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In modern portfolio theory, the efficient frontier (or portfolio frontier) is an investment portfolio which occupies the "efficient" parts of the risk–return spectrum.

The efficient-market hypothesis (EMH) is a hypothesis in financial economics that states that asset prices reflect all available information. A direct implication is that it is impossible to "beat the market" consistently on a risk-adjusted basis since market prices should only react to new information.

An electronic communication network (ECN) is a type of computerized forum or network that facilitates the trading of financial products outside traditional stock exchanges. An ECN is generally an electronic system accessed by an electronic trading platform that widely disseminates orders entered by market makers to third parties and permits the orders to be executed against them in whole

Employee stock options (ESO or ESOPs) is a label that refers to compensation contracts between an employer and an employee that carries some characteristics of financial options.

An energy derivative is a derivative contract based on (derived from) an underlying energy asset, such as natural gas, crude oil, or electricity. Energy derivatives are exotic derivatives and include exchange-traded contracts such as futures and options, and over-the-counter (i.e., privately negotiated) derivatives such as forwards, swaps and options. Major players in the energy derivati

In finance, an equity derivative is a class of derivatives whose value is at least partly derived from one or more underlying equity securities. Options and futures are by far the most common equity derivatives, however there are many other types of equity derivatives that are actively traded.

The equity premium puzzle refers to the inability of an important class of economic models to explain the average equity risk premium (ERP) provided by a diversified portfolio of equities over that of government bonds, which has been observed for more than 100 years. There is a significant disparity between returns produced by stocks compared to returns produced by government treasury bi

An equity swap is a financial derivative contract (a swap) where a set of future cash flows are agreed to be exchanged between two counterparties at set dates in the future. The two cash flows are usually referred to as "legs" of the swap; one of these "legs" is usually pegged to a floating rate such as LIBOR. This leg is also commonly referred to as the "floating leg". The other leg of

An equity-linked note (ELN) is a debt instrument, usually a bond issued by a financial institution such as an investment bank or a subsidiary of a commercial bank. ELNs are liabilities of the issuer, but the final payout to the investor is based on an unrelated company's stock price, a stock index or a group of stocks or stock indices. The underlying stocks typically have large market ca

Event-driven investing or Event-driven trading is a broad term encompassing hedge fund investment strategies that seeks to exploit pricing inefficiencies that may occur before or after an event. Examples of such events could be an earnings call, bankruptcy, merger, acquisition, or spinoff. In more recent times market practitioners have expanded this definition to include additional event

An exchange, bourse (), trading exchange or trading venue is an organized market where people can buy and sell financial instruments, such as tradable securities, commodities, foreign exchange and derivative contracts.

In finance, an exchange rate is the rate at which one currency will be exchanged for another currency. Currencies are most commonly national currencies, but may be sub-national as in the case of Hong Kong or supra-national as in the case of the euro.

The owner of an option contract has the right to exercise it, and thus require that the financial transaction specified by the contract is to be carried out immediately between the two parties, whereupon the option contract is terminated. When exercising a call option, the owner of the option purchases the underlying shares (or commodities, fixed interest securities, etc.) at the strike

In finance, an exotic option is an option which has features making it more complex than commonly traded vanilla options. Like the more general exotic derivatives they may have several triggers relating to determination of payoff. An exotic option may also include a non-standard underlying instrument, developed for a particular client or for a particular market. Exotic options are mor

In finance, the expiration date of an option contract (represented by Greek letter tau, τ) is the last date on which the holder of the option may exercise it according to its terms. In the case of options with "automatic exercise", the net value of the option is credited to the long and debited to the short position holders.

Extreme value theory or extreme value analysis (EVA) is the study of extremes in statistical distributions.

Factor investing is an investment approach that targets measurable characteristics of securities, known as factors, which help explain differences in risk and return. Commonly studied equity factors include size, value, momentum, quality, and low volatility. Other characteristics sometimes used in factor-based strategies include asset growth, leverage, term, carry and liquidity.

