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Asian Option
An Asian option (or ''average value'' option) is a special type of option contract. For Asian options the payoff is determined by the average underlying price over some pre-set period of time. This is different from the case of the usual European option and American option, where the payoff of the option contract depends on the price of the underlying instrument at exercise; Asian options are thus one of the basic forms of exotic options. There are two types of Asian options: fixed strike, where averaging price is used in place of underlying price; and fixed price, where averaging price is used in place of strike. One advantage of Asian options is that these reduce the risk of market manipulation of the underlying instrument at maturity. Another advantage of Asian options involves the relative cost of Asian options compared to European or American options. Because of the averaging feature, Asian options reduce the volatility inherent in the option; therefore, Asian options are ty ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Option Contract
An option contract, or simply option, is defined as "a promise which meets the requirements for the formation of a contract and limits the promisor's power to revoke an offer". Option contracts are common in professional sports. An option contract is a type of contract that protects an offeree from an offeror's ability to revoke their offer to engage in a contract. Under the common law, consideration for the option contract is required as it is still a form of contract, cf. Restatement (Second) of Contracts § 87(1). Typically, an offeree can provide consideration for the option contract by paying money for the contract or by providing value in some other form such as by rendering other performance or forbearance. Courts will generally try to find consideration if there are any grounds for doing so. See consideration for more information. The Uniform Commercial Code (UCC) has eliminated a need for consideration for firm offers between merchants in some limited circumstances. I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physical Review
''Physical Review'' is a peer-reviewed scientific journal established in 1893 by Edward Nichols. It publishes original research as well as scientific and literature reviews on all aspects of physics. It is published by the American Physical Society (APS). The journal is in its third series, and is split in several sub-journals each covering a particular field of physics. It has a sister journal, ''Physical Review Letters'', which publishes shorter articles of broader interest. History ''Physical Review'' commenced publication in July 1893, organized by Cornell University professor Edward Nichols and helped by the new president of Cornell, J. Gould Schurman. The journal was managed and edited at Cornell in upstate New York from 1893 to 1913 by Nichols, Ernest Merritt, and Frederick Bedell. The 33 volumes published during this time constitute ''Physical Review Series I''. The American Physical Society (APS), founded in 1899, took over its publication in 1913 and star ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Options (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 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 financial instrument at a specified s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
International Journal Of Theoretical And Applied Finance
The ''International Journal of Theoretical and Applied Finance'' was founded in 1998 and is published by World Scientific. It covers the use of quantitative tools in finance, including articles on development and simulation of mathematical models, their industrial usage, and application of modern stochastic methods. Abstracting and indexing The journal is abstracted and indexed in: * JEL electronic indexes, includes EconList, e-JEL, and JEL on CD * Social Science Research Network (SSRN) * Mathematical Reviews ''Mathematical Reviews'' is a journal published by the American Mathematical Society (AMS) that contains brief synopses, and in some cases evaluations, of many articles in mathematics, statistics, and theoretical computer science. The AMS also pu ... * The CFA Digest * CSA Risk Abstracts * International Bibliography of the Social Sciences * Zentralblatt MATH * Inspec Finance journals Publications established in 1998 World Scientific academic journals English-langu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
BNP Paribas
BNP Paribas is a French international banking group, founded in 2000 from the merger between Banque Nationale de Paris (BNP, "National Bank of Paris") and Paribas, formerly known as the Banque de Paris et des Pays-Bas. The full name of the group's parent entity is BNP Paribas S.A. With 190,000 employees as of February 2021, the bank is organized into three major business areas: Commercial, Personal Banking & Services (CPBS), Investment & Protection Services (IPS) and Corporate & Institutional Banking (CIB). The group is listed on the first market of Euronext Paris and a component of the Euro Stoxx 50 stock market index, while it also included in the French CAC 40 index. BNP Paribas is the largest banking group in Europe, after HSBC, and ninth largest Banking group in the world, essentially a bulge bracket. It became one of the five largest banks in the world following the 2008 financial crisis. Despite some legal difficulties in 2014, including being fined the largest ever ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Put–call Parity
