Local volatilityA local volatility model, in mathematical finance and financial engineering, is an option pricing model that treats volatility as a function of both the current asset level and of time . As such, it is a generalisation of the Black–Scholes model, where the volatility is a constant (i.e. a trivial function of and ). Local volatility models are often compared with stochastic volatility models, where the instantaneous volatility is not just a function of the asset level but depends also on a new "global" randomness coming from an additional random component.
Implied volatilityIn financial mathematics, the implied volatility (IV) of an option contract is that value of the volatility of the underlying instrument which, when input in an option pricing model (such as Black–Scholes), will return a theoretical value equal to the current market price of said option. A non-option financial instrument that has embedded optionality, such as an interest rate cap, can also have an implied volatility. Implied volatility, a forward-looking and subjective measure, differs from historical volatility because the latter is calculated from known past returns of a security.
Asset pricingIn financial economics, asset pricing refers to a formal treatment and development of two main pricing principles, outlined below, together with the resultant models. There have been many models developed for different situations, but correspondingly, these stem from either general equilibrium asset pricing or rational asset pricing, the latter corresponding to risk neutral pricing.
DividendA dividend is a distribution of profits by a corporation to its shareholders. When a corporation earns a profit or surplus, it is able to pay a portion of the profit as a dividend to shareholders. Any amount not distributed is taken to be re-invested in the business (called retained earnings). The current year profit as well as the retained earnings of previous years are available for distribution; a corporation is usually prohibited from paying a dividend out of its capital.
Rational pricingRational pricing is the assumption in financial economics that asset prices – and hence asset pricing models – will reflect the arbitrage-free price of the asset as any deviation from this price will be "arbitraged away". This assumption is useful in pricing fixed income securities, particularly bonds, and is fundamental to the pricing of derivative instruments. Arbitrage is the practice of taking advantage of a state of imbalance between two (or possibly more) markets. Where this mismatch can be exploited (i.
Dividend taxA dividend tax is a tax imposed by a jurisdiction on dividends paid by a corporation to its shareholders (stockholders). The primary tax liability is that of the shareholder, though a tax obligation may also be imposed on the corporation in the form of a withholding tax. In some cases the withholding tax may be the extent of the tax liability in relation to the dividend. A dividend tax is in addition to any tax imposed directly on the corporation on its profits. Some jurisdictions do not tax dividends.
Valuation of optionsIn finance, a price (premium) is paid or received for purchasing or selling options. This article discusses the calculation of this premium in general. For further detail, see: for discussion of the mathematics; Financial engineering for the implementation; as well as generally. This price can be split into two components: intrinsic value, and time value (also called "extrinsic value"). The intrinsic value is the difference between the underlying spot price and the strike price, to the extent that this is in favor of the option holder.
Algebraic structureIn mathematics, an algebraic structure consists of a nonempty set A (called the underlying set, carrier set or domain), a collection of operations on A (typically binary operations such as addition and multiplication), and a finite set of identities, known as axioms, that these operations must satisfy. An algebraic structure may be based on other algebraic structures with operations and axioms involving several structures.
Term (logic)In mathematical logic, a term denotes a mathematical object while a formula denotes a mathematical fact. In particular, terms appear as components of a formula. This is analogous to natural language, where a noun phrase refers to an object and a whole sentence refers to a fact. A first-order term is recursively constructed from constant symbols, variables and function symbols. An expression formed by applying a predicate symbol to an appropriate number of terms is called an atomic formula, which evaluates to true or false in bivalent logics, given an interpretation.
Financial economicsFinancial economics is the branch of economics characterized by a "concentration on monetary activities", in which "money of one type or another is likely to appear on both sides of a trade". Its concern is thus the interrelation of financial variables, such as share prices, interest rates and exchange rates, as opposed to those concerning the real economy. It has two main areas of focus: asset pricing and corporate finance; the first being the perspective of providers of capital, i.e.