Fairmat is a free-of-charge multi-platform software that allows to model financial contracts (e.g. a derivative contract) or projects with many contingencies (e.g. a Real Options model) by decomposing it into basic parts. Complex structures and dependencies are modelled using a graphical interface. Virtually any pay-off function and asset class( from interest rate derivatives to equity-l

In asset pricing and portfolio management, the Fama–French three-factor model is a statistical model designed in 1992 by Eugene Fama and Kenneth French to describe stock returns. Fama and French were colleagues at the University of Chicago Booth School of Business, where Fama still works. In 2013, Fama shared the Nobel Memorial Prize in Economic Sciences for his empirical analysis of ass

The "Fed model", or "Fed Stock Valuation Model" (FSVM), is a disputed theory of equity valuation that compares the stock market's forward earnings yield to the nominal yield on long-term government bonds, and that the stock market – as a whole – is fairly valued, when the one-year forward-looking I/B/E/S earnings yield equals the 10-year nominal Treasury yield; deviations suggest over-or

The Federation of Euro-Asian Stock Exchanges (FEAS) is a non-profit international organization comprising the main stock exchanges in Eastern Europe, the Middle East, and Central Asia. The purpose of the Federation is to contribute to the cooperation, development, support and promotion of capital markets in Eurasia, although membership in the Federation is open to markets internationally

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 econometrics is the application of statistical methods to financial data. Financial econometrics is a branch of financial economics, in the field of economics. Areas of study include capital markets, financial institutions, corporate finance and corporate governance. Topics often revolve around asset valuation of individual stocks, bonds, derivatives, currencies and other fina

Financial innovation is the act of creating new financial instruments as well as new financial technologies, institutions, and markets. Recent financial innovations include hedge funds, private equity, weather derivatives, retail-structured products, exchange-traded funds, multi-family offices, and Islamic bonds (Sukuk). The shadow banking system has spawned an array of financial innovat

Financial modeling

Financial regulation is a broad set of policies that apply to the financial sector in most jurisdictions, justified by two main features of finance: systemic risk, which implies that the failure of financial firms involves public interest considerations; and information asymmetry, which justifies curbs on freedom of contract in selected areas of financial services, particularly those tha

Financial risk is any of various types of risk associated with financing, including financial transactions that include company loans in risk of default. Often it is understood to include only downside risk, meaning the potential for financial loss and uncertainty about its extent.

Finite difference methods for option pricing are numerical methods used in mathematical finance for the valuation of options. Finite difference methods were first applied to option pricing by Eduardo Schwartz in 1977.

Fixed-income arbitrage is a group of market-neutral-investment strategies that are designed to take advantage of differences in interest rates between varying fixed-income securities or contracts (Jefferson, 2007). Arbitrage in terms of investment strategy, involves buying securities on one market for immediate resale on another market in order to profit from a price discrepancy.

Fixed-Income Relative-Value Investing (FI-RV) is a hedge fund investment strategy made popular by the failed hedge fund Long-Term Capital Management.

A flight-to-quality, or flight-to-safety, is a financial market phenomenon occurring when investors sell what they perceive to be higher-risk investments and purchase safer investments, such as gold and government bonds. This is considered a sign of fear in the marketplace, as investors seek less risk in exchange for lower profits.

A floor trader is a member of a stock or commodities exchange who trades on the floor of that exchange for their own account. The floor trader must abide by trading rules similar to those of the exchange specialists who trade on behalf of others. The term should not be confused with floor broker.

A foreign exchange derivative is a financial contract whose value changes depending on currency exchange rates.

In finance, a foreign exchange option (commonly shortened to just FX option or currency option) is a derivative financial instrument that gives the right but not the obligation to exchange money denominated in one currency into another currency at a pre-agreed exchange rate on a specified date. See Foreign exchange derivative.

