## Glossary

**American option**An option that can be exercised any time until its expiration date. Contrast with

**European option**.**arbitrary cash flow instrument**A set of generic cash flow amounts for which a price needs to be established.

**Asian option**An option whose payoff depends upon the average price of the underlying asset over a certain period of time.

**asset-or-nothing option**A digital option that pays the value of the underlying security if the option expires in the money.

**barrier option**An option that is activated or deactivated only if the price of the underlying asset crosses a barrier. See also

**knock-in**and**knock-out**. If the option fails to execute, the seller may pay to the purchaser a predetermined**rebate**.**barrier option**An option that is activated or deactivated only if the price of the underlying asset crosses a barrier. See also

**knock-in**and**knock-out**. If the option fails to execute, the seller may pay to the purchaser a predetermined**rebate**.**basis**Day count basis determines how interest accrues over time for various instruments and the amount transferred on interest payment dates. The calculation of accrued interest for dates between payments also uses day count basis. Day count basis is a fraction of

`Number of interest accrual days`

/`Days in the relevant coupon period`

. Supported day count conventions and basis values are:Basis Value

Day Count Convention

`0`

actual/actual (default) — Number of days in both a period and a year is the actual number of days.

`1`

30/360 SIA — Year fraction is calculated based on a 360 day year with 30-day months, after applying the following rules: If the first date and the second date are the last day of February, the second date is changed to the 30th. If the first date falls on the 31st or is the last day of February, it is changed to the 30th. If after the preceding test, the first day is the 30th and the second day is the 31st, then the second day is changed to the 30th.

`2`

actual/360 — Number of days in a period is equal to the actual number of days, however the number of days in a year is 360.

`3`

actual/365 — Number of days in a period is equal to the actual number of days, however the number of days in a year is 365 (even in a leap year).

`4`

30/360 PSA — Number of days in every month is set to 30 (including February). If the start date of the period is either the 31st of a month or the last day of February, the start date is set to the 30th, while if the start date is the 30th of a month and the end date is the 31st, the end date is set to the 30th. The number of days in a year is 360.

`5`

30/360 ISDA — Number of days in every month is set to 30, except for February where it is the actual number of days. If the start date of the period is the 31st of a month, the start date is set to the 30th while if the start date is the 30th of a month and the end date is the 31st, the end date is set to the 30th. The number of days in a year is 360.

`6`

30E /360 — Number of days in every month is set to 30 except for February where it is equal to the actual number of days. If the start date or the end date of the period is the 31st of a month, that date is set to the 30th. The number of days in a year is 360.

`7`

actual/365 Japanese — Number of days in a period is equal to the actual number of days, except for leap days (29th February) which are ignored. The number of days in a year is 365 (even in a leap year).

`8`

actual/actual ICMA — Number of days in both a period and a year is the actual number of days and the compounding frequency is annual.

`9`

actual/360 ICMA — Number of days in a period is equal to the actual number of days, however the number of days in a year is 360 and the compounding frequency is annual.

`10`

actual/365 ICMA — Number of days in a period is equal to the actual number of days, however the number of days in a year is 365 (even in a leap year) and the compounding frequency is annual.

`11`

30/360 ICMA — Number of days in every month is set to 30, except for February where it is equal to the actual number of days. If the start date or the end date of the period is the 31st of a month, that date is set to the 30th. The number of days in a year is 360 and the compounding frequency is annual.

`12`

actual/365 ISDA — The day count fraction is calculated using the following formula:

`(Actual number of days in period that fall in a leap year / 366)`

+`(Actual number of days in period that fall in a normal year / 365 )`

.`13`

bus/252 — The number of days in a period is equal to the actual number of business days. The number of business days in a year is 252.

**basket option**An option that provides a payoff dependent on the value of a portfolio of assets.

**beta**The price volatility of a financial instrument relative to the price volatility of a market or index as a whole. Beta is most commonly used with respect to equities. A high-beta instrument is riskier than a low-beta instrument.

**binomial model**A method in which the probability over time of each possible price or rate follows a binomial distribution. The basic assumption is that prices or rates can move to only two values (one higher and one lower) over any short time period. See also

**trinomial model**.**Black-Derman-Toy (BDT) model**A model for pricing interest rate derivatives where all security prices and rates depend upon the short rate (annualized one-period interest rate).

**bond**A long-term debt security with fixed interest payments and fixed maturity date.

**bond option**The right to sell a bond back to the issuer (put) or to redeem a bond from its current owner (call) at a specific price and on a specific date.

