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At The Money
In finance, moneyness is the relative position of the current price (or future price) of an underlying asset (e.g., a stock) with respect to the strike price of a derivative, most commonly a call option or a put option. Moneyness is firstly a three-fold classification: * If the derivative would have positive intrinsic value if it were to expire today, it is said to be in the money (ITM); * If the derivative would be worthless if expiring with the underlying at its current price, it is said to be out of the money (OTM); * And if the current underlying price and strike price are equal, the derivative is said to be at the money (ATM). There are two slightly different definitions, according to whether one uses the current price (spot) or future price (forward), specified as "at the money spot" or "at the money forward", etc. This rough classification can be quantified by various definitions to express the moneyness as a number, measuring how far the asset is in the money or out of ... [...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] |
Standard Deviations
In statistics, the standard deviation is a measure of the amount of variation of the values of a variable about its mean. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range. The standard deviation is commonly used in the determination of what constitutes an outlier and what does not. Standard deviation may be abbreviated SD or std dev, and is most commonly represented in mathematical texts and equations by the lowercase Greek letter σ (sigma), for the population standard deviation, or the Latin letter '' s'', for the sample standard deviation. The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance. (For a finite population, variance is the average of the squared deviations from the mean.) A useful property of the sta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Risk-free Rate
The risk-free rate of return, usually shortened to the risk-free rate, is the rate of return of a hypothetical investment with scheduled payments over a fixed period of time that is assumed to meet all payment obligations. Since the risk-free rate can be obtained with no risk, any other investment having some risk will have to have a higher rate of return in order to induce any investors to hold it. In practice, to infer the risk-free interest rate in a particular currency, market participants often choose the yield to maturity on a risk-free bond issued by a government of the same currency whose risks of default are so low as to be negligible. For example, the rate of return on zero-coupon Treasury bonds (T-bills) is sometimes seen as the risk-free rate of return in US dollars. Theoretical measurement As stated by Malcolm Kemp in chapter five of his book ''Market Consistency: Model Calibration in Imperfect Markets'', the risk-free rate means different things to different pe ... [...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] |
Change Of Variables
In mathematics, a change of variables is a basic technique used to simplify problems in which the original variables are replaced with functions of other variables. The intent is that when expressed in new variables, the problem may become simpler, or equivalent to a better understood problem. Change of variables is an operation that is related to substitution. However these are different operations, as can be seen when considering differentiation (chain rule) or integration (integration by substitution). A very simple example of a useful variable change can be seen in the problem of finding the roots of the sixth-degree polynomial: :x^6 - 9 x^3 + 8 = 0. Sixth-degree polynomial equations are generally impossible to solve in terms of radicals (see Abel–Ruffini theorem). This particular equation, however, may be written :(x^3)^2-9(x^3)+8=0 (this is a simple case of a polynomial decomposition). Thus the equation may be simplified by defining a new variable u = x^3. Subs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coordinate System
In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine and standardize the position of the points or other geometric elements on a manifold such as Euclidean space. The coordinates are not interchangeable; they are commonly distinguished by their position in an ordered tuple, or by a label, such as in "the ''x''-coordinate". The coordinates are taken to be real numbers in elementary mathematics, but may be complex numbers or elements of a more abstract system such as a commutative ring. The use of a coordinate system allows problems in geometry to be translated into problems about numbers and ''vice versa''; this is the basis of analytic geometry. Common coordinate systems Number line The simplest example of a coordinate system is the identification of points on a line with real numbers using the '' number line''. In this system, an arbitrary point ''O'' (the ''origin'') is chosen on a given line. The coordinate o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Option (finance)
In finance, an option is a contract which conveys to its owner, the ''holder'', the right, but not the obligation, to buy or sell a specific quantity of an underlying asset or instrument at a specified strike price on or before a specified date, depending on the style of the option. Options are typically acquired by purchase, as a form of compensation, or as part of a complex financial transaction. Thus, they are also a form of asset (or contingent liability) and have a valuation that may depend on a complex relationship between underlying asset price, time until expiration, market volatility, the risk-free rate of interest, and the strike price of the option. Options may be traded between private parties in '' over-the-counter'' (OTC) transactions, or they may be exchange-traded in live, public markets in the form of standardized contracts. Definition and application An option is a contract that allows the holder the right to buy or sell an underlying asset or financia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boundary Condition
In the study of differential equations, a boundary-value problem is a differential equation subjected to constraints called boundary conditions. A solution to a boundary value problem is a solution to the differential equation which also satisfies the boundary conditions. Boundary value problems arise in several branches of physics as any physical differential equation will have them. Problems involving the wave equation, such as the determination of normal modes, are often stated as boundary value problems. A large class of important boundary value problems are the Sturm–Liouville problems. The analysis of these problems, in the linear case, involves the eigenfunctions of a differential operator. To be useful in applications, a boundary value problem should be well posed. This means that given the input to the problem there exists a unique solution, which depends continuously on the input. Much theoretical work in the field of partial differential equations is devote ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Option Time Value
In finance, the time value (TV) (''extrinsic'' or ''instrumental'' value) of an option (finance), option is the premium a rational investor would pay over its ''current'' exercise value (intrinsic value (finance), intrinsic value), based on the probability it will increase in value before expiry. For an Option style, American option this value is always greater than zero in a fair market, thus an option is ''always'' worth more than its current exercise value. As an option can be thought of as 'price insurance' (e.g., an airline insuring against unexpected soaring fuel costs caused by a hurricane), TV can be thought of as the ''risk premium'' the option seller charges the buyer—the higher the expected risk (volatility \cdot time), the higher the premium. Conversely, TV can be thought of as the price an investor is willing to pay for potential upside. Time value decays to zero at expiration, with a general rule that it will lose of its value during the first half of its life and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Put Option
In finance, a put or put option is a derivative instrument in financial markets that gives the holder (i.e. the purchaser of the put option) the right to sell an asset (the ''underlying''), at a specified price (the ''strike''), by (or on) a specified date (the '' expiry'' or ''maturity'') to the ''writer'' (i.e. seller) of the put. The purchase of a put option is interpreted as a negative sentiment about the future value of the underlying stock. page 15 , 4.2.3 Positive and negative sentiment The term "put" comes from the fact that the owner has the right to "put up for sale" the stock or index. Puts may also be combined with other derivatives as part of more complex investment strategies, and in particular, may be useful for hedging. Holding a European put option is equivalent to holding the corresponding call option and selling an appropriate forward contract. This equivalence is called " put-call parity". Put options are most commonly used in the stock market to prot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Call Option
In finance, a call option, often simply labeled a "call", is a contract between the buyer and the seller of the call Option (finance), option to exchange a Security (finance), security at a set price. The buyer of the call option has the right, but not the obligation, to buy an agreed quantity of a particular commodity or financial instrument (the underlying) from the seller of the option at or before a certain time (the Expiration (options), expiration date) for a certain price (the strike price). This effectively gives the buyer a Long (finance), ''long'' position in the given asset. The seller (or "writer") is obliged to sell the commodity or financial instrument to the buyer if the buyer so decides. This effectively gives the seller a Short (finance), ''short'' position in the given asset. The buyer pays a fee (called a Insurance, premium) for this right. The term "call" comes from the fact that the owner has the right to "call the stock away" from the seller. Price of opt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
