| Financial Derivatives Toolbox | |
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.
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 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.
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 - a. An option to buy a certain quantity of a stock or commodity for a specified price within a specified time. See put. b. A demand to submit bonds to the issuer for redemption before the maturity date.
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; i.e., the holder has sold a call option to the issuer. See puttable bond.
cap - Interest-rate option that guarantees that the rate on a floating-rate loan will not exceed a certain level.
delta - The rate of change of the price of a derivative security relative to the price of the underlying asset; i.e., 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.
discount factor - Coefficient used to compute the present value of future cash flows.
European option - An option that can be exercised only on its expiration date. Contrast with American option.
exercise price - The price set for buying an asset (call) or selling an asset (put). The strike price.
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 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.
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 - The rate of change of delta for a derivative security relative to the price of the underlying asset; i.e., the second derivative of the option price relative to the security price.
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.
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.
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 call.
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; i.e., the holder has bought a put option. See callable bond.
rate specification - A MATLAB structure that holds all information needed to identify completely the evolution of interest rates.
recombining tree - A tree of prices or interest rates whose branches recombine over time. Opposite of a bushy tree.
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.
short rate - The annualized one-period interest rate.
spot curve, spot yield curve - See zero 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.
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.
swap - A contract between two parties to exchange cash flows in the future according to some formula.
time specification - A MATLAB structure that represents the mapping between times and dates for interest rate quoting.
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.
vanilla swap - A swap agreement to exchange a fixed rate for a floating rate.
vega - 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.
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.
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