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Financial Correlation
Financial correlations measure the relationship between the changes of two or more financial variables over time. For example, the prices of equity stocks and fixed interest bonds often move in opposite directions: when investors sell stocks, they often use the proceeds to buy bonds and vice versa. In this case, stock and bond prices are negatively correlated. Financial correlations play a key role in modern finance. Under the capital asset pricing model (CAPM; a model recognised by a Nobel prize), an increase in diversification increases the return/risk ratio. Measures of risk include value at risk, expected shortfall, and portfolio return variance. Financial correlation and the Pearson product-moment correlation coefficient There are several statistical measures of the degree of financial correlations. The Pearson product-moment correlation coefficient is sometimes applied to finance correlations. However, the limitations of Pearson correlation approach in finance are evide ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equity (finance)
In finance, equity is ownership of assets that may have debts or other liabilities attached to them. Equity is measured for accounting purposes by subtracting liabilities from the value of the assets. For example, if someone owns a car worth $24,000 and owes $10,000 on the loan used to buy the car, the difference of $14,000 is equity. Equity can apply to a single asset, such as a car or house, or to an entire business. A business that needs to start up or expand its operations can sell its equity in order to raise cash that does not have to be repaid on a set schedule. In government finance or other non-profit settings, equity is known as "net position" or "net assets". Origins The term "equity" describes this type of ownership in English because it was regulated through the system of equity law that developed in England during the Late Middle Ages to meet the growing demands of commercial activity. While the older common law courts dealt with questions of property title, eq ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic Differential Equations
A stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution which is also a stochastic process. SDEs are used to model various phenomena such as stock prices or physical systems subject to thermal fluctuations. Typically, SDEs contain a variable which represents random white noise calculated as the derivative of Brownian motion or the Wiener process. However, other types of random behaviour are possible, such as jump processes. Random differential equations are conjugate to stochastic differential equations. Background Stochastic differential equations originated in the theory of Brownian motion, in the work of Albert Einstein and Smoluchowski. These early examples were linear stochastic differential equations, also called 'Langevin' equations after French physicist Langevin, describing the motion of a harmonic oscillator subject to a random force. The mathematical theory of stochas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Basel II
Basel II is the second of the Basel Accords, which are recommendations on banking laws and regulations issued by the Basel Committee on Banking Supervision. It is now extended and partially superseded by Basel III. The Basel II Accord was published in June 2004. It was a new framework for international banking standards, superseding the Basel I framework, to determine the minimum capital that banks should hold to guard against the financial and operational risks. The regulations aimed to ensure that the more significant the risk a bank is exposed to, the greater the amount of capital the bank needs to hold to safeguard its solvency and overall economic stability. Basel II attempted to accomplish this by establishing risk and capital management requirements to ensure that a bank has adequate capital for the risk the bank exposes itself to through its lending, investment and trading activities. One focus was to maintain sufficient consistency of regulations so to limit competiti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Credit Default Swaps
A credit default swap (CDS) is a financial swap agreement that the seller of the CDS will compensate the buyer in the event of a debt default (by the debtor) or other credit event. That is, the seller of the CDS insures the buyer against some reference asset defaulting. The buyer of the CDS makes a series of payments (the CDS "fee" or "spread") to the seller and, in exchange, may expect to receive a payoff if the asset defaults. In the event of default, the buyer of the credit default swap receives compensation (usually the face value of the loan), and the seller of the CDS takes possession of the defaulted loan or its market value in cash. However, anyone can purchase a CDS, even buyers who do not hold the loan instrument and who have no direct insurable interest in the loan (these are called "naked" CDSs). If there are more CDS contracts outstanding than bonds in existence, a protocol exists to hold a credit event auction. The payment received is often substantially les ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tranches
In structured finance, a tranche is one of a number of related securities offered as part of the same transaction. In the financial sense of the word, each bond is a different slice of the deal's risk. Transaction documentation (see indenture) usually defines the tranches as different "classes" of notes, each identified by letter (e.g., the Class A, Class B, Class C securities) with different bond credit ratings. The term ''tranche'' is used in fields of finance other than structured finance (such as in straight lending, where ''multi-tranche loans'' are commonplace), but the term's use in structured finance may be singled out as particularly important. Use of "tranche" as a verb is limited almost exclusively to this field. The word ''tranche'' means ''a division or portion of a pool or whole'' and is derived from the French for 'slice', 'section', 'series', or 'portion', and is also a cognate of the English 'trench' ('ditch'). How tranching works All the tranches together ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Four Correlations
