NationMaster - Encyclopedia: Mathematical finance

Mathematical finance is the branch of applied mathematics concerned with the financial markets. Applied mathematics is a branch of mathematics that concerns itself with the mathematical techniques typically used in the application of mathematical knowledge to other domains. ... In finance, financial markets facilitate: The raising of capital (in the capital markets); The transfer of risk (in the derivatives markets); and International trade (in the currency markets). ...

The subject has a close relationship with the discipline of financial economics, which is concerned with much of the underlying theory. Generally, mathematical finance will derive, and extend, the mathematical or numerical models suggested by financial economics. Thus, for example, while a financial economist might study the structural reasons why a company may have a certain share price, a financial mathematician may take the share price as a given, and attempt to use stochastic calculus to obtain the fair value of derivatives of the stock. Financial economics is the branch of economics concerned with resource allocation over time. ... A mathematical model is an abstract model that uses mathematical language to describe the behaviour of a system. ... Numerical analysis is the study of approximate methods for the problems of continuous mathematics (as distinguished from discrete mathematics). ... In economics and financial theory, analysts use random walk techniques to model behavior of asset prices, in particular share prices on stock markets, currency exchange rates and commodity prices. ... Stochastic calculus is a branch of mathematics that operates on stochastic processes. ... Derivatives traders at the Chicago Board of Trade. ... For other uses, see Stock (disambiguation). ...

In terms of practice, mathematical finance also overlaps heavily with the fields of financial engineering and computational finance. Arguably, all three are largely synonymous, although the latter two focus on application, while the former focuses on modelling and derivation; see Quantitative analyst. Financial engineering is the application of science-based mathematical and statistical models to make a better decision about managing financial risks, investing, borrowing, lending, and saving. ... Computational finance (also known as financial engineering) is a cross-disciplinary field which relies on mathematical finance, numerical methods and computer simulations to make trading, hedging and investment decisions, as well as facilitating the risk management of those decisions. ... A quantitative analyst is a person who works in the financial markets developing mathematical models to assist the activities of traders and risk managers within banks and other large corporate institutions. ...

Many universities around the world now offer degree and research programs in mathematical finance.

Mathematical finance articles

Mathematical tools

Calculus [from Latin, literally pebble (used in reckoning)] is a major area in mathematics, with applications in science, engineering, business, and medicine. ... An illustration of a differential equation. ... Linear algebra is the branch of mathematics concerned with the study of vectors, vector spaces (also called linear spaces), linear maps (also called linear transformations), and systems of linear equations. ... Numerical analysis is the study of approximate methods for the problems of continuous mathematics (as distinguished from discrete mathematics). ... Real analysis is a branch of mathematical analysis dealing with the set of real numbers and functions of real numbers. ... Probability is the extent to which something is likely to happen or be the case[1]. Probability theory is used extensively in areas such as statistics, mathematics, science, philosophy to draw conclusions about the likelihood of potential events and the underlying mechanics of complex systems. ... In mathematics and statistics, a probability distribution, more properly called a probability density, assigns to every interval of the real numbers a probability, so that the probability axioms are satisfied. ... In probability theory and statistics, the binomial distribution is the discrete probability distribution of the number of successes in a sequence of n independent yes/no experiments, each of which yields success with probability p. ... In probability and statistics, the log-normal distribution is the probability distribution of any random variable whose logarithm is normally distributed. ... In probability theory the expected value (or mathematical expectation) of a random variable is the sum of the probability of each possible outcome of the experiment multiplied by its payoff (value). Thus, it represents the average amount one expects as the outcome of the random trial when identical odds are... Definition In economics and finance, the Value at risk, or VaR, is a measure used to estimate how the value of an asset or of a portfolio of assets will decrease over a certain time period (usually over 1 day or 10 days) under usual conditions. ... In mathematical finance, a risk-neutral measure is a probability measure in which todays fair (i. ... Stochastic calculus is a branch of mathematics that operates on stochastic processes. ... Three different views of Brownian motion, with 32 steps, 256 steps, and 2048 steps denoted by progressively lighter colors. ... In probability theory, a LÃ©vy process, named after the French mathematician Paul LÃ©vy, is any continuous-time stochastic process that has stationary independent increments -- this phrase will be explained below. ... In mathematics, ItÅs lemma is used in stochastic calculus to find the differential of a function of a particular type of stochastic process. ... In mathematics, the Fourier transform is a certain linear operator that maps functions to other functions. ... In probability theory, Girsanovs theorem tells how stochastic processes change under changes in measure. ... In mathematics, the Radon-Nikodym theorem is a result in functional analysis that states that if a measure Q is absolutely continuous with respect to another sigma-finite measure P then there is a measurable function f, taking values in [0,∞], on the underlying space such that for any... Monte Carlo methods are a widely used class of computational algorithms for simulating the behavior of various physical and mathematical systems, and for other computations. ... In mathematics, a partial differential equation (PDE) is a relation involving an unknown function of several independent variables and its partial derivatives with respect to those variables. ... The heat equation is an important partial differential equation which describes the variation of temperature in a given region over time. ... In probability theory, the Martingale Representation Theorem shows the existence of a hedging strategy. ... The Feynman-Kac formula establishes a link between partial differential equations (PDEs) and stochastic processes. ... A stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, thus resulting in a solution which is itself a stochastic process. ... Volatility most frequently refers to the standard deviation of the change in value of a financial instrument with a specific time horizon. ... In econometrics, an autoregressive conditional heteroskedasticity (ARCH) model considers the variance of the current error term to be a function of the variances of the previous time periods error terms. ... In econometrics, an autoregressive conditional heteroskedasticity (ARCH) model considers the variance of the current error term to be a function of the variances of the previous time periods error terms. ... Stochastic volatility models are used in the field of quantitative finance to evaluate derivative securities, such as options. ... A mathematical model is an abstract model that uses mathematical language to describe the behaviour of a system. ... Numerical analysis is the study of approximate methods for the problems of continuous mathematics (as distinguished from discrete mathematics). ... Numerical partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations. ... The Crank-Nicolson method is a finite difference method used for numerically solving the heat and related equations. ... A finite difference is a mathematical expression of the form f(x + b) âˆ’ f(x +a). ...