In finance, a foreign exchange swap, forex swap, or FX swap is a simultaneous purchase and sale of identical amounts of one currency for another with two different value dates (normally spot to forward) and may use foreign exchange derivatives. An FX swap allows sums of a certain currency to be used to fund charges designated in another currency without acquiring foreign exchange risk. I

In finance, a forward contract, or simply a forward, is a non-standardized contract between two parties to buy or sell an asset at a specified future time at a price agreed on in the contract, making it a type of derivative instrument. The party agreeing to buy the underlying asset in the future assumes a long position, and the party agreeing to sell the asset in the future assumes a sh

The forward price (or sometimes forward rate) is the agreed upon price of an asset in a forward contract. Using the rational pricing assumption, for a forward contract on an underlying asset that is tradeable, the forward price can be expressed in terms of the spot price and any dividends. For forwards on non-tradeables, pricing the forward may be a complex task.

In finance, a forward rate agreement (FRA) is an interest rate derivative (IRD). In particular, it is a linear IRD with strong associations with interest rate swaps (IRSs).

Front running, also known as tailgating, is the practice of entering into an equity (stock) trade, option, futures contract, derivative, or security-based swap to capitalize on advance, nonpublic knowledge of a large ("block") pending transaction that will influence the price of the underlying security. In essence, it means the use of knowledge of an impending trade to engage in a person

The FTSE MTIRS Indices are designed to accurately move in direct correlation to OTC Interest Rate Swaps market with a total of 45 indices covering the USD curve from 2 years to 30 years including spreads and butterflies. FTSE MTIRS Indices account for changes to both fixed and floating rates and are rebalanced daily.

A fund derivative (see also derivative) is a financial structured product related to a fund, normally using the underlying fund to determine the payoff. This may be a private equity fund, mutual fund or hedge fund. Purchasers obtain exposure to the underlying fund (or funds) whilst improving their risk profile over a direct investment.

Fund governance refers to a system of checks and balances and work performed by the governing body (board) of an investment fund to ensure that the fund is operated not only in accordance with law, but also in the best interests of the fund and its investors. The objective of fund governance is to uphold the regulatory principles commonly known as the four pillars of investor protection

A "fund of funds" (FOF) is an investment strategy of holding a portfolio of other investment funds rather than investing directly in stocks, bonds or other securities. This type of investing is often referred to as multi-manager investment. A fund of funds may be "fettered", meaning that it invests only in funds managed by the same investment company, or "unfettered", meaning that it can

Fundamental analysis, in accounting and finance, is the analysis of a business's financial statements (usually to analyze the business's assets, liabilities, and earnings); health; competitors and markets. It also considers the overall state of the economy and factors including interest rates, production, earnings, employment, GDP, housing, manufacturing and management. There are two bas

The fundamental theorems of asset pricing (also: of arbitrage, of finance), in both financial economics and mathematical finance, provide necessary and sufficient conditions for a market to be arbitrage-free, and for a market to be complete. An arbitrage opportunity is a way of making money with no initial investment without any possibility of loss. Though arbitrage opportunities do exis

Fundamentally based indexes or fundamental indexes, also called fundamentally weighted indexes, are indexes in which stocks are weighted according to factors related to their fundamentals such as earnings, dividends and assets, commonly used when performing corporate valuations. This fundamental weight may be calculated statically, or it may be adjusted by the security's fundamental to m

In finance, a futures contract (often just called a future) is a standardized legal contract to buy or sell something at a predetermined price for delivery at a specified time in the future, between parties not yet known to each other. The item transacted is usually a commodity or financial instrument. The predetermined price of the contract is known as the forward price or delivery pric

The Gibraltar Stock Exchange (GSX) was a stock exchange based in Gibraltar, a British overseas territory. until its closure in 2023.

In probability theory, Girsanov's theorem or the Cameron-Martin-Girsanov theorem explains how stochastic processes change under changes in measure.

