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Short-rate Model
A short-rate model, in the context of interest rate derivatives, is a mathematical model that describes the future evolution of interest rates by describing the future evolution of the short rate, usually written r_t \,. The short rate Under a short rate model, the stochastic state variable is taken to be the instantaneous spot rate. The short rate, r_t \,, then, is the ( continuously compounded, annualized) interest rate at which an entity can borrow money for an infinitesimally short period of time from time t. Specifying the current short rate does not specify the entire yield curve. However, no-arbitrage arguments show that, under some fairly relaxed technical conditions, if we model the evolution of r_t \, as a stochastic process under a risk-neutral measure Q, then the price at time t of a zero-coupon bond maturing at time T with a payoff of 1 is given by : P(t,T) = \operatorname^Q\left \mathcal_t \right where \mathcal is the natural filtration for the process. The inte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
OAS Valuation Tree (es)
OAS or Oas may refer to: Chemistry * O-Acetylserine, amino-acid involved in cysteine synthesis Computers * Open-Architecture-System, the main user interface of Wersi musical keyboards * OpenAPI Specification (originally Swagger Specification), specification for machine-readable interface files for RESTful Web services * Oracle Application Server, software platform Medicine * Open aortic surgery, surgical technique * Oral allergy syndrome, food-related allergic reaction in the mouth * 2'-5'-oligoadenylate synthase, an enzyme ** OAS1, OAS2, OAS3, anti-viral enzymes in humans Organizations * Office of Aviation Services, agency of the United States Department of the Interior * Ontario Archaeological Society, organization promoting archaeology within the Province of Ontario, Canada * Organisation Armée Secrète, French dissident terrorist organisation, active during the Algerian War (1954–62), fighting against Algerian independence * Organization of American States, continental ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Risk-neutral Measure
In mathematical finance, a risk-neutral measure (also called an equilibrium measure, or ''equivalent martingale measure'') is a probability measure such that each share price is exactly equal to the discounted expectation of the share price under this measure. This is heavily used in the pricing of financial derivatives due to the fundamental theorem of asset pricing, which implies that in a complete market, a derivative's price is the discounted expected value of the future payoff under the unique risk-neutral measure. Such a measure exists if and only if the market is arbitrage-free. The easiest way to remember what the risk-neutral measure is, or to explain it to a probability generalist who might not know much about finance, is to realize that it is: # The probability measure of a transformed random variable. Typically this transformation is the utility function of the payoff. The risk-neutral measure would be the measure corresponding to an expectation of the payoff with a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Martingale Measure
In mathematical finance, a risk-neutral measure (also called an equilibrium measure, or ''equivalent martingale measure'') is a probability measure such that each share price is exactly equal to the discounted expectation of the share price under this measure. This is heavily used in the pricing of financial derivatives due to the fundamental theorem of asset pricing, which implies that in a complete market, a derivative's price is the discounted expected value of the future payoff under the unique risk-neutral measure. Such a measure exists if and only if the market is arbitrage-free. The easiest way to remember what the risk-neutral measure is, or to explain it to a probability generalist who might not know much about finance, is to realize that it is: # The probability measure of a transformed random variable. Typically this transformation is the utility function of the payoff. The risk-neutral measure would be the measure corresponding to an expectation of the payoff with a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert C
The name Robert is an ancient Germanic given name, from Proto-Germanic "fame" and "bright" (''Hrōþiberhtaz''). Compare Old Dutch ''Robrecht'' and Old High German ''Hrodebert'' (a compound of '' Hruod'' ( non, Hróðr) "fame, glory, honour, praise, renown" and ''berht'' "bright, light, shining"). It is the second most frequently used given name of ancient Germanic origin. It is also in use as a surname. Another commonly used form of the name is Rupert. After becoming widely used in Continental Europe it entered England in its Old French form ''Robert'', where an Old English cognate form (''Hrēodbēorht'', ''Hrodberht'', ''Hrēodbēorð'', ''Hrœdbœrð'', ''Hrœdberð'', ''Hrōðberχtŕ'') had existed before the Norman Conquest. The feminine version is Roberta. The Italian, Portuguese, and Spanish form is Roberto. Robert is also a common name in many Germanic languages, including English, German, Dutch, Norwegian, Swedish, Scots, Danish, and Icelandic. It can be use ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monte Carlo Methods For Option Pricing
In mathematical finance, a Monte Carlo option model uses Monte Carlo methodsAlthough the term 'Monte Carlo method' was coined by Stanislaw Ulam in the 1940s, some trace such methods to the 18th century French naturalist Buffon, and a question he asked about the results of dropping a needle randomly on a striped floor or table. See Buffon's needle. to calculate the value of an option with multiple sources of uncertainty or with complicated features. The first application to option pricing was by Phelim Boyle in 1977 (for European options). In 1996, M. Broadie and P. Glasserman showed how to price Asian options by Monte Carlo. An important development was the introduction in 1996 by Carriere of Monte Carlo methods for options with early exercise features. Methodology In terms of theory, Monte Carlo valuation relies on risk neutral valuation.Marco DiasReal Options with Monte Carlo Simulation/ref> Here the price of the option is its discounted expected value; see risk neutrality an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binomial Options Pricing Model