**bushy tree**A tree of prices or interest rates in which the number of branches increases exponentially relative to observation times; branches never recombine. Opposite of a

**recombining tree**.**call**1. An option to buy a certain quantity of a stock or commodity for a specified price within a specified time. See also

**put**.2. A demand to submit bonds to the issuer for redemption before the maturity date.

**call swaption**Allows the option buyer to enter into an interest rate swap in which the buyer of the option pays the fixed rate and receives the floating rate.

**callable bond**A bond that allows the issuer to buy back the bond at a predetermined price at specified future dates. The bond contains an embedded call option; that is, the holder has sold a call option to the issuer. See also

**puttable bond**.**cap**Interest-rate option that guarantees that the rate on a floating-rate loan will not exceed a certain level.

**caplet**An interim cap component in a multiperiod interest-rate cap agreement.

**cash-or-nothing option**A digital option that pays some fixed amount of cash if the option expires in the money.

**compound option**An option on an option, such as a call on a call, a put on a put, a call on a put, or a put on a call.

**Delta**Delta measures the rate of change of the price of a derivative security relative to the price of the underlying asset; that is, the first derivative of the curve that relates the price of the derivative to the price of the underlying security.

**derivative**A financial instrument that is based on some underlying asset. For example, an option is a derivative instrument based on the right to buy or sell an underlying instrument.

**deterministic model**An interest rate model in which the values of the rates in the next time step are determined solely by the values of the rates in the current time step.

**digital option**An option whose payout is fixed after the underlying stock exceeds the predetermined threshold or strike price.

**discount factor**Coefficient used to compute the present value of future cash flows.

**dollar sensitivity**Sensitivity reported as a dollar price change instead of a percentage price change.

**down-and-in**A type of

**barrier option**that becomes active if the barrier is reached from above. See also**knock-in**.**down-and-out**A type of

**barrier option**that becomes deactivated if the barrier is reached from above. See also**knock-out**.**European option**An option that can be exercised only on its expiration date. Contrast with

**American option**.**ex-dividend date**Date when a declared dividend belongs to the seller rather than the buyer.

**exercise price**The price set for buying an asset (call) or selling an asset (put). The strike price.

**exotic option**Any nonstandard option. Opposite of

**vanilla option**.**fixed lookback option**Strike price is fixed at purchase. The underlying is priced at its highest or lowest level, depending whether it is a call or put, during the life of the option rather than expiring at market.

**fixed-rate note**A long-term debt security with preset interest rate and maturity, by which the interest must be paid. The principal may or may not be paid at maturity.

**floating lookback option**Strike price is fixed at maturity. For a call, the price is fixed at the lowest price during the life of the option; for a put it is fixed at the highest price.

**floating-rate note**A security similar to a bond, but in which the note's interest rate is reset periodically, relative to a reference index rate, to reflect fluctuations in market interest rates.

**floor**Interest-rate option that guarantees that the rate on a floating-rate loan will not fall below a certain level.

**floorlet**One of the interim period floors in a multiple period floor agreement.

**forward curve**The curve of forward interest rates vs. maturity dates for bonds.

**forward rate**The future interest rate of a bond inferred from the term structure, especially from the yield curve of zero-coupon bonds, calculated from the growth factor of an investment in a zero held until maturity.

**Gamma**Gamma measures the rate of change of delta for a derivative security relative to the price of the underlying asset; that is, the second derivative of the option price relative to the security price.

**gap option**A digital option in which one strike decides if the option is in or out of money and another strike decides the size the size of the payoff.

**Heath-Jarrow-Morton (HJM) model**A model of the interest rate term structure that works with a type of interest rate tree called a

**bushy tree**.**hedge**A securities transaction that reduces or offsets the risk on an existing investment position.

**instrument set**A collection of financial assets. A portfolio.

**inverse discount**A factor by which the present value of an asset is multiplied to find its future value. The reciprocal of the discount factor.

**irregular coupon**A bond interest payment for more or less than six-months' interest. The first coupon on many bonds is irregular because payment is other than six months from the dated date.

**knock-in**A

**barrier option**that is activated when the price of the underlying asset achieves a designated target. There are two types:**up-and-in**and**down-and-in**.**knock-out**A

**barrier option**that is deactivated when the price of the underlying asset achieves a designated target. There are two types:**up-and-out**and**down-and-out**.**Lambda**The percentage change in an option price divided by the percentage change in an underlying price.

**least-squares method**A mathematical method of determining the best fit of a curve to a series of observations by choosing the curve that minimizes the sum of the squares of all deviations from the curve.