Global macro trading is an investment strategy that leverages macroeconomic and geopolitical data to analyze and predict moves in financial markets. Large-scale or "macro" political and economic events can disproportionately impact certain sectors, such as the energy, commodity, and currency markets, over others. The strategy typically employs forecasts and analysis of interest rate tren

In business and finance, a golden share is a type of share of stock that lets its owner outvote all other shareholders in certain circumstances. Golden shares often belong to the government when a government-owned company is undergoing the process of privatization and transformation into a stock company.

In mathematical finance, the Greeks are the quantities (known in calculus as partial derivatives; first-order or higher) representing the sensitivity of the price of a derivative instrument, such as an option or future, to changes in one or more underlying parameters on which the value of an instrument or portfolio of financial instruments is dependent. The name is used because the most

The Greenspan put was a monetary policy that Alan Greenspan, during his tenure as chair of the Federal Reserve, exercised in response to financial crises. It was used for the first time with the crash of 1987. Though it was successful in addressing various crises, it became controversial as it led to periods of extreme speculation led by Wall Street investment banks overusing the put's r

In finance, a growth stock is a stock of a company that generates substantial and sustainable positive cash flow and whose revenues and earnings are expected to increase at a faster rate than the average company within the same industry. A growth company typically has some sort of competitive advantage (a new product, a breakthrough patent, overseas expansion) that allows it to fend off

In finance, a haircut is the difference between the current market value of an asset and the value ascribed to that asset for purposes of calculating regulatory capital or loan collateral. The amount of the haircut reflects the perceived risk of the asset falling in value in an immediate cash sale or liquidation. The larger the risk or volatility of the asset price, the larger the haircu

In corporate finance, Hamada’s equation is an equation used as a way to separate the financial risk of a levered firm from its business risk. The equation combines the Modigliani–Miller theorem with the capital asset pricing model. It is used to help determine the levered beta and, through this, the optimal capital structure of firms. It was named after Robert Hamada, the Professor of Fi

In probability theory and statistics, a Hawkes process is an age-dependent branching process driven by immigration from an inhomogeneous Poisson process. The process, named after Alan G. Hawkes, is also called a self-exciting point process., i.e., the occurrence of an event increases the likelihood of another event occurring. It has arrivals at times

The Heath–Jarrow–Morton (HJM) framework is a general framework to model the evolution of interest rate curves – instantaneous forward rate curves in particular (as opposed to simple forward rates). When the volatility and drift of the instantaneous forward rate are assumed to be deterministic, this is known as the Gaussian Heath–Jarrow–Morton (HJM) model of forward rates. For direct mode

A hedge is an investment position intended to offset potential losses or gains that may be incurred by a companion investment. A hedge can be constructed from many types of financial instruments, including stocks, exchange-traded funds, insurance, forward contracts, swaps, options, gambles, many types of over-the-counter and derivative products, and futures contracts.

In finance, the Heston model, named after Steven L. Heston, is a mathematical model that describes the evolution of the volatility of an underlying asset. It is a stochastic volatility model: such a model assumes that the volatility of the asset is not constant, nor even deterministic, but follows a random process.

High-frequency trading (HFT) is a type of algorithmic automated trading system in finance characterized by high speeds, high turnover rates, and high order-to-trade ratios that leverages high-frequency financial data and electronic trading tools. While there is no single definition of HFT, among its key attributes are highly sophisticated algorithms, co-location, and very short-term inve

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.

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 de

In finance, economics, and decision theory, hyperbolic absolute risk aversion (HARA) refers to a type of risk aversion that is particularly convenient to model mathematically and to obtain empirical predictions from. It refers specifically to a property of von Neumann–Morgenstern utility functions, which are typically functions of final wealth (or some related variable), and which des

Institutional Capital Network, Inc (doing business as iCapital) is an American fintech company that provides platform solutions related to alternative investments in the private markets.

In 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 (usually Black–Scholes), will return a theoretical value equal to the price of the option. A non-option financial instrument that has embedded optionality, such as an interest rate cap, can also have an impl

In economics, incomplete markets are markets in which there does not exist an Arrow–Debreu security for every possible state of nature. In contrast with complete markets, this shortage of securities will likely restrict individuals from transferring the desired level of wealth among states.

