Interest rate swapIn finance, an interest rate swap (IRS) is an interest rate derivative (IRD). It involves exchange of interest rates between two parties. In particular it is a "linear" IRD and one of the most liquid, benchmark products. It has associations with forward rate agreements (FRAs), and with zero coupon swaps (ZCSs). In its December 2014 statistics release, the Bank for International Settlements reported that interest rate swaps were the largest component of the global OTC derivative market, representing 60%, with the notional amount outstanding in OTC interest rate swaps of 381trillion,andthegrossmarketvalueof14 trillion. Yield curveIn finance, the yield curve is a graph which depicts how the yields on debt instruments – such as bonds – vary as a function of their years remaining to maturity. Typically, the graph's horizontal or x-axis is a time line of months or years remaining to maturity, with the shortest maturity on the left and progressively longer time periods on the right. The vertical or y-axis depicts the annualized yield to maturity. Those who issue and trade in forms of debt, such as loans and bonds, use yield curves to determine their value.
Interest rateAn interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited, or borrowed (called the principal sum). The total interest on an amount lent or borrowed depends on the principal sum, the interest rate, the compounding frequency, and the length of time over which it is lent, deposited, or borrowed. The annual interest rate is the rate over a period of one year. Other interest rates apply over different periods, such as a month or a day, but they are usually annualized.
Linear interpolationIn mathematics, linear interpolation is a method of curve fitting using linear polynomials to construct new data points within the range of a discrete set of known data points. If the two known points are given by the coordinates and , the linear interpolant is the straight line between these points. For a value in the interval , the value along the straight line is given from the equation of slopes which can be derived geometrically from the figure on the right. It is a special case of polynomial interpolation with .
InterpolationIn the mathematical field of numerical analysis, interpolation is a type of estimation, a method of constructing (finding) new data points based on the range of a discrete set of known data points. In engineering and science, one often has a number of data points, obtained by sampling or experimentation, which represent the values of a function for a limited number of values of the independent variable. It is often required to interpolate; that is, estimate the value of that function for an intermediate value of the independent variable.
Bilinear interpolationIn mathematics, bilinear interpolation is a method for interpolating functions of two variables (e.g., x and y) using repeated linear interpolation. It is usually applied to functions sampled on a 2D rectilinear grid, though it can be generalized to functions defined on the vertices of (a mesh of) arbitrary convex quadrilaterals. Bilinear interpolation is performed using linear interpolation first in one direction, and then again in another direction.
Interest rate derivativeIn finance, an interest rate derivative (IRD) is a derivative whose payments are determined through calculation techniques where the underlying benchmark product is an interest rate, or set of different interest rates. There are a multitude of different interest rate indices that can be used in this definition. IRDs are popular with all financial market participants given the need for almost any area of finance to either hedge or speculate on the movement of interest rates.
Multivariate interpolationIn numerical analysis, multivariate interpolation is interpolation on functions of more than one variable (multivariate functions); when the variates are spatial coordinates, it is also known as spatial interpolation. The function to be interpolated is known at given points and the interpolation problem consists of yielding values at arbitrary points . Multivariate interpolation is particularly important in geostatistics, where it is used to create a digital elevation model from a set of points on the Earth's surface (for example, spot heights in a topographic survey or depths in a hydrographic survey).
Polynomial interpolationIn numerical analysis, polynomial interpolation is the interpolation of a given bivariate data set by the polynomial of lowest possible degree that passes through the points of the dataset. Given a set of n + 1 data points , with no two the same, a polynomial function is said to interpolate the data if for each . There is always a unique such polynomial, commonly given by two explicit formulas, the Lagrange polynomials and Newton polynomials.
InterestIn finance and economics, interest is payment from a borrower or deposit-taking financial institution to a lender or depositor of an amount above repayment of the principal sum (that is, the amount borrowed), at a particular rate. It is distinct from a fee which the borrower may pay to the lender or some third party. It is also distinct from dividend which is paid by a company to its shareholders (owners) from its profit or reserve, but not at a particular rate decided beforehand, rather on a pro rata basis as a share in the reward gained by risk taking entrepreneurs when the revenue earned exceeds the total costs.
