In economics, inflation is a sustained increase in the general price level of goods and services in an economy over a period of time. When the general price level rises, each unit of currency buys fewer goods and services; consequently, inflation reflects a reduction in the purchasing power per unit of money – a loss of real value in the medium of exchange and unit of account within the economy. The measure of inflation is the inflation rate, the annualized percentage change in a general price index, usually the consumer price index, over time. The opposite of inflation is deflation.
An actuary is a business professional who deals with the measurement and management of risk and uncertainty. The name of the corresponding field is actuarial science. These risks can affect both sides of the balance sheet and require asset management, liability management, and valuation skills. Actuaries provide assessments of financial security systems, with a focus on their complexity, their mathematics, and their mechanisms.
Actuarial science is the discipline that applies mathematical and statistical methods to assess risk in insurance, finance and other industries and professions. Actuaries are professionals trained in this discipline. In many countries, actuaries must demonstrate their competence by passing a series of rigorous professional examinations.
A quantitative analyst is a person who specializes in the application of mathematical and statistical methods to financial and risk management problems. The occupation is similar to those in industrial mathematics in other industries.
In finance, the yield curve is a curve showing several yields or interest rates across different contract lengths for a similar debt contract. The curve shows the relation between the interest rate and the time to maturity, known as the "term", of the debt for a given borrower in a given currency. For example, the U.S. dollar interest rates paid on U.S. Treasury securities for various maturities are closely watched by many traders, and are commonly plotted on a graph such as the one on the right which is informally called "the yield curve". More formal mathematical descriptions of this relation are often called the term structure of interest rates.
In finance, arbitrage pricing theory (APT) is a general theory of asset pricing that holds that the expected return of a financial asset can be modeled as a linear function of various factors or theoretical market indices, where sensitivity to changes in each factor is represented by a factor-specific beta coefficient. The model-derived rate of return will then be used to price the asset correctly—the asset price should equal the expected end of period price discounted at the rate implied by the model. If the price diverges, arbitrage should bring it back into line. The theory was proposed by the economist Stephen Ross in 1976. The linear factor model structure of the APT is used as the basis for many of the commercial risk systems employed by asset managers.
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 .
In mathematical finance, the Black–Derman–Toy model (BDT) is a popular short rate model used in the pricing of bond options, swaptions and other interest rate derivatives; see Lattice model (finance) #Interest rate derivatives. It is a one-factor model; that is, a single stochastic factor—the short rate—determines the future evolution of all interest rates. It was the first model to combine the mean-reverting behaviour of the short rate with the lognormal distribution, and is still widely used.
The "Fed model" is a theory of equity valuation that has found broad application in the investment community. The model compares the stock market’s earnings yield (E/P) to the yield on long-term government bonds. In its strongest form the Fed model states that bond and stock market are in equilibrium, and fairly valued, when the one-year forward-looking earnings yield equals the 10-year Treasury note yield :
The following outline is provided as an overview of and topical guide to actuarial science:
"Stochastic" means being or having a random variable. A stochastic model is a tool for estimating probability distributions of potential outcomes by allowing for random variation in one or more inputs over time. The random variation is usually based on fluctuations observed in historical data for a selected period using standard time-series techniques. Distributions of potential outcomes are derived from a large number of simulations which reflect the random variation in the input(s).
Dynamic financial analysis (DFA) is a simulation approach that looks at an insurance enterprise's risks holistically as opposed to traditional actuarial analysis, which analyzes risks individually. Specifically, DFA reveals the dependencies of hazards and their impacts on the insurance company's financial well being such as business mix, reinsurance, asset allocation, profitability, solvency, and compliance.
The following outline is provided as an overview of and topical guide to finance:
In finance, the Chen model is a mathematical model describing the evolution of interest rates. It is a type of "three-factor model" as it describes interest rate movements as driven by three sources of market risk. It was the first stochastic mean and stochastic volatility model and it was published in 1994 by Lin Chen, economist, theoretical physicist and former lecturer/professor at Beijing Institute of Technology, Yonsei University of Korea, and Nanyang Tech University of Singapore.
The Rendleman–Bartter model in finance is a short rate model describing the evolution of interest rates. It is a "one factor model" as it describes interest rate movements as driven by only one source of market risk. It can be used in the valuation of interest rate derivatives. It is a stochastic asset model.
In monetary economics, the demand for money is the desired holding of financial assets in the form of money: that is, cash or bank deposits rather than investments. It can refer to the demand for money narrowly defined as M1, or for money in the broader sense of M2 or M3.
In financial mathematics, the Black–Karasinski model is a mathematical model of the term structure of interest rates; see short rate model. It is a one-factor model as it describes interest rate movements as driven by a single source of randomness. It belongs to the class of no-arbitrage models, i.e. it can fit today's zero-coupon bond prices, and in its most general form, today's prices for a set of caps, floors or European swaptions. The model was introduced by Fischer Black and Piotr Karasinski in 1991.
The Institute and Faculty of Actuaries is the professional body which represents and regulates actuaries in the United Kingdom.
Dedicated portfolio theory, in finance, deals with the characteristics and features of a portfolio built to generate a predictable stream of future cash inflows. This is achieved by purchasing bonds and/or other fixed income securities that can and usually are held to maturity to generate this predictable stream from the coupon interest and/or the repayment of the face value of each bond when it matures. The goal is for the stream of cash inflows to exactly match the timing of a predictable stream of cash outflows due to future liabilities. For this reason it is sometimes called cash matching, or liability-driven investing. Determining the least expensive collection of bonds in the right quantities with the right maturities to match the cash flows is an analytical challenge that requires some degree of mathematical sophistication. College level textbooks typically cover the idea of “dedicated portfolios” or “dedicated bond portfolios” in their chapters devoted to the uses of fixed income securities.
A stochastic investment model tries to forecast how returns and prices on different assets or asset classes, vary over time. Stochastic models are not applied for making point estimation rather interval estimation and they use different stochastic processes. Investment models can be classified into single-asset and multi-asset models. They are often used for actuarial work and financial planning to allow optimization in asset allocation or asset-liability-management (ALM).