In financial mathematics, put–call parity defines a relationship between the price of a European call option and European put option, both with the identical strike price and expiry, namely that a portfolio of a long call option and a short put option is equivalent to (and hence has the same value as) a single forward contract at this strike price and expiry. This is because if the price at expiry is above the strike price, the call will be exercised, while if it is below, the put will be exercised, and thus in either case one unit of the asset will be purchased for the strike price, exactly as in a forward contract. The validity of this relationship requires that certain assumptions be satisfied; these are specified and the relationship is derived below. In practice transaction costs and financing costs (leverage) mean this relationship will not exactly hold, but in liquid markets the relationship is close to exact. Assumptions Put–call parity is a static replication, and th ... [...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 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 European-style 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 the option by buying and selling the underlying asset in a specific way to eliminate risk. This type of hedging is called "continuously revised delta hedging" and is the basis of more complicated ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normal Distribution
In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is : f(x) = \frac e^ The parameter \mu is the mean or expectation of the distribution (and also its median and mode), while the parameter \sigma is its standard deviation. The variance of the distribution is \sigma^2. A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known. Their importance is partly due to the central limit theorem. It states that, under some conditions, the average of many samples (observations) of a random variable with finite mean and variance is itself a random variable—whose distribution converges to a normal dist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Martingale Pricing
Martingale pricing is a pricing approach based on the notions of martingale and risk neutrality. The martingale pricing approach is a cornerstone of modern quantitative finance and can be applied to a variety of derivatives contracts, e.g. options, futures, interest rate derivatives, credit derivatives, etc. In contrast to the PDE approach to pricing, martingale pricing formulae are in the form of expectations which can be efficiently solved numerically using a Monte Carlo approach. As such, Martingale pricing is preferred when valuing high-dimensional contracts such as a basket of options. On the other hand, valuing American-style contracts is troublesome and requires discretizing the problem (making it like a Bermudan option) and only in 2001 F. A. Longstaff and E. S. Schwartz developed a practical Monte Carlo method for pricing American options. Measure theory representation Suppose the state of the market can be represented by the filtered probability space,(\Omega,(\math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Itô's Lemma
In mathematics, Itô's lemma or Itô's formula (also called the Itô-Doeblin formula, especially in French literature) is an identity used in Itô calculus to find the differential of a time-dependent function of a stochastic process. It serves as the stochastic calculus counterpart of the chain rule. It can be heuristically derived by forming the Taylor series expansion of the function up to its second derivatives and retaining terms up to first order in the time increment and second order in the Wiener process increment. The lemma is widely employed in mathematical finance, and its best known application is in the derivation of the Black–Scholes equation for option values. Motivation Suppose we are given the stochastic differential equation dX_t = \mu_t\ dt + \sigma_t\ dB_t, where is a Wiener process and the functions \mu_t, \sigma_t are deterministic (not stochastic) functions of time. In general, it's not possible to write a solution X_t directly in terms of B_t. H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Brownian Motion
A geometric Brownian motion (GBM) (also known as exponential Brownian motion) is a continuous-time stochastic process in which the logarithm of the randomly varying quantity follows a Brownian motion (also called a Wiener process) with drift. It is an important example of stochastic processes satisfying a stochastic differential equation (SDE); in particular, it is used in mathematical finance to model stock prices in the Black–Scholes model. Technical definition: the SDE A stochastic process ''S''''t'' is said to follow a GBM if it satisfies the following stochastic differential equation (SDE): : dS_t = \mu S_t\,dt + \sigma S_t\,dW_t where W_t is a Wiener process or Brownian motion, and \mu ('the percentage drift') and \sigma ('the percentage volatility') are constants. The former is used to model deterministic trends, while the latter term is often used to model a set of unpredictable events occurring during this motion. Solving the SDE For an arbitrary ini ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Control Variates
The control variates method is a variance reduction technique used in Monte Carlo methods. It exploits information about the errors in estimates of known quantities to reduce the error of an estimate of an unknown quantity. Glasserman, P. (2004). ''Monte Carlo Methods in Financial Engineering''. New York: Springer. (p. 185) Underlying principle Let the unknown parameter of interest be \mu, and assume we have a statistic m such that the expected value of ''m'' is μ: \mathbb\left \right\mu, i.e. ''m'' is an unbiased estimator for μ. Suppose we calculate another statistic t such that \mathbb\left \right\tau is a known value. Then :m^\star = m + c\left(t-\tau\right) \, is also an unbiased estimator for \mu for any choice of the coefficient c. The variance of the resulting estimator m^ is :\textrm\left(m^\right)=\textrm\left(m\right) + c^2\,\textrm\left(t\right) + 2c\,\textrm\left(m,t\right). By differentiating the above expression with respect to c, it can be shown that ch ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