4 (four) is a number, numeral and digit. It is the natural number following 3 and preceding 5. It is the smallest semiprime and composite number, and is considered unlucky in many East Asian cultures. In mathematics Four is the smallest composite number, its proper divisors being and . Four is the sum and product of two with itself: 2 + 2 = 4 = 2 x 2, the only number b such that a + a = b = a x a, which also makes four the smallest squared prime number p^. In Knuth's up-arrow notation, , and so forth, for any number of up arrows. By consequence, four is the only square one more than a prime number, specifically three. The sum of the first four prime numbers two + three + five + seven is the only sum of four consecutive prime numbers that yields an odd prime number, seventeen, which is the fourth super-prime. Four lies between the first proper pair of twin primes, three and five, which are the first two Fermat primes, like seventeen, which is the third. On the other ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Collateralized Debt Obligation
A collateralized debt obligation (CDO) is a type of structured asset-backed security (ABS). Originally developed as instruments for the corporate debt markets, after 2002 CDOs became vehicles for refinancing mortgage-backed securities (MBS).Lepke, Lins and Pi card, ''Mortgage-Backed Securities'', §5:15 (Thomson West, 2014). Like other private label securities backed by assets, a CDO can be thought of as a promise to pay investors in a prescribed sequence, based on the cash flow the CDO collects from the pool of bonds or other assets it owns. Distinctively, CDO credit risk is typically assessed based on a probability of default (PD) derived from ratings on those bonds or assets. The CDO is "sliced" into sections known as "tranches", which "catch" the cash flow of interest and principal payments in sequence based on seniority. If some loans default and the cash collected by the CDO is insufficient to pay all of its investors, those in the lowest, most "junior" tranches suffer l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abe Sklar
Abe Sklar (November 25, 1925 – October 30, 2020) was an American mathematician and a professor of applied mathematics at the Illinois Institute of Technology (IIT) and the inventor of copulas in probability theory. Education and career Sklar was born in Chicago to Jewish parents who immigrated to the United States from Ukraine. He attended Von Steuben High School and later enrolled at the University of Chicago in 1942, when he was only 16. Sklar went on to become a student of Tom M. Apostol at the California Institute of Technology, where he earned his Ph.D. in 1956. His students at IIT have included geometers Clark Kimberling and Marjorie Senechal. In 1959, Sklar introduced the notion of and the name of " copulas" into probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it thro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Copula (probability Theory)
In probability theory and statistics, a copula is a multivariate cumulative distribution function for which the marginal probability distribution of each variable is uniform on the interval , 1 Copulas are used to describe/model the dependence (inter-correlation) between random variables. Their name, introduced by applied mathematician Abe Sklar in 1959, comes from the Latin for "link" or "tie", similar but unrelated to grammatical copulas in linguistics. Copulas have been used widely in quantitative finance to model and minimize tail risk and portfolio-optimization applications. Sklar's theorem states that any multivariate joint distribution can be written in terms of univariate marginal distribution functions and a copula which describes the dependence structure between the variables. Copulas are popular in high-dimensional statistical applications as they allow one to easily model and estimate the distribution of random vectors by estimating marginals and co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Of Default
Probability of default (PD) is a financial term describing the likelihood of a default over a particular time horizon. It provides an estimate of the likelihood that a borrower will be unable to meet its debt obligations. PD is used in a variety of credit analyses and risk management frameworks. Under Basel II, it is a key parameter used in the calculation of economic capital or regulatory capital for a banking institution. PD is closely linked to the expected loss, which is defined as the product of the PD, the loss given default (LGD) and the exposure at default (EAD). Overview The probability of default is an estimate of the likelihood that the default event will occur. It applies to a particular assessment horizon, usually one year. Credit scores, such as FICO for consumers or bond ratings from S&P, Fitch or Moodys for corporations or governments, typically imply a certain probability of default. For group of obligors sharing similar credit risk characteristics suc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Black–Scholes Model
The Black–Scholes or Black–Scholes–Merton model is a mathematical model for the dynamics of a financial market containing derivative investment instruments. From the parabolic partial differential equation in the model, known as the Black–Scholes equation, one can deduce the Black–Scholes formula, which gives a theoretical estimate of the price of European-style options and shows that the option has a ''unique'' price given the risk of the security and its expected return (instead replacing the security's expected return with the risk-neutral rate). The equation and model are named after economists Fischer Black and Myron Scholes; Robert C. Merton, who first wrote an academic paper on the subject, is sometimes also credited. The main principle behind the model is to hedge the option by buying and selling the underlying asset in a specific way to eliminate risk. This type of hedging is called "continuously revised delta hedging" and is the basis of more complicated he ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Independent And Identically Distributed Random Variables
In probability theory and statistics, a collection of random variables is independent and identically distributed if each random variable has the same probability distribution as the others and all are mutually independent. This property is usually abbreviated as ''i.i.d.'', ''iid'', or ''IID''. IID was first defined in statistics and finds application in different fields such as data mining and signal processing. Introduction In statistics, we commonly deal with random samples. A random sample can be thought of as a set of objects that are chosen randomly. Or, more formally, it’s “a sequence of independent, identically distributed (IID) random variables”. In other words, the terms ''random sample'' and ''IID'' are basically one and the same. In statistics, we usually say “random sample,” but in probability it’s more common to say “IID.” * Identically Distributed means that there are no overall trends–the distribution doesn’t fluctuate and all items in th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