In finance, the binomial options pricing model (BOPM) provides a generalizable numerical method for the valuation of options. Essentially, the model uses a "discrete-time" ( lattice based) model of the varying price over time of the underlying financial instrument, addressing cases where the closed-form Black–Scholes formula is wanting. The binomial model was first proposed by William Sharpe in the 1978 edition of ''Investments'' (), and formalized by Cox, Ross and Rubinstein in 1979 and by Rendleman and Bartter in that same year. For binomial trees as applied to fixed income and interest rate derivatives see . Use of the model The Binomial options pricing model approach has been widely used since it is able to handle a variety of conditions for which other models cannot easily be applied. This is largely because the BOPM is based on the description of an underlying instrument over a period of time rather than a single point. As a consequence, it is used to value Am ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Columbia University
Columbia University (also known as Columbia, and officially as Columbia University in the City of New York) is a private research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church in Manhattan, Columbia is the oldest institution of higher education in New York and the fifth-oldest institution of higher learning in the United States. It is one of nine colonial colleges founded prior to the Declaration of Independence. It is a member of the Ivy League. Columbia is ranked among the top universities in the world. Columbia was established by royal charter under George II of Great Britain. It was renamed Columbia College in 1784 following the American Revolution, and in 1787 was placed under a private board of trustees headed by former students Alexander Hamilton and John Jay. In 1896, the campus was moved to its current location in Morningside Heights and renamed Columbia University. Columbia scientists and scholars have ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Twente
The University of Twente (Dutch: ''Universiteit Twente''; , abbr. ) is a public technical university located in Enschede, Netherlands. The university has been placed in the top 170 universities in the world by multiple central ranking tables. In addition, the UT was ranked the best technical university in The Netherlands by Keuzegids Universiteiten, the most significant national university ranking. The UT collaborates with Delft University of Technology, Eindhoven University of Technology and the Wageningen University and Research Centre under the umbrella of 4TU and is also a partner in the European Consortium of Innovative Universities (ECIU). History The university was founded in 1961 as ''Technische Hogeschool Twente'' or ''(THT)''. After Delft University of Technology and Eindhoven University of Technology, it became the third polytechnic institute in the Netherlands to become a university. The institution was later renamed to Universiteit Twente (University of Twente) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Farshid Jamshidian
Farshid Jamshidian is a finance researcher, academic and practitioner. His experience covers both fixed-income and equity research and trading. Dr. Jamshidian has made important contributions to the theory of derivatives pricing, and has published extensively, especially on interest rate modelling, amongst other contributions, developing the use of the forward measure, and "Jamshidian's trick", widely applied in the pricing of bond options. He is professor of Applied Mathematics at the University of Twente, and is at NIBC Bank. He is a member of the Editorial Board of ''The Journal of Fixed Income''. Previously he was managing director of NetAnalytic, a risk management products and services company he founded in 1999; Managing Director of New Products and Equity Derivatives at Sakura Global Capital; Executive Director of Technical Trading at Fuji International Finance; and head of quantitative fixed-income research at Merrill Lynch. As an academic, he was an associate editor o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parameter
A parameter (), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when identifying the system, or when evaluating its performance, status, condition, etc. ''Parameter'' has more specific meanings within various disciplines, including mathematics, computer programming, engineering, statistics, logic, linguistics, and electronic musical composition. In addition to its technical uses, there are also extended uses, especially in non-scientific contexts, where it is used to mean defining characteristics or boundaries, as in the phrases 'test parameters' or 'game play parameters'. Modelization When a system is modeled by equations, the values that describe the system are called ''parameters''. For example, in mechanics, the masses, the dimensions and shapes (for solid bodies), the densities and the viscosities ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free Parameter
A free parameter is a variable in a mathematical model which cannot be predicted precisely or constrained by the model and must be estimated experimentally or theoretically. A mathematical model, theory, or conjecture is more likely to be right and less likely to be the product of wishful thinking if it relies on few free parameters and is consistent with large amounts of data. See also * Decision variables * Exogenous variables * Random variables * State variable A state variable is one of the set of variables that are used to describe the mathematical "state" of a dynamical system. Intuitively, the state of a system describes enough about the system to determine its future behaviour in the absence of a ...s References Philosophy of science Scientific method Ignorance {{science-philo-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mean Reversion (finance)
Mean reversion is a financial term for the assumption that an asset's price will tend to converge to the average price over time. Using mean reversion as a timing strategy involves both the identification of the trading range for a security and the computation of the average price using quantitative methods. Mean reversion is a phenomenon that can be exhibited in a host of financial time-series data, from price data, earnings data, and book value. When the current market price is less than the average past price, the security is considered attractive for purchase, with the expectation that the price will rise. When the current market price is above the average past price, the market price is expected to fall. In other words, deviations from the average price are expected to revert to the average. This knowledge serves as the cornerstone of multiple trading strategies. Stock reporting services commonly offer moving averages for periods such as 50 and 100 days. While reporting ser ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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