NationMaster - Encyclopedia: Financial mathematics

Mathematical finance is the branch of applied mathematics concerned with the financial markets. The subject naturally has a close relationship with the discipline of financial economics, however the subject is narrower in scope and more abstract. A central difference is that whilst a financial economist might study the structural reasons why a company may have a certain share price, a 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. Applied mathematics is a branch of mathematics that concerns itself with 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). ... Financial economics is the branch of economics concerned with the workings of financial markets, such as the stock market, and the financing of companies. ... 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. ... A derivative is a financial contract whose payoffs over a period of time are derived from the performance of assets, interest rates, exchange rates, or indices. ...

Mathematical finance articles

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The word probability derives from the Latin probare (to prove, or to test). ... In mathematics, a probability distribution assigns to every interval of the real numbers a probability, so that the probability axioms are satisfied. ... See binomial (disambiguation) for a list of other topics using that name. ... In probability and statistics, the log-normal distribution is the probability distribution of any random variable whose logarithm is normally distributed (the base of the logarithmic function is immaterial in that loga X is normally distributed if and only if logb X is normally distributed). ... In probability theory (and especially gambling), 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 to win per bet if bets with identical... 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. ... An example of 1000 simulated steps of Brownian motion in two dimensions. ... In mathematics, ItÅs lemma is used in stochastic calculus to find the differential of a function of a particular type of stochastic process. ... 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 measurable... Monte Carlo methods are a class of computational algorithms for simulating the behavior of various physical and mathematical systems. ... In mathematics, a partial differential equation (PDE) is an equation relating the partial derivatives of an unknown function of several variables. ... The heat equation is an important partial differential equation which describes the variation of temperature in a given region over time. ... 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 is 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. ... A mathematical model is an abstract model that uses mathematical language to describe the behaviour of a system. ... Numerical analysis is the study of algorithms for the problems of continuous mathematics (as distinguished from discrete mathematics). ...

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 state of imbalance between two or more markets: a combination of matching deals are struck that exploit 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 set price specified on the last trading date. ... 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. ... Conceptually, 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. ... In financial mathematics, the implied volatility of a financial instrument is the volatility implied by the market price of a derivative security based on a theoretical pricing model. ... --219. ... In mathematical finance, the Greeks are the quantities representing the market sensitivities of options or other derivatives, with each measuring a different aspect of the risk in an option position, and corresponding to the set of parameters on which the value of an instrument or portfolio of financial instruments is... An interest rate derivative is a derivative where the underlying asset is the right to pay or receive a (usually notional) amount of money at a given interest rate. ... 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. ... Heath-Jarrow-Morton framework is a set of techniques to price interest-rate derivatives that stems from the work of D. Heath, R.A. Jarrow and A. Morton in the late 1980s, especially Bond pricing and the term structure of interest rates: a new methodology (1987) -- working paper, Cornell University...

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Mathematical economics is the sub-field of economics that explores the mathematical aspects of economic systems. ... Extreme value theory is a branch of statistics dealing with the extreme deviations from the median of probability distributions. ...

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