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 .
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. Futures contractIn finance, a futures contract (sometimes called futures) is a standardized legal contract to buy or sell something at a predetermined price for delivery at a specified time in the future, between parties not yet known to each other. The asset transacted is usually a commodity or financial instrument. The predetermined price of the contract is known as the forward price. The specified time in the future when delivery and payment occur is known as the delivery date.
Futures exchangeA futures exchange or futures market is a central financial exchange where people can trade standardized futures contracts defined by the exchange. Futures contracts are derivatives contracts to buy or sell specific quantities of a commodity or financial instrument at a specified price with delivery set at a specified time in the future. Futures exchanges provide physical or electronic trading venues, details of standardized contracts, market and price data, clearing houses, exchange self-regulations, margin mechanisms, settlement procedures, delivery times, delivery procedures and other services to foster trading in futures contracts.
Option-adjusted spreadOption-adjusted spread (OAS) is the yield spread which has to be added to a benchmark yield curve to discount a security's payments to match its market price, using a dynamic pricing model that accounts for embedded options. OAS is hence model-dependent. This concept can be applied to a mortgage-backed security (MBS), or another bond with embedded options, or any other interest rate derivative or option. More loosely, the OAS of a security can be interpreted as its "expected outperformance" versus the benchmarks, if the cash flows and the yield curve behave consistently with the valuation model.
Bond valuationBond valuation is the determination of the fair price of a bond. As with any security or capital investment, the theoretical fair value of a bond is the present value of the stream of cash flows it is expected to generate. Hence, the value of a bond is obtained by discounting the bond's expected cash flows to the present using an appropriate discount rate. In practice, this discount rate is often determined by reference to similar instruments, provided that such instruments exist.
Vasicek modelIn finance, the Vasicek model is a mathematical model describing the evolution of interest rates. It is a type of one-factor short-rate model as it describes interest rate movements as driven by only one source of market risk. The model can be used in the valuation of interest rate derivatives, and has also been adapted for credit markets. It was introduced in 1977 by Oldřich Vašíček, and can be also seen as a stochastic investment model.
Bond durationIn finance, the duration of a financial asset that consists of fixed cash flows, such as a bond, is the weighted average of the times until those fixed cash flows are received. When the price of an asset is considered as a function of yield, duration also measures the price sensitivity to yield, the rate of change of price with respect to yield, or the percentage change in price for a parallel shift in yields. The dual use of the word "duration", as both the weighted average time until repayment and as the percentage change in price, often causes confusion.
Mathematical financeMathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling of financial markets. In general, there exist two separate branches of finance that require advanced quantitative techniques: derivatives pricing on the one hand, and risk and portfolio management on the other. Mathematical finance overlaps heavily with the fields of computational finance and financial engineering.
Single-stock futuresIn finance, a single-stock future (SSF) is a type of futures contract between two parties to exchange a specified number of stocks in a company for a price agreed today (the futures price or the strike price) with delivery occurring at a specified future date, the delivery date. The contracts can be later traded on a futures exchange. The party agreeing to take delivery of the underlying stock in the future, the "buyer" of the contract, is said to be "long", and the party agreeing to deliver the stock in the future, the "seller" of the contract, is said to be "short".
Lattice model (finance)In finance, a lattice model is a technique applied to the valuation of derivatives, where a discrete time model is required. For equity options, a typical example would be pricing an American option, where a decision as to option exercise is required at "all" times (any time) before and including maturity. A continuous model, on the other hand, such as Black–Scholes, would only allow for the valuation of European options, where exercise is on the option's maturity date.
Quantitative analysis (finance)Quantitative analysis is the use of mathematical and statistical methods in finance and investment management. Those working in the field are quantitative analysts (quants). Quants tend to specialize in specific areas which may include derivative structuring or pricing, risk management, investment management and other related finance occupations. The occupation is similar to those in industrial mathematics in other industries.
Mark-to-market accountingMark-to-market (MTM or M2M) or fair value accounting is accounting for the "fair value" of an asset or liability based on the current market price, or the price for similar assets and liabilities, or based on another objectively assessed "fair" value. Fair value accounting has been a part of Generally Accepted Accounting Principles (GAAP) in the United States since the early 1990s.
Financial economicsFinancial economics is the branch of economics characterized by a "concentration on monetary activities", in which "money of one type or another is likely to appear on both sides of a trade". Its concern is thus the interrelation of financial variables, such as share prices, interest rates and exchange rates, as opposed to those concerning the real economy. It has two main areas of focus: asset pricing and corporate finance; the first being the perspective of providers of capital, i.e.
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.
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.
Forward rate agreementIn finance, a forward rate agreement (FRA) is an interest rate derivative (IRD). In particular it is a linear IRD with strong associations with interest rate swaps (IRSs). A forward rate agreement's (FRA's) effective description is a cash for difference derivative contract, between two parties, benchmarked against an interest rate index. That index is commonly an interbank offered rate (-IBOR) of specific tenor in different currencies, for example LIBOR in USD, GBP, EURIBOR in EUR or STIBOR in SEK.
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.
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.
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.
