainty from the past.

Discount

Amount below the par value; difference between a bond principal and the present value.

Discount bond

Zero coupon bond.

Discount factor

Present value of EUR 1 received some time in the future.

Discount function

Function measuring the present value of one unit due at a later time.

Distribution (log-normal)

Function measuring the probability density of an event using a log-normal law; incremental changes of stock prices are almost log-normally distributed.

Distribution (normal)

Function measuring the probability density of an event using the famous bell-shaped curve; incremental changes of bond prices are sometimes normally distributed.

Diversification

Dividing the investment into a variety of securities.

Dividend

Portion of a company's profits payed out in cash to the shareholders.

Drift

Slow systematic movement in the same direction.

Efficient market

Economy in which prices immediately and fully reflect all relevant information.

Efficient frontier

In the modern portfolio theory, it is the locus of all the portfolios where the highest possible return is achieved after reducing the specific risk through diversification.

Entrepreneur

Person who tries to make money by starting or running a business, especially when this involves taking a financial risk.

Equilibrium swap rate

Fixed coupon making the swap worthless when it is initially issued.

European exercise style

Contract that can be exercised only at the expiry date.

Exercise an option

Use the right to exchange the underlying for a fixed amount of cash.

Exercise (or strike) price

The price at which the underlying may be bought or sold.

Exotic option

Option that is not plain vanilla and is generally not traded on an exchange.

Expected value

Average value obtained by weighting possible realizations by their probabilities.

Expiry time

Date when an option contract ends.

Face (or principal) value

Amount of cash an issuer (borrower) agrees to pay at the maturity.

Fannie Mae

US government-sponsored federal national mortgage association.

Fee

Part of a cost that does not depend on the total value of a trade.

Fixed income instruments

Bonds and preferred stock that pay a predetermined amount of cash.

Fixed interest rate

Predetermined return on investment of a bond, which remains independent of the market spot rate.

Fixed leg (of a swap)

Part of the contract involving payments that are predetermined (risk-free) and remain independent of the spot rate.

Floating leg (of a swap)

Part of the contract involving payments that depend on the spot rate and therefore carry a financial risk.

Floor

Collection of floorlets maturing at different times.

Floorlet

Interest rate option providing for a lower limit on the interest rate; it entitles the holder to the difference between the strike and the spot rate if this is positive, or zero otherwise.

Forward rate

Interest payed today at time for a loan with a specified maturity and starting at some point in the future , where .

Forward rate agreement (FRA)

Agreement to borrow or lend an amount of cash some time in the future at an interest rate that is fixed today.

Forward contracts

Agreement between a buyer and a seller to exchange certain goods for a fixed price some time in the future.

Forward price

The delivery price in a forward contract chosen so as to make it worthless.

Freddie Mac

US government-sponsored federal home mortgage loan corporation.

Futures contract

Special type of standardized forward contract enabling anonymous trades on an exchange with a protection against defaults through a clearing margin.

Gearing

Strategy increasing the return of portfolio by increasing the investment risk.

Gross domestic product (GDP)

Total value of goods and services produced by a country.

Go long

Purchase an asset in exchange of cash.

Go (or sell) short

Sell an asset that has been borrowed from another investor.

Hedger

Person who buys securities to reduce the investment risk in a portfolio.

Hedging

Strategy reducing the investment risk of a portfolio at the expense of smaller returns.

Holder

The purchaser of an option.

Implied volatility

Volatility of an underlying asset, as measured from the price of derivatives assuming a standard pricing model.

In-the-money

Subset of an option series that has a finite intrinsic value that is payed out to the holder at the expiry.

Initial / Terminal conditions

Value of a function of time that is known at the beginning of a calculation.

Initial public offering (IPO)

First sale of a company's shares to the public.

Intrinsic value

The value of an option if it would expire with the underlying at its current price.

Investor

Person or organization that buys property in the hope of making a profit.

Investment

Money used to realize a project in the hope of making a profit.

Itô's lemma

Mathematical formula relating the differential of a stochastic function to differential of its stochastic arguments.

London inter bank offered rate (LIBOR)

The rate of interest that major international banks in London charge each other for borrowings.

Market

Occasion when people buy and sell goods.

Market maker

Person who's job it is to determine a fair price of a certain asset and to help buyers and sellers exchange that over-the-counter outside the market.

Market price of risk

Parameter measuring how much the investors are risk seeking or risk averse.

Market value

Spot price obtained via offer and demand from sellers and buyers on the market.

Markov process

Stochastic process where consecutive increments are independent from the past.

Martingales

Maturity date

The end of the life of a contract.

Maximum likelyhood estimation

Statistical method built so as to maximize the chance that a model fits a given dataset.

Mean reversion

Tendency of a quantity to evolve towards a long term average.

