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Vasicek Model
In Mathematical finance, 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. Details The model specifies that the force of interest, instantaneous interest rate follows the stochastic differential equation: :dr_t= a(b-r_t)\, dt + \sigma \, dW_t where ''Wt'' is a Wiener process under the risk neutral framework modelling the random market risk factor, in that it models the continuous inflow of randomness into the system. The standard deviation parameter, \sigma, determines the Volatility (finance), volatility of the interest rate and in a way characterizes the amplitude of the instantaneous random ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Common Stock
Common stock is a form of corporate equity ownership, a type of security. The terms voting share and ordinary share are also used frequently outside of the United States. They are known as equity shares or ordinary shares in the UK and other Commonwealth realms. This type of share gives the stockholder the right to share in the profits of the company, and to vote on matters of corporate policy and the composition of the members of the board of directors. The owners of common stock do not directly own any assets of the company; instead each stockholder owns a fractional interest in the company, which in turn owns the assets. As owners of a company, common stockholders are eligible to receive dividends from its recent or past earnings, proceeds from a sale of the company, and distributions of residual (left-over) money if it is liquidated. In general, common stockholders have lowest priority to receive payouts from the company. They may not receive dividends until the company ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interest Rates
An 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. The interest rate has been characterized as "an index of the preference . . . for a dollar of present ncomeover a dollar of future income". The borrower wants, or needs, to have money sooner, and is willing to pay a fee—the interest rate—for that privilege. Influencing factors Interest rates vary according to: * the government's directives to the central bank to accomplish the government's goals * the currency of the principal sum lent or borrowed * the term to mat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Middle East Technical University
Middle East Technical University (commonly referred to as METU; in Turkish language, Turkish, ''Orta Doğu Teknik Üniversitesi'', ODTÜ) is a prestigious public university, public Institute of technology, technical university located in Ankara, Turkey. As Turkey’s top ranked university, they focus on research and education in engineering, Natural science, natural sciences and Social science, social sciences, offering 41 undergraduate programs across five faculties and 105 master's and 70 doctoral programs through five graduate schools. The main campus of METU spans an area of , comprising, in addition to academic and auxiliary facilities, a forest area of , and the natural Lake Eymir. METU has more than 120,000 alumni worldwide. The official language of instruction at METU is English. Over one third of the 1,000 highest scoring students in the Student Selection and Placement System, national university entrance examination choose to enroll in METU; most of its departments acce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wisconsin School Of Business
Wisconsin ( ) is a U.S. state, state in the Great Lakes region, Great Lakes region of the Upper Midwest of the United States. It borders Minnesota to the west, Iowa to the southwest, Illinois to the south, Lake Michigan to the east, Michigan to the northeast, and Lake Superior to the north. With a population of about 6 million and an area of about 65,500 square miles, Wisconsin is the List of U.S. states and territories by population, 20th-largest state by population and the List of U.S. states and territories by area, 23rd-largest by area. It has List of counties in Wisconsin, 72 counties. Its List of municipalities in Wisconsin by population, most populous city is Milwaukee; its List of capitals in the United States, capital and second-most populous city is Madison, Wisconsin, Madison. Other urban areas include Green Bay, Wisconsin, Green Bay, Kenosha, Wisconsin, Kenosha, Racine, Wisconsin, Racine, Eau Claire, Wisconsin, Eau Claire, and the Fox Cities. Geography of Wiscon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prentice Hall
Prentice Hall was a major American publishing#Textbook_publishing, educational publisher. It published print and digital content for the 6–12 and higher-education market. It was an independent company throughout the bulk of the twentieth century. In its last few years it was owned by, then absorbed into, Savvas Learning Company. In the Web era, it distributed its technical titles through the Safari Books Online e-reference service for some years. History On October 13, 1913, law professor Charles Gerstenberg and his student Richard Ettinger founded Prentice Hall. Gerstenberg and Ettinger took their mothers' maiden names, Prentice and Hall, to name their new company. At the time the name was usually styled as Prentice-Hall (as seen for example on many title pages), per an orthographic norm for Dash#Relationships and connections, coordinate elements within such compounds (compare also ''McGraw-Hill'' with later styling as ''McGraw Hill''). Prentice-Hall became known as a publi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zero-coupon Bond