Swap (finance)In finance, a swap is an agreement between two counterparties to exchange financial instruments, cashflows, or payments for a certain time. The instruments can be almost anything but most swaps involve cash based on a notional principal amount. The general swap can also be seen as a series of forward contracts through which two parties exchange financial instruments, resulting in a common series of exchange dates and two streams of instruments, the legs of the swap.
Trigonometric interpolationIn mathematics, trigonometric interpolation is interpolation with trigonometric polynomials. Interpolation is the process of finding a function which goes through some given data points. For trigonometric interpolation, this function has to be a trigonometric polynomial, that is, a sum of sines and cosines of given periods. This form is especially suited for interpolation of periodic functions. An important special case is when the given data points are equally spaced, in which case the solution is given by the discrete Fourier transform.
Hermite interpolationIn numerical analysis, Hermite interpolation, named after Charles Hermite, is a method of polynomial interpolation, which generalizes Lagrange interpolation. Lagrange interpolation allows computing a polynomial of degree less than n that takes the same value at n given points as a given function. Instead, Hermite interpolation computes a polynomial of degree less than mn such that the polynomial and its m − 1 first derivatives have the same values at n given points as a given function and its m − 1 first derivatives.
DiscountingIn finance, discounting is a mechanism in which a debtor obtains the right to delay payments to a creditor, for a defined period of time, in exchange for a charge or fee. Essentially, the party that owes money in the present purchases the right to delay the payment until some future date. This transaction is based on the fact that most people prefer current interest to delayed interest because of mortality effects, impatience effects, and salience effects.
Trilinear interpolationTrilinear interpolation is a method of multivariate interpolation on a 3-dimensional regular grid. It approximates the value of a function at an intermediate point within the local axial rectangular prism linearly, using function data on the lattice points. For an arbitrary, unstructured mesh (as used in finite element analysis), other methods of interpolation must be used; if all the mesh elements are tetrahedra (3D simplices), then barycentric coordinates provide a straightforward procedure.
Risk-free rateThe risk-free rate of return, usually shortened to the risk-free rate, is the rate of return of a hypothetical investment with scheduled payments over a fixed period of time that is assumed to meet all payment obligations. Since the risk-free rate can be obtained with no risk, any other investment having some risk will have to have a higher rate of return in order to induce any investors to hold it.
Compound interestCompound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest. It is the result of reinvesting interest, or adding it to the loaned capital rather than paying it out, or requiring payment from borrower, so that interest in the next period is then earned on the principal sum plus previously accumulated interest. Compound interest is standard in finance and economics.
Short-rate modelA short-rate model, in the context of interest rate derivatives, is a mathematical model that describes the future evolution of interest rates by describing the future evolution of the short rate, usually written . Under a short rate model, the stochastic state variable is taken to be the instantaneous spot rate. The short rate, , then, is the (continuously compounded, annualized) interest rate at which an entity can borrow money for an infinitesimally short period of time from time .
Basis swapA basis swap is an interest rate swap which involves the exchange of two floating rate financial instruments. A basis swap functions as a floating-floating interest rate swap under which the floating rate payments are referenced to different bases. The existence of a basis arises from demand and supply imbalances and where, for example, a basis is due for a borrower seeking dollars, this is indicative of a synthetic dollar interest rate in the FX market pricing higher than the direct dollar interest rate.
Currency swapIn finance, a currency swap (more typically termed a cross-currency swap, XCS) is an interest rate derivative (IRD). In particular it is a linear IRD, and one of the most liquid benchmark products spanning multiple currencies simultaneously. It has pricing associations with interest rate swaps (IRSs), foreign exchange (FX) rates, and FX swaps (FXSs). A cross-currency swap's (XCS's) effective description is a derivative contract, agreed between two counterparties, which specifies the nature of an exchange of payments benchmarked against two interest rate indexes denominated in two different currencies.