Modern Portfolio Theory (MPT)

Description of rational investment choices based on risk-return trade-offs and efficient diversification.

Monte-Carlo simulation

Computer calculation performed with a crowd of random walkers to statistically sample the evolution of market prices by adding small increments.

Net asset Value (NAV)

Total value of the fund's investment.

Notional principal

The amount of cash used to calculate the payments in an interest rate swap; the principal is ``notional'' because it is never really exchanged.

Numeraire asset

Arbitrary asset chosen to measure the relative performance of an investment in dimensionless units.

Offer price

The price a seller is asking in exchange for a security.

Open-end fund

Mutual fund where the holdings are continually reinvested and new shares are created on demand.

Option

Security giving its holder a right, but not the obligation, to buy or sell an asset at a set price on or before a given date.

Option class

Options having the same underlying and the same type of contract (put, call, etc).

Option series

Option from the same class having the same exercise price and expiry date.

Out-of-the-money

Subset of an option series that has no intrinsic value and expires worthless.

Over-the-counter (OTC)

Non-standard exchange of goods carried out between two parties outside the market, generally without disclosing the price to the public.

Par

Equal to the principalkeywd:principal or face value of a security.

Parameters: financial / numerical

Financial parameters entirely specify the problem; numerical parameters only serve to control the calculation and should never affect the result.

Path dependent option

Option with a payoff depending on the price history of the underlying.

Portfolio

Set of shares and financial instruments held by a person or an organization.

Possible realizations

Outcomes of a random variable that have a finite probability to occur.

Premium

Amount that is in excess of the par value, i.e. the positive difference between the present value and the nominal principal value.

Principal (or face) value

Amount of cash an issuer (borrower) agrees to pay at the maturity.

Principal components

Partly uncorrelated random varialbles that can explain most of the statistical observations from the markets.

Probability

Measure of the likelihood that something will occur.

Put-call parity

Relation between the price of vanilla options with the same strike price and expiry.

Put option

Security giving its holder the right and no obligation to sell an underlying asset.

Random

Which cannot be predicted with certainty from the past.

Redemption date

Date when a debt security is has to be payed back, marking the end of the lifetime of a bond.

Random walk

Unpredictable motion resulting from increments that are generally assumed to be independent of the past (Markov property).

Reset and payment times

Beginning and end of the time interval (accrual period) between the payment of coupons in a bond or the exchange of interest payments in a swap.

Risk

The possibility of something bad happening sometime in the future.

Risk premium

Reward the investors ask for taking a larger investment risk.

Security

Document proving that somebody is the owner of certain goods or has a right to acquire them in the future.

Smile

Graph with a minimum implied volatility for an underlying at-the-money.

Specific risk

The uncertain outcome of an investment can be divided in specific and non-specific risks. Specific risk can entirely be eliminated through combination of anti-correlated assets and diversification; non-specific risk affects the entire market.

Speculator

Person who buys and sells goods in the hope of making a profit from his view on the evolution of the market.

Split

When a growing company emits new shares to reduce the price quoted in the market. In a 2-for-1 split, 2 new shares are exchanged for every share that was previously owned.

Spot

The value for immediate delivery.

Stochastic

Something that includes an unpredictable random component.

Strike (or exercise) price

The price at which the underlying may be bought or sold.

Suzerain

In the Middle Ages, the suzerain was a person who owned the right over another (called the vassal) who promised to fight and be loyal in return for being given land to live on.

Swap (of interest rates, currency exchange rates, etc)

Contract whereby two parties agree to exchange, at known dates in the future, a fixed for a floating set of rates without ever exchanging the principal.

Tenor of a bond

Time interval between the payment of consecutive coupons.

Term structure of interest rates

Interest rates calculated for bonds of different maturities.

Time value

Difference between the intrinsic value and the value of an option before it expires.

Transaction costs

The cost of carrying out a trade (fees, commissions, plus the difference between the price obtained and the middle of the bid-offer prices quoted on the market).

Treasury rate

Interest rate payed by the central bank responsible for a given currency.

Tree

Method to approximate a dynamical system by recursively adding / subtracting a fixed number of increments to all the possible outcomes.

Underlying

Security that parties agree to exchange under conditions in a derivative contract.

Vanilla

Simplest form of a contract.

Venture capital

High risk investment given in return for a participation in the control and the future earnings of a start-up company that develops a new product.

Volatility

A measure of the uncertainty of the price of an asset.

Wiener process

Markov process where the increments are normally distributed with zero mean and a variance proportional to the time step.

Writer

The seller of an option, usually a large financial institution.

Zero-coupon bond

A bond without coupon, where the principal and the interest are paid at the maturity date.

Zero-sum game

Game where the earning from one player exactly equals the loss from another.

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