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Vasicek Model
In 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 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 of the interest rate and in a way characterizes the amplitude of the instantaneous randomness inflow. The typical parameters b, a and \sigma, tog ... [...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 own any particular assets of the company, which belong to all the shareholders in common. A corporation may issue both ordinary and preference shares, in which case the preference shareholders have priority to receive dividends. In the event of liquidation, ordinary shareholders receive any remaining funds after bondholders, creditors (including employees), and preference shareholders are paid. When the liquidation happens through bankruptcy, the ordinary shareholders typically receive nothing. ... [...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 rather than later, 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 * ... [...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 public university, public Institute of technology, technical university located in Ankara, Turkey. The university emphasizes research and education in engineering and natural sciences, offering about 41 undergraduate programs within 5 faculties, 105 masters and 70 doctorate programs within 5 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 language, English. Over one third of the 1,000 highest scoring students in the Education in Turkey, national university entrance examination choose to enroll in METU; and most of its departments accept the top 0.1% of the nearly 3 million applicants. METU had the greatest share in nation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wisconsin School Of Business
The Wisconsin School of Business (WSB) is the business school of the University of Wisconsin–Madison, a public research university in Madison, Wisconsin and consistently ranks among the top business schools in the world. Founded in 1900, it has more than 45,000 living alumni. The undergraduate program prepares students for business careers, while its Master of Business Administration (MBA) program is based on focused career specializations, and its PhD program prepares students for careers in academia. The school offers student services, such as Accenture Leadership Center, The Huber Business Analytics Lab and International Programs. In the 2019 ''U.S. News & World Report'' rankings, the Wisconsin School of Business's undergraduate program was ranked 18th overall among business schools. The University of Wisconsin-Madison currently has the most Fortune 500 CEOs alumni of any school in the world, with 14. School name In 2005 the Wisconsin School of Business Dean Michael Knette ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prentice Hall
Prentice Hall was an American major educational publisher owned by Savvas Learning Company. Prentice Hall publishes print and digital content for the 6–12 and higher-education market, and distributes its technical titles through the Safari Books Online e-reference service. 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. Prentice Hall became known as a publisher of trade books by authors such as Norman Vincent Peale; elementary, secondary, and college textbooks; loose-leaf information services; and professional books. Prentice Hall acquired the training provider Deltak in 1979. Prentice Hall was acquired by Gulf+Western in 1984, and became part of that company's publishing division Simon & Schuster. S&S sold several Prentice Hall subsidiaries: Deltak and Resource Systems were sold to National Education ... [...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 se ... [...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 Karasi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Black–Derman–Toy Model
In mathematical finance, 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-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 of the model is provided in Emanuel Derman's memoir '' My Life as a Quant''. Formulae Under BDT, using a binomial lattice, one calibrates the model parameters to fit both the current term structure of interest rates (yield curve), and the volatility structure for interest rate ... [...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. The model The CIR model specifies that the instantaneous interest rate r_t follows the stochastic differential equation, also named the CIR Process: :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 reversion of the interest rate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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