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Johnson Binomial Tree
In finance, a lattice model is a technique applied to the valuation of derivatives, where a discrete time model is required. For equity options, a typical example would be pricing an American option, where a decision as to option exercise is required at "all" times (any time) before and including maturity. A continuous model, on the other hand, such as Black–Scholes, would only allow for the valuation of European options, where exercise is on the option's maturity date. For interest rate derivatives lattices are additionally useful in that they address many of the issues encountered with continuous models, such as pull to par. The method is also used for valuing certain exotic options, where because of path dependence in the payoff, Monte Carlo methods for option pricing fail to account for optimal decisions to terminate the derivative by early exercise, though methods now exist for solving this problem. Equity and commodity derivatives In general the approach is to divid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arbre Binomial Options Reelles
* , a 2007 song by French singer Yannick Noah
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Arbre may refer to: * Arbre, Ath, a commune in Ath, Belgium * , a village in Profondeville, Belgium * Arbre, a planet in ''Anathem'' by Neal Stephenson See also * ' or liberty trees, a symbol of the French Revolution * Arbre du Ténéré, once considered the most isolated tree on Earth * Arbre Magique, a line of disposable air fresheners * ''L'arbre de ciència'' or ''Tree of Science'', a 1295 encyclopedia by Ramon Llull * , a 1996 song written by Philippe Tatartcheff and Anna McGarrigle Anna McGarrigle, CM (born December 4, 1944) is a Canadian folk music singer and songwriter who recorded and performed with her sister, Kate McGarrigle, who died in 2010. Early life Anna McGarrigle studied at the École des beaux-arts de Montréa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Expectation Value
In probability theory, the expected value (also called expectation, expectancy, mathematical expectation, mean, average, or first moment) is a generalization of the weighted average. Informally, the expected value is the arithmetic mean of a large number of independently selected outcomes of a random variable. The expected value of a random variable with a finite number of outcomes is a weighted average of all possible outcomes. In the case of a continuum of possible outcomes, the expectation is defined by integration. In the axiomatic foundation for probability provided by measure theory, the expectation is given by Lebesgue integration. The expected value of a random variable is often denoted by , , or , with also often stylized as or \mathbb. History The idea of the expected value originated in the middle of the 17th century from the study of the so-called problem of points, which seeks to divide the stakes ''in a fair way'' between two players, who have to en ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Barrier Options
A barrier or barricade is a physical structure which blocks or impedes something. Barrier may also refer to: Places * Barrier, Kentucky, a community in the United States * Barrier, Voerendaal, a place in the municipality of Voerendaal, Netherlands * Barrier Bay, an open bay in Antarctica * Barrier Canyon, the former name of Horseshoe Canyon (Utah) * Barrier Lake, Alberta, Canada * Barrier Mountain, the former name of Mount Baldy (Alberta) * Barrier Ranges, a mountain range in New South Wales, Australia * Division of Barrier, a former Australian Electoral Division in New South Wales * The Barrier, a lava dam in British Columbia, Canada * The Barrier (Kenya), an active shield volcano in Kenya * The Barrier, a common synonym for the city of Broken Hill, New South Wales * The Barrier, an early name for the Ross Ice Shelf, Antarctica In arts and entertainment Film * ''The Barrier'' (1917 film), a lost 1917 American silent drama film * ''The Barrier'' (1926 film), a silent film * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exotic Options
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 more complex than options that trade on an exchange, and are generally traded over-the-counter. Etymology The term "exotic option" was popularized by Mark Rubinstein's 1990 working paper (published 1992, with Eric Reiner) "Exotic Options", with the term based either on exotic wagers in horse racing, or due to the use of international terms such as "Asian option", suggesting the "exotic Orient". Journalist Brian Palmer used the "successful $1 bet on the superfecta" in the 2010 Kentucky Derby that "paid a whopping $101,284.60" as an example of the controversial high-risk, high-payout exotic bets that w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Employee Stock Option
Employee stock options (ESO) is a label that refers to compensation contracts between an employer and an employee that carries some characteristics of financial options. Employee stock options are commonly viewed as an internal agreement providing the possibility to participate in the share capital of a company, granted by the company to an employee as part of the employee's remuneration package. Regulators and economists have since specified that ESOs are compensation contracts. These nonstandard contracts exist between employee and employer, whereby the employer has the liability of delivering a certain number of shares of the employer stock, when and if the employee stock options are exercised by the employee. The contract length varies, and often carries terms that may change depending on the employer and the current employment status of the employee. In the United States, the terms are detailed within an employer's "Stock Option Agreement for Incentive Equity Plan". Es ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Real Options Valuation