In finance, inflation derivative (or inflation-indexed derivatives) refers to an over-the-counter and exchange-traded derivative that is used to transfer inflation risk from one counterparty to another. See Exotic derivative.

An inflation swap is an over-the-counter derivative in which one party pays a fixed inflation rate and the other pays the realised change in a price index such as CPI, RPI or HICP. Markets trade two main structures: the zero-coupon inflation swap, which settles once at maturity, and the year-on-year inflation swap, which pays periodic coupons. Users include pension funds, insurers and ot

An Inter-dealer broker (IDB) is specialist financial intermediary that facilitates transactions between broker-dealers, dealer banks and other financial institutions rather than private individuals.

In finance, an interest rate derivative (IRD) is a derivative whose payments are determined through calculation techniques where the underlying benchmark product is an interest rate, or set of different interest rates. There are a multitude of different interest rate indices that can be used in this definition.

An interest rate future is a futures contract (a financial derivative) with an interest-bearing instrument as the underlying asset. It is a particular type of interest rate derivative. Examples include Treasury-bill futures, Treasury-bond futures and Eurodollar futures.

In finance, an interest rate swap (IRS) is an interest rate derivative (IRD). It involves exchange of interest rates between two parties. In particular it is a "linear" IRD and one of the most liquid, benchmark products. It has associations with forward rate agreements (FRAs), and with zero coupon swaps (ZCSs).

Intertemporal portfolio choice is the process of allocating one's investable wealth to various assets, especially financial assets, repeatedly over time, in such a way as to optimize some criterion. The set of asset proportions at any time defines a portfolio. Since the returns on almost all assets are not fully predictable, the criterion has to take financial risk into account. Typicall

In finance, the intrinsic value of an asset or security is its value as calculated with regard to an inherent, objective measure. As a distinction, the asset's price is determined relative to other similar assets.

Investment management (sometimes referred to more generally as financial asset management) is the professional asset management of various securities, including shareholdings, bonds, and other assets, such as real estate, to meet specified investment goals for the benefit of investors. Investors may be institutions, such as insurance companies, pension funds, corporations, charities, edu

An investor is a person or entity that allocates financial capital with the expectation of a future return (profit) or to gain an advantage (interest). Through this allocated capital the investor usually purchases some species of property. Types of investments include equity, debt, securities, real estate, infrastructure, currency, commodity, token, derivatives such as put and call optio

In finance an iron butterfly, also known as the ironfly, is the name of an advanced, neutral-outlook, options trading strategy that involves buying and holding four different options at three different strike prices. It is a limited-risk, limited-profit trading strategy that is structured for a larger probability of earning smaller limited profit when the underlying stock is perceived to

The iron condor is an options trading strategy utilizing two vertical spreads – a put spread and a call spread with the same expiration and four different strikes. A long iron condor is essentially selling both sides of the underlying instrument by simultaneously shorting the same number of calls and puts, then covering each position with the purchase of further out of the money call(s)

Itô calculus, named after Kiyosi Itô, extends the methods of calculus to stochastic processes such as Brownian motion (see Wiener process). It has important applications in mathematical finance, in stochastic differential equations, and more recently even in machine learning.

J.P. Morgan & Co. was an American financial institution specialized in investment banking, asset management and private banking founded by financier J. P. Morgan in 1871. Through a series of mergers and acquisitions, the company is now a subsidiary of JPMorgan Chase, the largest banking institution in the world by market capitalization. The company has been historically referred to as th

A jelly roll, or simply a roll, is an options trading strategy that captures the cost of carry of the underlying asset while remaining otherwise neutral. It is often used to take a position on dividends or interest rates, or to profit from mispriced calendar spreads.

In finance, Jensen's alpha (or Jensen's Performance Index, ex-post alpha) is used to determine the abnormal return of a security or portfolio of securities over the theoretical expected return. It is a version of the standard alpha based on a theoretical performance instead of a market index.