**long rate**The yield on a zero-coupon Treasury bond.

**lookback option**An option that reduces uncertainties associated with the timing of market entry. Lookback options can be either

**fixed lookback option**and**floating lookback option**.**mean reversion**The tendency of a variable to return to its mean value after reaching a point of excessive positive or negative valuation relative to the mean.

**option**A right to buy or sell specific securities or commodities at a stated price (exercise or strike price) within a specified time. An option is a type of derivative.

**per-dollar sensitivity**The dollar

**sensitivity**divided by the corresponding instrument price.**portfolio**A collection of financial assets. Also called an instrument set.

**price tree structure**A MATLAB

^{®}structure that holds all pricing information.**price vector**A vector of instrument prices.

**pricing options structure**A MATLAB structure that defines how the price tree is used to find the price of instruments in the portfolio, and how much additional information is displayed in the command window when the pricing function is called.

**put**An option to sell a stipulated amount of stock or securities within a specified time and at a fixed exercise price. See also

**call**.**put swaption**Allows the option buyer to enter into an interest rate swap in which the buyer of the option receives the fixed rate and pays the floating rate.

**puttable bond**A bond that allows the holder to redeem the bond at a predetermined price at specified future dates. The bond contains an embedded put option; that is, the holder has bought a put option. See also

**callable bond**.**rainbow option**A single option linked to two or more underlying assets. In order for the option to pay off, all the underlying assets must move in the intended direction.

**rate specification**A MATLAB structure that holds all information needed to identify completely the evolution of interest rates.

**rebate**A predetermined amount of money paid to the purchaser of a

**barrier option**if the option fails to execute.**recombining tree**A tree of prices or interest rates whose branches recombine over time. Opposite of a

**bushy tree**.**Rho**Rho measures sensitivity to the interest rate; it is the derivative of the option value with respect to the risk-free interest rate.

**self-financing hedge**A trading strategy whereby the value of a portfolio after rebalancing is equal to its value at any previous time.

**sensitivity**The “what if” relationship between variables; the degree to which changes in one variable cause changes in another variable. A specific synonym is volatility. See also

**dollar sensitivity**.**short rate**The annualized one-period interest rate.

**sinking fund bond**A sinking fund bond is a coupon bond with a sinking fund provision. This provision obligates the issuer to amortize portions of the principal prior to maturity, affecting bond prices since the time of the principal repayment changes.

**spot curve, spot yield curve****spot rate**The current interest rate appropriate for discounting a cash flow of some given maturity.

**spread**For options, a combination of call or put options on the same stock with differing exercise prices or maturity dates.

**stepped coupon bond**A step-up and step-down bond is a debt security with a predetermined coupon structure over time.

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

**strike**Exercise a put or call option.

**strike price**See

**exercise price**.**supershare option**A digital option that pays out a proportion of the assets underlying a portfolio if the asset lies between a lower and an upper bound at the expiry of the option.

**swap**A contract between two parties to exchange cash flows in the future according to some formula.

**swaption**An option on an interest rate swap. It grants the option buyer the right to enter into an interest rate swap at a future date.

**Theta**Theta measures the sensitivity of the value of the derivative to the passage of time.

**time specification**A MATLAB structure that represents the mapping between times and dates for interest rate quoting.

**trinomial model**A method in which the basic assumption is that prices or rates can move to one of three possible values over any short time period. At any time step the price or rate direction can be upward, neutral, or downward. See also

**binomial model**.**under-determined system**A set of simultaneous equations in which the number of independent variables exceeds the number of equations in the set, leading to an infinite number of solutions.

**up-and-in**A type of

**barrier option**that becomes active if the barrier is reached from below. See also**knock-in**.**up-and-out**A type of

**barrier option**that becomes deactivated if the barrier is reached from below. See also**knock-out**.**vanilla option**A common option, such as a put or call. Opposite of

**exotic option**.**vanilla swap**A

**swap**agreement to exchange a fixed rate for a floating rate.**Vega**Vega measures the rate of change in the price of a derivative security relative to the volatility of the underlying security. When Vega is large, the security is sensitive to small changes in volatility.

**volatility specification**A MATLAB structure that specifies the forward rate volatility process.

**yields**The zero coupon rate.

**yield curve**The zero curve.

**yield volatility**The zero coupon volatilities.

**zero curve, zero-coupon yield curve**A yield curve for zero-coupon bonds; zero rates versus maturity dates. Since the maturity and duration (Macaulay duration) are identical for zeros, the zero curve is a pure depiction of supply/demand conditions for loanable funds across a continuum of durations and maturities. Also known as spot curve or spot yield curve.

**zero-coupon bond, or zero**A bond that, instead of carrying a coupon, is sold at a discount from its face value, pays no interest during its life, and pays the principal only at maturity.