Derivatives pricing

Rational pricing is the assumption in financial economics that asset prices (and hence asset pricing models) will reflect the arbitrage-free price of the asset as any deviation from this price will be arbitraged away. This assumption is useful in pricing fixed income securities, particularly bonds, and is fundamental to... In mathematical finance, a risk-neutral measure is a probability measure in which todays fair (i. ... In economics, arbitrage is the practice of taking advantage of a price differential between two or more markets: a combination of matching deals are struck that capitalize upon the imbalance, the profit being the difference between the market prices. ... In finance, a futures contract is a standardized contract, traded on a futures exchange, to buy or sell a certain underlying instrument at a certain date in the future, at a specified price. ... In financial mathematics, put-call parity defines a relationship between the price of a European call option and a European put option - both with the identical strike price and expiry. ... In finance, moneyness is a measure of the degree to which a derivative security is likely to have positive monetary value at its expiration. ... Option Value In finance, the value of an option consists of two components, its intrinsic value and its time value. ... A mathematical model is an abstract model that uses mathematical language to describe the behaviour of a system. ... The Black-Scholes model, often simply called Black-Scholes, is a model of the varying price over time of financial instruments, and in particular stocks. ... The Black model (sometimes known as the Black-76 model) is a variant the Black-Scholes option pricing model. ... In finance, the binomial options model provides a generalisable numerical method for the valuation of options. ... A Monte Carlo model, in its most general description, includes any method of estimating a value by the random generation of numbers and statistical principles. ... In financial mathematics, the implied volatility of an option contract is the volatility implied by the market price of the option based on an option pricing model. ... Volatility Smile refers to the long-observed pattern in which at-the-money options tend to have lower implied volatilities than other options. ... In mathematical finance, the Greeks are the quantities representing the market sensitivities of options or other derivatives. ... To meet Wikipedias quality standards, this article may require cleanup. ... In the context of interest rate derivatives, a short rate model is a mathematical model that describes the future evolution of interest rates by describing the future evolution of the short rate. ... The Hull-White model is a mathematical model of future interest rates. ... The LIBOR Market Model, also referred to as the BGM model, is an interest rate model used for the pricing of interest rate derivatives, especially complex derivatives such as exotics. ... Heath-Jarrow-Morton framework is a general framework to model the evolution of interest rates (forward rates in particular). ...

See also

Computational finance (also known as financial engineering) is a cross-disciplinary field which relies on mathematical finance, numerical methods and computer simulations to make trading, hedging and investment decisions, as well as facilitating the risk management of those decisions. ... Financial engineering is the application of science-based mathematical and statistical models to make a better decision about managing financial risks, investing, borrowing, lending, and saving. ... Derivatives traders at the Chicago Board of Trade. ... What follows is a list of over 250 Wikipedia articles on finance topics. ... Much effort has gone into the study of financial markets and how prices vary with time. ... What follows is a list of over 250 Wikipedia articles on finance topics. ... A diagram of the IS/LM model In economics, a model is a theoretical construct that represents economic processes by a set of variables and a set of logical and quantitative relationships between them. ... QuantLib is a free/open-source cross-platform software library for quantitative finance, issued under the BSD License. ... What follows is a list of over 250 Wikipedia articles on finance topics. ... This list provides an alphabetical index of articles on finance related topics. ... This aims to be a complete list of the articles on economics. ... This is an alphabetical list of well-known economists. ... This is a list of topics which are relevant to Accountancy. ... This is a list of over 200 articles on marketing topics. ... This is a list of articles on general management and strategic management topics. ...

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Resources

Institutional

Theory

PDF is an abbreviation with several meanings: Portable Document Format Post-doctoral fellowship Probability density function There also is an electronic design automation company named PDF Solutions. ... Royal School of Mines Entrance Imperial College London is a college of the University of London which focuses on science and technology, and is located in South Kensington in London. ...

Research

Education

Training

Categories: Wikipedia external links cleanup | Mathematical finance | Applied mathematics | Actuarial science | Mathematical science occupations Finance studies and addresses the ways in which individuals, businesses, and organizations raise, allocate, and use monetary resources over time, taking into account the risks entailed in their projects. ... In economics a financial market is a mechanism that allows people to easily buy and sell (trade) financial securities (such as stocks and bonds), commodities (such as precious metals or agricultural goods), and other fungible items of value at low transaction costs and at prices that reflect efficient markets. ... Investment management, the professional management of various securities (shares, bonds etc) and other assets (e. ... In Financial economics, a financial institution acts as an agent that provides financial services for its clients. ... United States Personal finance is the application of the principles of finance to the monetary decisions of an individual or family unit. ... Public finance (government finance) is the field of economics that deals with budgeting the revenues and expenditures of a public sector entity, usually government. ... Financial economics is the branch of economics concerned with resource allocation over time. ... The goals of experimental finance are to establish different market settings and environments to observe experimentally and analyze agents behavior and the resulting characteristics of trading flows, information diffusion and aggregation, price setting mechanism and returns processes. ... Computational finance (also known as financial engineering) is a cross-disciplinary field which relies on mathematical finance, numerical methods and computer simulations to make trading, hedging and investment decisions, as well as facilitating the risk management of those decisions. ...

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