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Correlation Swap
A correlation swap is an over-the-counter financial derivative that allows one to speculate on or hedge risks associated with the observed average correlation, of a collection of underlying products, where each product has periodically observable prices, as with a commodity, exchange rate, interest rate, or stock index. Payoff Definition The fixed leg of a correlation swap pays the notional N_ times the agreed strike \rho_, while the floating leg pays the realized correlation \rho_. The contract value at expiration from the pay-fixed perspective is therefore :N_ (\rho_-\rho_) Given a set of nonnegative weights w_i on n securities, the realized correlation is defined as the weighted average of all pairwise correlation coefficients \rho_: :\rho_ := \frac Typically \rho_ would be calculated as the Pearson correlation coefficient between the daily log-returns of assets ''i'' and ''j'', possibly under zero-mean assumption. Most correlation swaps trade using equal weights, in which ...
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Over-the-counter (finance)
Over-the-counter (OTC) or off-exchange trading or pink sheet trading is done directly between two parties, without the supervision of an exchange (organized market), exchange. It is contrasted with exchange trading, which occurs via exchanges. A stock exchange has the benefit of facilitating liquidity, providing transparency, and maintaining the current market price. In an OTC trade, the price is not necessarily publicly disclosed. OTC trading, as well as exchange trading, occurs with commodities, financial instruments (including stocks), and derivative (finance), derivatives of such products. Products traded traditional stock exchanges, and other regulated bourse platforms, must be well standardized. This means that exchanged deliverables match a narrow range of quantity, quality, and identity which is defined by the exchange and identical to all transactions of that product. This is necessary for there to be transparency in stock exchange-based equities trading. The OTC ...
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Stock Index
In finance, a stock index, or stock market index, is an index that measures a stock market, or a subset of the stock market, that helps investors compare current stock price levels with past prices to calculate market performance. Two of the primary criteria of an index are that it is ''investable'' and ''transparent'': The methods of its construction are specified. Investors can invest in a stock market index by buying an index fund, which are structured as either a mutual fund or an exchange-traded fund, and "track" an index. The difference between an index fund's performance and the index, if any, is called ''tracking error''. For a list of major stock market indices, see List of stock market indices. Types of indices by weighting method Stock market indices could be segmented by their index weight methodology, or the rules on how stocks are allocated in the index, independent of its stock coverage. For example, the S&P 500 and the S&P 500 Equal Weight both covers the same gro ...
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Mathematical Finance
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 fina ...
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Derivatives (finance)
The derivative of a function is the rate of change of the function's output relative to its input value. Derivative may also refer to: In mathematics and economics *Brzozowski derivative in the theory of formal languages *Formal derivative, an operation on elements of a polynomial ring which mimics the form of the derivative from calculus * Radon–Nikodym derivative in measure theory *Derivative (set theory), a concept applicable to normal functions *Derivative (graph theory), an alternative term for a line graph deva *Derivative (finance), a contract whose value is derived from that of other quantities *Derivative suit or derivative action, a type of lawsuit filed by shareholders of a corporation In science and engineering *Derivative (chemistry), a type of compound which is a product of the process of derivatization *Derivative (linguistics), the process of forming a new word on the basis of an existing word, e.g. happiness and unhappy from happy * Aeroderivative gas turbine, ...
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Rainbow Option
Rainbow option is a derivative exposed to two or more sources of uncertainty, as opposed to a simple option that is exposed to one source of uncertainty, such as the price of underlying asset. The name of ''rainbow'' comes from Rubinstein (1991), who emphasises that this option was based on a combination of various assets like a rainbow is a combination of various colors. More generally, rainbow options are multiasset options, also referred to as correlation options, or basket options. Rainbow can take various other forms but the combining idea is to have a payoff that is depending on the assets sorted by their performance at maturity. When the rainbow only pays the best (or worst) performing asset of the basket, it is also called ''best-of'' (or ''worst-of''). Other popular options that can be reformulated as a rainbow option are spread and exchange options. Overview Rainbow options are usually calls or puts on the best or worst of ''n'' underlying assets. Like the basket option, ...
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Variance Swap
A variance swap is an over-the-counter financial derivative that allows one to speculate on or hedge risks associated with the magnitude of movement, i.e. volatility, of some underlying product, like an exchange rate, interest rate, or stock index. One leg of the swap will pay an amount based upon the realized variance of the price changes of the underlying product. Conventionally, these price changes will be daily log returns, based upon the most commonly used closing price. The other leg of the swap will pay a fixed amount, which is the strike, quoted at the deal's inception. Thus the net payoff to the counterparties will be the difference between these two and will be settled in cash at the expiration of the deal, though some cash payments will likely be made along the way by one or the other counterparty to maintain agreed upon margin. Structure and features The features of a variance swap include: * the variance strike * the realized variance * the vega notional: Like ot ...
