|
Ho–Lee Model
In financial mathematics, the Ho–Lee model is a short-rate model widely used in the pricing of bond options, swaptions and other interest rate derivatives, and in modeling future interest rates. It was developed in 1986 by Thomas Ho and Sang Bin Lee. Under this model, the short rate follows a normal process: :dr_t = \theta_t\, dt + \sigma\, dW_t The model can be calibrated to market data by implying the form of \theta_t from market prices, meaning that it can exactly return the price of bonds comprising the yield curve. This calibration, and subsequent valuation of bond options, swaptions and other interest rate derivatives, is typically performed via a binomial lattice based model. Closed form valuations of bonds, and " Black-like" bond option formulae are also available.Graeme West, (2010)''Interest Rate Derivatives'', Financial Modelling Agency. As the model generates a symmetric ("bell shaped") distribution of rates in the future, negative rates are possible. Further, i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Financial Mathematics
Mathematical 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. The latter focuses on applications and modeling, often by help of stochastic asset models, while the former focuses, in addition to analysis, on building tools of implementation for the models. Also related is quantitative investing, which relies on statistical and numerical models (and lately machine learning) as opposed to traditional fundamental analysis when managing portfolios. French mathematician Louis Bachelier's doctoral thesis, defended in 1900, is considered the first scholarly work on mathematical finan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Black Model
The Black model (sometimes known as the Black-76 model) is a variant of the Black–Scholes option pricing model. Its primary applications are for pricing options on future contracts, bond options, interest rate cap and floors, and swaptions. It was first presented in a paper written by Fischer Black in 1976. Black's model can be generalized into a class of models known as log-normal forward models, also referred to as LIBOR market model. The Black formula The Black formula is similar to the Black–Scholes formula for valuing stock options except that the spot price of the underlying is replaced by a discounted futures price F. Suppose there is constant risk-free interest rate ''r'' and the futures price ''F(t)'' of a particular underlying is log-normal with constant volatility ''σ''. Then the Black formula states the price for a European call option of maturity ''T'' on a futures contract with strike price ''K'' and delivery date ''T (with T' \geq T) is : c = e^ N(d_1) - K ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fixed Income Analysis
Fixed income analysis is the process of determining the value of a debt security based on an assessment of its risk profile, which can include interest rate risk, risk of the issuer failing to repay the debt, market supply and demand for the security, call provisions and macroeconomic considerations affecting its value in the future. It also addresses the likely price behavior in hedging portfolios. Based on such an analysis, a fixed income analyst tries to reach a conclusion as to whether to buy, sell, hold, hedge or avoid the particular security. Fixed income products are generally bonds: debt instruments requiring the issuer (i.e. the debtor or borrower) to repay the lender the amount borrowed (principal) plus interest over a specified period of time (coupon payments) until maturity. They are issued by government treasuries, government agencies, companies or international organizations. Calculating Value To determine the value of a fixed income security, the analyst mus ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Columbia University
Columbia University (also known as Columbia, and officially as Columbia University in the City of New York) is a private research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church in Manhattan, Columbia is the oldest institution of higher education in New York and the fifth-oldest institution of higher learning in the United States. It is one of nine colonial colleges founded prior to the Declaration of Independence. It is a member of the Ivy League. Columbia is ranked among the top universities in the world. Columbia was established by royal charter under George II of Great Britain. It was renamed Columbia College in 1784 following the American Revolution, and in 1787 was placed under a private board of trustees headed by former students Alexander Hamilton and John Jay. In 1896, the campus was moved to its current location in Morningside Heights and renamed Columbia University. Columbia scientists and scholars have ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wharton School
The Wharton School of the University of Pennsylvania ( ; also known as Wharton Business School, the Wharton School, Penn Wharton, and Wharton) is the business school of the University of Pennsylvania, a private Ivy League research university in Philadelphia. Generally considered to be one of the most prestigious business schools in the world, the Wharton School is the world's oldest collegiate business school, having been established in 1881 through a donation from Joseph Wharton. The Wharton School awards the Bachelor of Science with a school-specific economics major, with concentrations in over 18 disciplines in Wharton's academic departments. The degree is a general business degree focused on core business skills. At the graduate level, the Master of Business Administration (MBA) program can be pursued standalone or offers dual studies leading to a joint degree from other schools (e.g., law, engineering, government). Similarly, in addition to its tracks in accounting, finance, ... [...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] |
Journal Of Finance
''The Journal of Finance'' is a peer-reviewed academic journal published by Wiley-Blackwell on behalf of the American Finance Association. It was established in 1946 and is considered to be one of the premier finance journals. The editor-in-chief is Antoinette Schoar. According to the ''Journal Citation Reports'', the journal has a 2020 impact factor of 7.544. It is listed as one of the 50 journals used by the ''Financial Times'' to compile its business-school research ranking and ''Bloomberg Businessweek''s Top 20 Journals. Editors The editorial board of the journal of finance consists of the editor, co-editors and associate editors. The executive editor is Antoinette Schoar (MIT The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the m ...), the first female in the position. The following ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kalotay–Williams–Fabozzi Model
A 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 r_t \,. The short rate Under a short rate model, the stochastic state variable is taken to be the instantaneous spot rate. The short rate, r_t \,, then, is the (Compound interest#Continuous compounding, continuously compounded, annualized) interest rate at which an entity can borrow money for an infinitesimally short period of time from time t. Specifying the current short rate does not specify the entire yield curve. However, arbitrage, no-arbitrage arguments show that, under some fairly relaxed technical conditions, if we model the evolution of r_t \, as a stochastic process under a risk-neutral measure Q, then the price at time t of a zero-coupon bond maturing at time T with a payoff of 1 is given by : P(t,T) = \operatorname^Q\left[\left. \exp \ \mathcal_t \right], wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Wiley & Sons
John Wiley & Sons, Inc., commonly known as Wiley (), is an American multinational publishing company founded in 1807 that focuses on academic publishing and instructional materials. The company produces books, journals, and encyclopedias, in print and electronically, as well as online products and services, training materials, and educational materials for undergraduate, graduate, and continuing education students. History The company was established in 1807 when Charles Wiley opened a print shop in Manhattan. The company was the publisher of 19th century American literary figures like James Fenimore Cooper, Washington Irving, Herman Melville, and Edgar Allan Poe, as well as of legal, religious, and other non-fiction titles. The firm took its current name in 1865. Wiley later shifted its focus to scientific, technical, and engineering subject areas, abandoning its literary interests. Wiley's son John (born in Flatbush, New York, October 4, 1808; died in East Orange, New Je ... [...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] |
Lognormal
In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. Thus, if the random variable is log-normally distributed, then has a normal distribution. Equivalently, if has a normal distribution, then the exponential function of , , has a log-normal distribution. A random variable which is log-normally distributed takes only positive real values. It is a convenient and useful model for measurements in exact and engineering sciences, as well as medicine, economics and other topics (e.g., energies, concentrations, lengths, prices of financial instruments, and other metrics). The distribution is occasionally referred to as the Galton distribution or Galton's distribution, after Francis Galton. The log-normal distribution has also been associated with other names, such as McAlister, Gibrat and Cobb–Douglas. A log-normal process is the statistical realization of the multipl ... [...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] |
.png "Click for more on -> Kalotay–Williams–Fabozzi Model")