Yield curveIn finance, the yield curve is a graph which depicts how the yields on debt instruments – such as bonds – vary as a function of their years remaining to maturity. Typically, the graph's horizontal or x-axis is a time line of months or years remaining to maturity, with the shortest maturity on the left and progressively longer time periods on the right. The vertical or y-axis depicts the annualized yield to maturity. Those who issue and trade in forms of debt, such as loans and bonds, use yield curves to determine their value.
Leverage (finance)In finance, leverage (or gearing in the United Kingdom and Australia) is any technique involving borrowing funds to buy things, estimating that future profits will be many times more than the cost of borrowing. This technique is named after a lever in physics, which amplifies a small input force into a greater output force, because successful leverage amplifies the smaller amounts of money needed for borrowing into large amounts of profit. However, the technique also involves the high risk of not being able to pay back a large loan.
Capital gainCapital gain is an economic concept defined as the profit earned on the sale of an asset which has increased in value over the holding period. An asset may include tangible property, a car, a business, or intangible property such as shares. A capital gain is only possible when the selling price of the asset is greater than the original purchase price. In the event that the purchase price exceeds the sale price, a capital loss occurs. Capital gains are often subject to taxation, of which rates and exemptions may differ between countries.
Capital structureIn corporate finance, capital structure refers to the mix of various forms of external funds, known as capital, used to finance a business. It consists of shareholders' equity, debt (borrowed funds), and preferred stock, and is detailed in the company's balance sheet. The larger the debt component is in relation to the other sources of capital, the greater financial leverage (or gearing, in the United Kingdom) the firm is said to have.
Shift workShift work is an employment practice designed to make use of, or provide service across, all 24 hours of the clock each day of the week (often abbreviated as 24/7). The practice typically sees the day divided into shifts, set periods of time during which different groups of workers perform their duties. The term "shift work" includes both long-term night shifts and work schedules in which employees change or rotate shifts.
Share (finance)In financial markets, a share (sometimes referred to as stock) is a unit of equity ownership in the capital stock of a corporation, and can refer to units of mutual funds, limited partnerships, and real estate investment trusts. Share capital refers to all of the shares of an enterprise. The owner of shares in a company is a shareholder (or stockholder) of the corporation. A share is an indivisible unit of capital, expressing the ownership relationship between the company and the shareholder.
Japanese asset price bubbleThe Japanese asset price bubble was an economic bubble in Japan from 1986 to 1991 in which real estate and stock market prices were greatly inflated. In early 1992, this price bubble burst and Japan's economy stagnated. The bubble was characterized by rapid acceleration of asset prices and overheated economic activity, as well as an uncontrolled money supply and credit expansion. More specifically, over-confidence and speculation regarding asset and stock prices were closely associated with excessive monetary easing policy at the time.
Economic bubbleAn economic bubble (also called a speculative bubble or a financial bubble) is a period when current asset prices greatly exceed their intrinsic valuation, being the valuation that the underlying long-term fundamentals justify. Bubbles can be caused by overly optimistic projections about the scale and sustainability of growth (e.g. dot-com bubble), and/or by the belief that intrinsic valuation is no longer relevant when making an investment (e.g. Tulip mania). They have appeared in most asset classes, including equities (e.
Empirical evidenceEmpirical evidence for a proposition is evidence, i.e. what supports or counters this proposition, that is constituted by or accessible to sense experience or experimental procedure. Empirical evidence is of central importance to the sciences and plays a role in various other fields, like epistemology and law. There is no general agreement on how the terms evidence and empirical are to be defined. Often different fields work with quite different conceptions.
Predictive modellingPredictive modelling uses statistics to predict outcomes. Most often the event one wants to predict is in the future, but predictive modelling can be applied to any type of unknown event, regardless of when it occurred. For example, predictive models are often used to detect crimes and identify suspects, after the crime has taken place. In many cases, the model is chosen on the basis of detection theory to try to guess the probability of an outcome given a set amount of input data, for example given an email determining how likely that it is spam.
