Category: Mathematical finance

Autoregressive conditional duration
In financial econometrics, an autoregressive conditional duration (ACD, Engle and Russell (1998)) model considers irregularly spaced and autocorrelated intertrade durations. ACD is analogous to GARCH.
Regular distribution (economics)
Regularity, sometimes called Myerson's regularity, is a property of probability distributions used in auction theory and revenue management. Examples of distributions that satisfy this condition inclu
Taleb distribution
In economics and finance, a Taleb distribution is the statistical profile of an investment which normally provides a payoff of small positive returns, while carrying a small but significant risk of ca
Inverse demand function
In economics, an inverse demand function is the inverse function of a demand function. The inverse demand function views price as a function of quantity. Quantity demanded, Q, is a function (the deman
Put–call parity
In financial mathematics, put–call parity defines a relationship between the price of a European call option and European put option, both with the identical strike price and expiry, namely that a por
Snell envelope
The Snell envelope, used in stochastics and mathematical finance, is the smallest supermartingale dominating a stochastic process. The Snell envelope is named after James Laurie Snell.
Volatility smile
Volatility smiles are implied volatility patterns that arise in pricing financial options. It is a parameter (implied volatility) that is needed to be modified for the Black–Scholes formula to fit mar
Finite difference methods for option pricing
Finite difference methods for option pricing are numerical methods used in mathematical finance for the valuation of options. Finite difference methods were first applied to option pricing by Eduardo
Girsanov theorem
In probability theory, the Girsanov theorem tells how stochastic processes change under changes in measure. The theorem is especially important in the theory of financial mathematics as it tells how t
Stochastic differential equation
A stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution which is also a stochastic process. SDEs are used
Heath–Jarrow–Morton framework
The Heath–Jarrow–Morton (HJM) framework is a general framework to model the evolution of interest rate curves – instantaneous forward rate curves in particular (as opposed to simple forward rates). Wh
Johnson binomial tree
No description available.
Volfefe index
The Volfefe Index was a stock market index of volatility in market sentiment for US Treasury bonds caused by tweets by former President Donald Trump. Bloomberg News observed Volfefe was created due to
Fundamental theorem of asset pricing
The fundamental theorems of asset pricing (also: of arbitrage, of finance), in both financial economics and mathematical finance, provide necessary and sufficient conditions for a market to be arbitra
Interest rate
An interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited, or borrowed (called the principal sum). The total interest on an amount lent or borrowed depen
Fisher equation
In financial mathematics and economics, the Fisher equation expresses the relationship between nominal interest rates and real interest rates under inflation. Named after Irving Fisher, an American ec
Greeks (finance)
In mathematical finance, the Greeks are the quantities representing the sensitivity of the price of derivatives such as options to a change in underlying parameters on which the value of an instrument
Feynman–Kac formula
The Feynman–Kac formula, named after Richard Feynman and Mark Kac, establishes a link between parabolic partial differential equations (PDEs) and stochastic processes. In 1947, when Kac and Feynman we
Rocket science (finance)
"Rocket science" in finance is a metaphor for activity carried out by specialised quantitative staff to provide detailed output from mathematical modeling and computational simulations to support inve
Continuous-repayment mortgage
Analogous to continuous compounding, a continuous annuity is an ordinary annuity in which the payment interval is narrowed indefinitely. A (theoretical) continuous repayment mortgage is a mortgage loa
Volatility risk premium
In mathematical finance, the volatility risk premium is a measure of the extra amount investors demand in order to hold a volatile security, above what can be computed based on expected returns. It ca
Ohlson O-score
The Ohlson O-score for predicting bankruptcy is a multi-factor financial formula postulated in 1980 by Dr. of the New York University Stern Accounting Department as an alternative to the Altman Z-scor
Implied binomial tree
No description available.
