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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 (Compound interest#Continuous compounding, 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, arbitrage, 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[\left. \exp \ \mathcal_t \right], w ... [...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 (1954–1962), fighting against Algerian independence * Organization of American States, continenta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Forward Rate
The forward rate is the future yield on a bond. It is calculated using the yield curve. For example, the yield on a three-month Treasury bill six months from now is a ''forward rate''.. Forward rate calculation To extract the forward rate, we need the zero-coupon yield curve. We are trying to find the future interest rate r_ for time period (t_1, t_2), t_1 and t_2 expressed in years, given the rate r_1 for time period (0, t_1) and rate r_2 for time period (0, t_2). To do this, we use the property that the proceeds from investing at rate r_1 for time period (0, t_1) and then reinvesting those proceeds at rate r_ for time period (t_1, t_2) is equal to the proceeds from investing at rate r_2 for time period (0, t_2). r_ depends on the rate calculation mode (simple, yearly compounded or continuously compounded), which yields three different results. Mathematically it reads as follows: Simple rate : (1+r_1t_1)(1+ r_(t_2-t_1)) = 1+r_2t_2 Solving for r_ yields: Thus r_ = ... [...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 As is standard, 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 ... [...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, which in general does not exist for the BOPM. 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Columbia University
Columbia University in the City of New York, commonly referred to as Columbia University, is a Private university, private Ivy League research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church (Manhattan), Trinity Church in Manhattan, it is the oldest institution of higher education in New York (state), New York and the fifth-First university in the United States, oldest in the United States. Columbia was established as a Colonial colleges, colonial college by royal charter under George II of Great Britain. It was renamed Columbia College (New York), Columbia College in 1784 following the American Revolution, and in 1787 was placed under Trustees of Columbia University in the City of New York, 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 is organized into twenty schoo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Twente
The University of Twente ( ; Abbreviation, abbr. ) is a Public university, 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 3TU, 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'' (''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 ed ... [...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 theory, 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 t ... [...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 * Overfitting * Random variables * State variable A state variable is one of the set of Variable (mathematics), 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 behavi ...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 expectation 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 s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ornstein–Uhlenbeck Process
In mathematics, the Ornstein–Uhlenbeck process is a stochastic process with applications in financial mathematics and the physical sciences. Its original application in physics was as a model for the velocity of a massive Brownian particle under the influence of friction. It is named after Leonard Ornstein and George Eugene Uhlenbeck. The Ornstein–Uhlenbeck process is a stationary Gauss–Markov process, which means that it is a Gaussian process, a Markov process, and is temporally homogeneous. In fact, it is the only nontrivial process that satisfies these three conditions, up to allowing linear transformations of the space and time variables. Over time, the process tends to drift towards its mean function: such a process is called ''mean-reverting''. The process can be considered to be a modification of the random walk in continuous time, or Wiener process, in which the properties of the process have been changed so that there is a tendency of the walk to move bac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lognormal
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] |
