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Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling in the financial field. In general, there exist two separate branches of finance that require advanced quantitative techniques: derivatives pricing on the one hand, and risk and portfolio ...
A formula that is accurate to within a few percent can be found by noting that for typical U.S. note rates (< % and terms =10–30 years), the monthly note rate is small compared to 1. r << 1 {\displaystyle r<<1} so that the ln ( 1 + r ) ≈ r {\displaystyle \ln(1+r)\approx r} which yields the simplification:
Carr–Madan formula; Cash flow at risk; Certificate in Quantitative Finance; Cheyette model; Cointegration; Complete market; Compound annual growth rate; Compound interest; Computational finance; Consistent pricing process; Consumer math; Continuous-repayment mortgage; Convexity (finance) Convexity correction; Correlation swap; Counterparty ...
The formula above can be used for more than calculating the doubling time. If one wants to know the tripling time, for example, replace the constant 2 in the numerator with 3. As another example, if one wants to know the number of periods it takes for the initial value to rise by 50%, replace the constant 2 with 1.5.
In mathematical finance, the Greeks are the quantities (known in calculus as partial derivatives; first-order or higher) representing the sensitivity of the price of a derivative instrument such as an option to changes in one or more underlying parameters on which the value of an instrument or portfolio of financial instruments is dependent.
Actuarial notation is a shorthand method to allow actuaries to record mathematical formulas that deal with interest rates and life tables. Traditional notation uses a halo system, where symbols are placed as superscript or subscript before or after the main letter. Example notation using the halo system can be seen below.
In a discrete (i.e. finite state) market, the following hold: [2] The First Fundamental Theorem of Asset Pricing: A discrete market on a discrete probability space (,,) is arbitrage-free if, and only if, there exists at least one risk neutral probability measure that is equivalent to the original probability measure, P.
The Brownian motion models for financial markets are based on the work of Robert C. Merton and Paul A. Samuelson, as extensions to the one-period market models of Harold Markowitz and William F. Sharpe, and are concerned with defining the concepts of financial assets and markets, portfolios, gains and wealth in terms of continuous-time stochastic processes.