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Delta Hedging
In finance, delta neutral describes a portfolio of related financial securities, in which the portfolio value remains unchanged when small changes occur in the value of the underlying security (having zero delta). Such a portfolio typically contains options and their corresponding underlying securities such that positive and negative delta components offset, resulting in the portfolio's value being relatively insensitive to changes in the value of the underlying security. A related term, delta hedging, is the process of setting or keeping a portfolio as close to delta-neutral as possible. In practice, maintaining a zero delta is very complex because there are risks associated with re-hedging on large movements in the underlying stock's price, and research indicates portfolios tend to have lower cash flows if re-hedged too frequently.De Weert F. pp. 74-81 Delta hedging may be accomplished by trading underlying securities of the portfolio. See for details. Mathematical interpret ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finance
Finance refers to monetary resources and to the study and Academic discipline, discipline of money, currency, assets and Liability (financial accounting), liabilities. As a subject of study, is a field of Business administration, Business Administration wich study the planning, organizing, leading, and controlling of an organization's resources to achieve its goals. Based on the scope of financial activities in financial systems, the discipline can be divided into Personal finance, personal, Corporate finance, corporate, and public finance. In these financial systems, assets are bought, sold, or traded as financial instruments, such as Currency, currencies, loans, Bond (finance), bonds, Share (finance), shares, stocks, Option (finance), options, Futures contract, futures, etc. Assets can also be banked, Investment, invested, and Insurance, insured to maximize value and minimize loss. In practice, Financial risk, risks are always present in any financial action and entities. Due ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Market Maker
A market maker or liquidity provider is a company or an individual that quotes both a buy and a sell price in a tradable asset held in inventory, hoping to make a profit on the difference, which is called the ''bid–ask spread'' or ''turn.'' This stabilizes the market, reducing price variation (Volatility (finance), volatility) by setting a trading price range for the asset. In U.S. markets, the U.S. Securities and Exchange Commission defines a "market maker" as a firm that stands ready to buy and sell stock on a regular and continuous basis at a publicly quoted price. A Designated Primary Market Maker (DPM) is a specialized market maker approved by an exchange to guarantee a buy or sell position in a particular assigned security, option, or option index. In currency exchange Most foreign exchange trading firms are market makers, as are many banks. The foreign exchange market maker both buys foreign currency from clients and sells it to other clients. They derive income from the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Financial Markets
A financial market is a market in which people trade financial securities and derivatives at low transaction costs. Some of the securities include stocks and bonds, raw materials and precious metals, which are known in the financial markets as commodities. The term "market" is sometimes used for what are more strictly ''exchanges'', that is, organizations that facilitate the trade in financial securities, e.g., a stock exchange or commodity exchange. This may be a physical location (such as the New York Stock Exchange (NYSE), London Stock Exchange (LSE), Bombay Stock Exchange (BSE) or Johannesburg Stock Exchange (JSE Limited)) or an electronic system such as NASDAQ. Much trading of stocks takes place on an exchange; still, corporate actions (mergers, spinoffs) are outside an exchange, while any two companies or people, for whatever reason, may agree to sell the stock from the one to the other without using an exchange. Trading of currencies and bonds is largely on a bi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convexity (finance)
In mathematical finance, convexity refers to non-linearities in a financial model. In other words, if the price of an underlying variable changes, the price of an output does not change linearly, but depends on the second derivative (or, loosely speaking, higher-order terms) of the modeling function. Geometrically, the model is no longer flat but curved, and the degree of curvature is called the convexity. Terminology Strictly speaking, convexity refers to the second derivative of output price with respect to an input price. In derivative pricing, this is referred to as Gamma (Γ), one of the Greeks. In practice the most significant of these is bond convexity, the second derivative of bond price with respect to interest rates. As the second derivative is the first non-linear term, and thus often the most significant, "convexity" is also used loosely to refer to non-linearities generally, including higher-order terms. Refining a model to account for non-linearities is referred ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orders Of Approximation
In science, engineering, and other quantitative disciplines, order of approximation refers to formal or informal expressions for how accurate an approximation is. Usage in science and engineering In formal expressions, the ordinal number used before the word order refers to the highest power in the series expansion used in the approximation. The expressions: a ''zeroth-order approximation'', a ''first-order approximation'', a ''second-order approximation'', and so forth are used as fixed phrases. The expression a ''zero-order approximation'' is also common. Cardinal numerals are occasionally used in expressions like an ''order-zero approximation'', an ''order-one approximation'', etc. The omission of the word ''order'' leads to phrases that have less formal meaning. Phrases like first approximation or to a first approximation may refer to ''a roughly approximate value of a quantity''. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Taylor Expansion
