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Implied Trinomial Tree
In quantitative finance, a lattice model is a numerical methods, numerical approach to the Valuation of options, valuation of derivatives in situations requiring a discrete time model. For dividend paying stock option, equity options, a typical application would correspond to the pricing of an American option, American-style option, where a decision to Exercise (options), exercise is allowed at the closing of any calendar day up to the maturity. A continuous model, on the other hand, such as the standard Black–Scholes model, Black–Scholes one, would only allow for the valuation of European options, where exercise is limited to the Expiration (options), 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, because of path dependence in the payoff. Traditional Monte Carlo methods for option ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arbre Binomial Options Reelles
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 Ramon Llull (; ; – 1316), sometimes anglicized as ''Raymond Lully'', was a philosopher, theologian, poet, missionary, Christian apologist and former knight from the Kingdom of Majorca. He invented a philosophical system known as the ''Art ... * , a 1996 song written by Philippe Tatartcheff and Anna McGarrigle * , a 2007 song by French singer Yannick Noah {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Expectation Value
In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first moment) is a generalization of the weighted average. Informally, the expected value is the mean of the possible values a random variable can take, weighted by the probability of those outcomes. Since it is obtained through arithmetic, the expected value sometimes may not even be included in the sample data set; it is not the value you would expect to get in reality. 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 \mathbb or . Histo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Employee Stock Option
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 Options (finance), 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, 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 A ... [...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 (finance), option Valuation of options, 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 Project#Corporate_finance, 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)''Entrepreneurial Marketing; an effectual approach. Chapter 2'' Routelegde, 2014. Real options are most valuable when uncertainty is high; management has significant flexibility to change the course of the project in a favorable direction a ... [...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 (PDV), 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 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 Renting, 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 ... [...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] |
Brownian Motion
Brownian motion is the random motion of particles suspended in a medium (a liquid or a gas). The traditional mathematical formulation of Brownian motion is that of the Wiener process, which is often called Brownian motion, even in mathematical sources. This motion pattern typically consists of Randomness, 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 momentum, linear and Angular momentum, angular momenta remain null over time. The Kinetic energy, 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 in ... [...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 normal distribution, 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 Donald MacAlister#log-normal, McAlister, Gibrat's law, Gibrat and Cobb–Douglas. A l ... [...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 in a probability space, where the index of the family often has the interpretation of time. 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 Ecology () is the natural science of the relationships among living organisms and their Natural environment, environment. Ecology considers organisms at the individual, population, community (ecology), community, ecosystem, and biosphere lev ..., neuroscience, physics, image processing, signal processing, stochastic control, control theory, information theory, computer scien ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spot Price
In finance, a spot contract, spot transaction, or simply spot, is a contract of buying or selling a commodity, security or currency for immediate settlement (payment and delivery) on the spot date, which is normally two business days after the trade date. The settlement price (or rate) is called spot price (or spot rate). A spot contract is in contrast with a forward contract or futures contract where contract terms are agreed now but delivery and payment will occur at a future date. Spot prices and future price expectations Depending on the item being traded, spot prices can indicate market expectations of future price movements in different ways. For a security or non-perishable commodity (e.g. silver), the spot price reflects market expectations of future price movements. In theory, the difference in spot and forward prices should be equal to the finance charges, plus any earnings due to the holder of the security, according to the cost of carry model. For example, on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Commodity Market
A commodity market is a market that trades in the primary economic sector rather than manufactured products. The primary sector includes agricultural products, energy products, and metals. Soft commodities may be perishable and harvested, while hard commodities are usually mined, such as gold and oil. Futures contracts are the oldest way of investing in commodities. Commodity markets can include physical trading and derivatives trading using spot prices, forwards, futures, and options on futures. Farmers have used a simple form of derivative trading in the commodities market for centuries for price risk management. A financial derivative is a financial instrument whose value is derived from a commodity termed an underlier. Derivatives are either exchange-traded or over-the-counter (OTC). An increasing number of derivatives are traded via clearing houses some with central counterparty clearing, which provide clearing and settlement services on a futures exchange, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