Jump diffusion is a stochastic process that involves jumps and diffusion. It is a type of Lévy process. It has important applications in magnetic reconnection, coronal mass ejections, condensed matter physics, and pattern theory and computational vision.

The Korn–Kreer–Lenssen model (KKL model) is a discrete trinomial model proposed in 1998 by Ralf Korn, Markus Kreer and Mark Lenssen to model illiquid securities and to value financial derivatives on these.

In statistics and decision theory, kurtosis risk is the risk that results when a statistical model assumes the normal distribution, but is applied to observations which have a tendency to occasionally be much further (in terms of number of standard deviations) from the average than is expected for a normal distribution.

Since the financial crisis, regulation of financial activities is at the center of economic and political events. The crisis has indeed led regulators but also the academic world to ask new questions about the effectiveness of regulation policies. To answer these questions, the French laboratory of excellence on financial regulation (Labex ReFi) was established at the initiative of the C

In finance, a ladder, also known as a Christmas tree, is a combination of three options of the same type (all calls or all puts) at three different strike prices. A long ladder is used by traders who expect low volatility, while a short ladder is used by traders who expect high volatility. Ladders are in some ways similar to strangles, vertical spreads, condors, or ratio spreads.

In quantitative finance, a lattice model is a numerical approach to the valuation of derivatives in situations requiring a discrete time model. For dividend paying equity options, a typical application would correspond to the pricing of an American-style option, where a decision to exercise is allowed at the closing of any calendar day up to the maturity. A continuous model, on the othe

The LIBOR market model, also known as the BGM Model (Brace Gatarek Musiela Model, in reference to the names of some of the inventors) is a financial model of interest rates. It is used for pricing interest rate derivatives, especially exotic derivatives like Bermudan swaptions, ratchet caps and floors, target redemption notes, autocaps, zero coupon swaptions, constant maturity swaps and

This is a list of abbreviations used in a business or financial context.

This is a list of notable futures exchanges. Those stock exchanges that also offer trading in futures contracts besides trading in securities are listed both here and the list of stock exchanges.

This is a list of major stock exchange mergers and acquisitions in the Americas. It also features the name of any resultant stock exchanges from mergers or acquisitions. According to Robert E. Wright of Bloomberg in 2013, historians assert that "rather than exhibiting a trend of constant consolidation, the number of exchanges active across the globe has waxed and waned several times over

In corporate finance, a listing refers to the company's shares being on the list (or board) of stock that are publicly listed. Some stock exchanges allow shares of a foreign company to be listed and may allow dual listing, subject to conditions.

A 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

In finance, a long position in a financial instrument means the holder of the position owns a positive amount of the instrument. The holder of the position has the expectation that the financial instrument will increase in value. This is known as a bullish position. The term "long position" is often used in context of buying options contracts.

Long/short equity is an investment strategy generally associated with hedge funds. It involves buying equities that are expected to increase in value and selling short equities that are expected to decrease in value. This is different from the risk reversal strategies where investors will simultaneously buy a call option and sell a put option to simulate being long in a stock.

Lookback options, in the terminology of finance, are a type of exotic option with path dependency, among many other kind of options. The payoff depends on the optimal (maximum or minimum) underlying asset's price occurring over the life of the option. The option allows the holder to "look back" over time to determine the payoff. There exist two kinds of lookback options: with floating st

In investing and finance, the low-volatility anomaly is the observation that low-volatility securities have higher returns than high-volatility securities in most markets studied. In other words, assets whose prices or returns change wildly pay worse than assets whose prices or returns are steady. This is an example of a stock market anomaly since it contradicts the central prediction of

Low-volatility investing is an investment style that buys stocks or securities with low volatility and avoids those with high volatility. This investment style exploits the low-volatility anomaly. According to financial theory risk and return should be positively related, however in practice this is not true. Low-volatility investors aim to achieve market-like returns, but with lower ris