In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor series are equal near this point. Taylor series are named after Brook Taylor, who introduced them in 1715. A Taylor series is also called a Maclaurin series when 0 is the point where the derivatives are considered, after Colin Maclaurin, who made extensive use of this special case of Taylor series in the 18th century. The partial sum formed by the first terms of a Taylor series is a polynomial of degree that is called the th Taylor polynomial of the function. Taylor polynomials are approximations of a function, which become generally more accurate as increases. Taylor's theorem gives quantitative estimates on the error introduced by the use of such approximations. If the Taylor series of a function is convergent, its sum is the limit o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Derivation
Derivation may refer to: Language * Morphological derivation, a word-formation process * Parse tree or concrete syntax tree, representing a string's syntax in formal grammars Law * Derivative work, in copyright law * Derivation proceeding, a proceeding in United States patent law Music * The creation of a derived row, in the twelve-tone musical technique Science and mathematics * Derivation (differential algebra), a unary function satisfying the Leibniz product law * Formal proof or derivation, a sequence of sentences each of which is an axiom or follows from the preceding sentences in the sequence by a rule of inference * An after-the-fact justification for an action, in the work of sociologist Vilfredo Pareto See also * Derive (other), for meanings of "derive" and "derived" *Derivative In mathematics, the derivative is a fundamental tool that quantifies the sensitivity to change of a function's output with respect to its input. The derivative of a function ... [...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 (finance), 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 option style, European-style option (finance), 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 (finance), hedge the option by buying and selling the underlying asset in a specific way to eliminate risk. This type of hedging is called "continuou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear
In mathematics, the term ''linear'' is used in two distinct senses for two different properties: * linearity of a '' function'' (or '' mapping''); * linearity of a '' polynomial''. An example of a linear function is the function defined by f(x)=(ax,bx) that maps the real line to a line in the Euclidean plane R2 that passes through the origin. An example of a linear polynomial in the variables X, Y and Z is aX+bY+cZ+d. Linearity of a mapping is closely related to '' proportionality''. Examples in physics include the linear relationship of voltage and current in an electrical conductor ( Ohm's law), and the relationship of mass and weight. By contrast, more complicated relationships, such as between velocity and kinetic energy, are '' nonlinear''. Generalized for functions in more than one dimension, linearity means the property of a function of being compatible with addition and scaling, also known as the superposition principle. Linearity of a polynomial means that its de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Short Selling
In finance, being short in an asset means investing in such a way that the investor will profit if the market value of the asset falls. This is the opposite of the more common Long (finance), long Position (finance), position, where the investor will profit if the market value of the asset rises. An investor that sells an asset short is, as to that asset, a short seller. There are a number of ways of achieving a short position. The most basic is physical selling short or short-selling, by which the short seller Securities lending, borrows an asset (often a security (finance), security such as a share (finance), share of stock or a bond (finance), bond) and sells it. The short seller must later buy the same amount of the asset to return it to the lender. If the market price of the asset has fallen in the meantime, the short seller will have made a profit equal to the difference in price. Conversely, if the price has risen then the short seller will bear a loss. The short seller ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stock
Stocks (also capital stock, or sometimes interchangeably, shares) consist of all the Share (finance), shares by which ownership of a corporation or company is divided. A single share of the stock means fractional ownership of the corporation in proportion to the total number of shares. This typically entitles the shareholder (stockholder) to that fraction of the company's earnings, proceeds from liquidation of assets (after discharge of all Seniority (financial), senior claims such as secured and unsecured debt), or Voting interest, voting power, often dividing these up in proportion to the number of like shares each stockholder owns. Not all stock is necessarily equal, as certain classes of stock may be issued, for example, without voting rights, with enhanced voting rights, or with a certain priority to receive profits or liquidation proceeds before or after other classes of Shareholder, shareholders. Stock can be bought and sold over-the-counter (finance), privately or on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Derivative (finance)
In finance, a derivative is a contract between a buyer and a seller. The derivative can take various forms, depending on the transaction, but every derivative has the following four elements: # an item (the "underlier") that can or must be bought or sold, # a future act which must occur (such as a sale or purchase of the underlier), # a price at which the future transaction must take place, and # a future date by which the act (such as a purchase or sale) must take place. A derivative's value depends on the performance of the underlier, which can be a commodity (for example, corn or oil), a financial instrument (e.g. a stock or a bond), price index, a price index, a currency, or an interest rate. Derivatives can be used to insure against price movements (Hedge (finance)#Etymology, hedging), increase exposure to price movements for speculation, or get access to otherwise hard-to-trade assets or markets. Most derivatives are price guarantees. But some are based on an event or p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