Real options valuation, also often termed real options analysis,Adam Borison (Stanford University)''Real Options Analysis: Where are the Emperor's Clothes?'' (ROV or ROA) applies option valuation techniques to capital budgeting decisions.Campbell, R. Harvey''Identifying real options'' Duke University, 2002. A real option itself, is the right—but not the obligation—to undertake certain business initiatives, such as deferring, abandoning, expanding, staging, or contracting a capital investment project. For example, real options valuation could examine the opportunity to invest in the expansion of a firm's factory and the alternative option to sell the factory.Nijssen, E. (2014) Routelegde, 2014. Real options are generally distinguished from conventional financial options in that they are not typically traded as securities, and do not usually involve decisions on an underlying asset that is traded as a financial security. A further distinction is that option holders here, i.e. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bermudan Option
In finance, the style or family of an option is the class into which the option falls, usually defined by the dates on which the option may be exercised. The vast majority of options are either European or American (style) options. These options—as well as others where the payoff is calculated similarly—are referred to as "vanilla options". Options where the payoff is calculated differently are categorized as "exotic options". Exotic options can pose challenging problems in valuation and hedging. American and European options The key difference between American and European options relates to when the options can be exercised: * A European option may be exercised only at the expiration date of the option, i.e. at a single pre-defined point in time. * An American option on the other hand may be exercised at any time before the expiration date. For both, the payoff—when it occurs—is given by * \max\, for a call option * \max\, for a put option where K is the strike ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Present Value
In economics and finance, present value (PV), also known as present discounted value, is the value of an expected income stream determined as of the date of valuation. The present value is usually less than the future value because money has interest-earning potential, a characteristic referred to as the time value of money, except during times of zero- or negative interest rates, when the present value will be equal or more than the future value. Time value can be described with the simplified phrase, "A dollar today is worth more than a dollar tomorrow". Here, 'worth more' means that its value is greater than tomorrow. A dollar today is worth more than a dollar tomorrow because the dollar can be invested and earn a day's worth of interest, making the total accumulate to a value more than a dollar by tomorrow. Interest can be compared to rent. Just as rent is paid to a landlord by a tenant without the ownership of the asset being transferred, interest is paid to a lender by a borr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Option Time Value
In finance, the time value (TV) (''extrinsic'' or ''instrumental'' value) of an option is the premium a rational investor would pay over its ''current'' exercise value ( intrinsic value), based on the probability it will increase in value before expiry. For an 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 in the second half. As an option moves closer to expiry, m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brownian Motion
Brownian motion, or pedesis (from grc, πήδησις "leaping"), is the random motion of particles suspended in a medium (a liquid or a gas). This pattern of motion typically consists of random fluctuations in a particle's position inside a fluid sub-domain, followed by a relocation to another sub-domain. Each relocation is followed by more fluctuations within the new closed volume. This pattern describes a fluid at thermal equilibrium, defined by a given temperature. Within such a fluid, there exists no preferential direction of flow (as in transport phenomena). More specifically, the fluid's overall linear and angular momenta remain null over time. The kinetic energies of the molecular Brownian motions, together with those of molecular rotations and vibrations, sum up to the caloric component of a fluid's internal energy (the equipartition theorem). This motion is named after the botanist Robert Brown, who first described the phenomenon in 1827, while looking throu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Log-normal Distribution
In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. Thus, if the random variable is log-normally distributed, then has a normal distribution. Equivalently, if has a normal distribution, then the exponential function of , , has a log-normal distribution. A random variable which is log-normally distributed takes only positive real values. It is a convenient and useful model for measurements in exact and engineering sciences, as well as medicine, economics and other topics (e.g., energies, concentrations, lengths, prices of financial instruments, and other metrics). The distribution is occasionally referred to as the Galton distribution or Galton's distribution, after Francis Galton. The log-normal distribution has also been associated with other names, such as McAlister, Gibrat and Cobb–Douglas. A log-normal process is the statistical realization of the multipl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic Process
In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner. Examples include the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule. Stochastic processes have applications in many disciplines such as biology, chemistry, ecology, neuroscience, physics, image processing, signal processing, control theory, information theory, computer science, cryptography and telecommunications. Furthermore, seemingly random changes in financial markets have motivated the extensive use of stochastic processes in finance. Applications and the study of phenomena have in turn inspired the proposal of new stochastic processes. Examples of such stochastic processes include the Wiener process or Brownian motion process, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