A zero-coupon bond (also discount bond or deep discount bond) is a bond in which the face value is repaid at the time of maturity. Unlike regular bonds, it does not make periodic interest payments or have so-called coupons, hence the term zero-coupon bond. When the bond reaches maturity, its investor receives its par (or face) value. Examples of zero-coupon bonds include US Treasury bills, US savings bonds, long-term zero-coupon bonds, and any type of coupon bond that has been stripped of its coupons. Zero coupon and deep discount bonds are terms that are used interchangeably. In contrast, an investor who has a regular bond receives income from coupon payments, which are made semi-annually or annually. The investor also receives the principal or face value of the investment when the bond matures. Some zero coupon bonds are inflation indexed, and the amount of money that will be paid to the bond holder is calculated to have a set amount of purchasing power, rather than a s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Affine Term Structure Model
An affine term structure model is a financial model that relates zero-coupon bond prices (i.e. the discount curve) to a spot rate model. It is particularly useful for deriving the yield curve – the process of determining spot rate model inputs from observable bond market data. The affine class of term structure models implies the convenient form that log bond prices are linear functions of the spot rate (and potentially additional state variables). Background Start with a stochastic short rate model r(t) with dynamics: : dr(t)=\mu(t,r(t)) \, dt + \sigma(t,r(t)) \, dW(t) and a risk-free zero-coupon bond maturing at time T with price P(t,T) at time t. The price of a zero-coupon bond is given by:P(t,T) = \mathbb^\left\where T=t+\tau, with \tau being is the bond's maturity. The expectation is taken with respect to the risk-neutral probability measure \mathbb. If the bond's price has the form: :P(t,T)=e^ where A and B are deterministic functions, then the short rate model is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hull–White Model
In financial mathematics, the Hull–White model is a model of future interest rates. In its most generic formulation, it belongs to the class of no-arbitrage models that are able to fit today's term structure of interest rates. It is relatively straightforward to translate the mathematical description of the evolution of future interest rates onto a tree or lattice and so interest rate derivatives such as bermudan swaptions can be valued in the model. The first Hull–White model was described by John C. Hull and Alan White in 1990. The model is still popular in the market today. The model One-factor model The model is a short-rate model. In general, it has the following dynamics: :dr(t) = \left theta(t) - \alpha(t) r(t)\right,dt + \sigma(t)\, dW(t). There is a degree of ambiguity among practitioners about exactly which parameters in the model are time-dependent or what name to apply to the model in each case. The most commonly accepted naming convention is the following: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Black–Karasinski Model
In financial mathematics, the Black–Karasinski model is a mathematical model of the term structure of interest rates; see short-rate model. It is a one-factor model as it describes interest rate movements as driven by a single source of randomness. It belongs to the class of no-arbitrage models, i.e. it can fit today's zero-coupon bond prices, and in its most general form, today's prices for a set of caps, floors or European swaptions. The model was introduced by Fischer Black and Piotr Karasinski in 1991. Model The main state variable of the model is the short rate, which is assumed to follow the stochastic differential equation (under the risk-neutral measure): : d\ln(r) = theta_t-\phi_t \ln(r)\, dt + \sigma_t\, dW_t where ''dW''''t'' is a standard Brownian motion. The model implies a log-normal distribution for the short rate and therefore the expected value of the money-market account is infinite for any maturity. In the original article by Fischer Black and Piotr Kara ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Black–Derman–Toy Model
In mathematical finance Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling in the financial field. In general, there exist two separate branches of finance that req ..., the Black–Derman–Toy model (BDT) is a popular short-rate model used in the pricing of bond options, swaptions and other interest rate derivatives; see . It is a one-factor model; that is, a single stochastic factor—the short rate—determines the future evolution of all interest rates. It was the first model to combine the mean reversion (finance), mean-reverting behaviour of the short rate with the log-normal distribution, and is still widely used. History The model was introduced by Fischer Black, Emanuel Derman, and Bill Toy. It was first developed for in-house use by Goldman Sachs in the 1980s and was published in the ''Financial Analysts Journal'' in 1990. A personal account of the development o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cox–Ingersoll–Ross Model
In mathematical finance, the Cox–Ingersoll–Ross (CIR) model describes the evolution of interest rates. It is a type of "one factor model" (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. It was introduced in 1985 by John C. Cox, Jonathan E. Ingersoll and Stephen A. Ross as an extension of the Vasicek model, itself an Ornstein–Uhlenbeck process. The model The CIR model describes the instantaneous interest rate r_t with a Feller square-root process, whose stochastic differential equation is :dr_t = a(b-r_t)\, dt + \sigma\sqrt\, dW_t, where W_t is a Wiener process (modelling the random market risk factor) and a , b , and \sigma\, are the parameters. The parameter a corresponds to the speed of adjustment to the mean b , and \sigma\, to volatility. The drift factor, a(b-r_t), is exactly the same as in the Vasicek model. It ensures mean rev ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