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Arbitrage
In economics and finance, arbitrage (, ) is the practice of taking advantage of a difference in prices in two or more markets; striking a combination of matching deals to capitalise on the difference, the profit being the difference between the market prices at which the unit is traded. When used by academics, an arbitrage is a transaction that involves no negative cash flow at any probabilistic or temporal state and a positive cash flow in at least one state; in simple terms, it is the possibility of a risk-free profit after transaction costs. For example, an arbitrage opportunity is present when there is the possibility to instantaneously buy something for a low price and sell it for a higher price. In principle and in academic use, an arbitrage is risk-free; in common use, as in statistical arbitrage, it may refer to ''expected'' profit, though losses may occur, and in practice, there are always risks in arbitrage, some minor (such as fluctuation of prices decreasing profit ...
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Pearson Correlation Coefficient
In statistics, the Pearson correlation coefficient (PCC, pronounced ) ― also known as Pearson's ''r'', the Pearson product-moment correlation coefficient (PPMCC), the bivariate correlation, or colloquially simply as the correlation coefficient ― is a measure of linear correlation between two sets of data. It is the ratio between the covariance of two variables and the product of their standard deviations; thus, it is essentially a normalized measurement of the covariance, such that the result always has a value between −1 and 1. As with covariance itself, the measure can only reflect a linear correlation of variables, and ignores many other types of relationships or correlations. As a simple example, one would expect the age and height of a sample of teenagers from a high school to have a Pearson correlation coefficient significantly greater than 0, but less than 1 (as 1 would represent an unrealistically perfect correlation). Naming and history It was developed by Kar ...
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Interest Rate
An interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited, or borrowed (called the principal sum). The total interest on an amount lent or borrowed depends on the principal sum, the interest rate, the compounding frequency, and the length of time over which it is lent, deposited, or borrowed. The annual interest rate is the rate over a period of one year. Other interest rates apply over different periods, such as a month or a day, but they are usually annualized. The interest rate has been characterized as "an index of the preference . . . for a dollar of present ncomeover a dollar of future income." The borrower wants, or needs, to have money sooner rather than later, and is willing to pay a fee—the interest rate—for that privilege. Influencing factors Interest rates vary according to: * the government's directives to the central bank to accomplish the government's goals * the currency of the principal sum lent or borrowed * ...
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Financial Derivative
In finance, a derivative is a contract that ''derives'' its value from the performance of an underlying entity. This underlying entity can be an asset, index, or interest rate, and is often simply called the "underlying". Derivatives can be used for a number of purposes, including insuring against price movements ( hedging), increasing exposure to price movements for speculation, or getting access to otherwise hard-to-trade assets or markets. Some of the more common derivatives include forwards, futures, options, swaps, and variations of these such as synthetic collateralized debt obligations and credit default swaps. Most derivatives are traded over-the-counter (off-exchange) or on an exchange such as the Chicago Mercantile Exchange, while most insurance contracts have developed into a separate industry. In the United States, after the financial crisis of 2007–2009, there has been increased pressure to move derivatives to trade on exchanges. Derivatives are one of the ...
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Exchange Rate
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 exchange rate is also regarded as the value of one country's currency in relation to another currency. For example, an interbank exchange rate of 114 Japanese yen to the United States dollar means that ¥114 will be exchanged for or that will be exchanged for ¥114. In this case it is said that the price of a dollar in relation to yen is ¥114, or equivalently that the price of a yen in relation to dollars is $1/114. Each country determines the exchange rate regime that will apply to its currency. For example, a currency may be floating, pegged (fixed), or a hybrid. Governments can impose certain limits and controls on exchange rates. Countries can also have a strong or weak currency. There is no agreement in the econ ...
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Commodity
In economics, a commodity is an economic good, usually a resource, that has full or substantial fungibility: that is, the market treats instances of the good as equivalent or nearly so with no regard to who produced them. The price of a commodity good is typically determined as a function of its market as a whole: well-established physical commodities have actively traded spot and derivative markets. The wide availability of commodities typically leads to smaller profit margins and diminishes the importance of factors (such as brand name) other than price. Most commodities are raw materials, basic resources, agricultural, or mining products, such as iron ore, sugar, or grains like rice and wheat. Commodities can also be mass-produced unspecialized products such as chemical substance, chemicals and computer memory. Popular commodities include Petroleum, crude oil, Maize, corn, and gold. Other definitions of commodity include something useful or valued and an alternative ter ...
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