Credit card interest
Credit card interest is a way in which credit card issuers generate revenue. A card issuer is a bank or credit union that gives a consumer (the cardholder) a card or account number that can be used wi
Itô calculus
Itô calculus, named after Kiyosi Itô, extends the methods of calculus to stochastic processes such as Brownian motion (see Wiener process). It has important applications in mathematical finance and st
Computational finance
Computational finance is a branch of applied computer science that deals with problems of practical interest in finance. Some slightly different definitions are the study of data and algorithms curren
Factor theory
In finance, factor theory is a collection of related mathematical models that explain asset returns as driven by distinct economic risks called factors. In less formal usage, a factor is simply an att
Graham number
The Graham number or Benjamin Graham number is a figure used in securities investing that measures a stock's so-called fair value. Named after Benjamin Graham, the founder of value investing, the Grah
Early repayment charge
No description available.
Shadow rate
The shadow rate is an interest rate in some financial models. It is used to measure the economy when nominal interest rates come close to the zero lower bound. It was created by Fischer Black in his f
Master of Financial Engineering
No description available.
Marginal conditional stochastic dominance
In finance, marginal conditional stochastic dominance is a condition under which a portfolio can be improved in the eyes of all risk-averse investors by incrementally moving funds out of one asset (or
Barone-Adesi and Whaley
No description available.
Compound annual growth rate
Compound annual growth rate (CAGR) is a business and investing specific term for the geometric progression ratio that provides a constant rate of return over the time period. CAGR is not an accounting
No-arbitrage bounds
In financial mathematics, no-arbitrage bounds are mathematical relationships specifying limits on financial portfolio prices. These price bounds are a specific example of good–deal bounds, and are in
Realized kernel
The realized kernel (RK) is an estimator of volatility. The estimator is typically computed with high frequency return data, such as second-by-second returns. Unlike the realized variance, the realize
Realized variance
Realized variance or realised variance (RV, see spelling differences) is the sum of squared returns. For instance the RV can be the sum of squared daily returns for a particular month, which would yie
Certificate in Quantitative Finance
No description available.
High-frequency trading
High-frequency trading (HFT) is a type of algorithmic financial trading characterized by high speeds, high turnover rates, and high order-to-trade ratios that leverages high-frequency financial data a
Mortgage constant
Mortgage constant, also called "mortgage capitalization rate", is the capitalization rate for debt. It is usually computed monthly by dividing the monthly payment by the mortgage principal. An annuali
Weighted average cost of capital
The weighted average cost of capital (WACC) is the rate that a company is expected to pay on average to all its security holders to finance its assets. The WACC is commonly referred to as the firm's c
Rule of 72
In finance, the rule of 72, the rule of 70 and the rule of 69.3 are methods for estimating an investment's doubling time. The rule number (e.g., 72) is divided by the interest percentage per period (u
Bootstrapping (finance)
In finance, bootstrapping is a method for constructing a (zero-coupon) fixed-income yield curve from the prices of a set of coupon-bearing products, e.g. bonds and swaps. A bootstrapped curve, corresp
Optimal stopping
In mathematics, the theory of optimal stopping or early stopping is concerned with the problem of choosing a time to take a particular action, in order to maximise an expected reward or minimise an ex
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
Good–deal bounds
Good–deal bounds are price bounds for a financial portfolio which depends on an individual trader's preferences. Mathematically, if is a set of portfolios with future outcomes which are "acceptable" t
Ruin theory
In actuarial science and applied probability, ruin theory (sometimes risk theory or collective risk theory) uses mathematical models to describe an insurer's vulnerability to insolvency/ruin. In such
Martingale pricing
Martingale pricing is a pricing approach based on the notions of martingale and risk neutrality. The martingale pricing approach is a cornerstone of modern quantitative finance and can be applied to a
Quantum finance
Quantum finance is an interdisciplinary research field, applying theories and methods developed by quantum physicists and economists in order to solve problems in finance. It is a branch of econophysi
Margin at risk
The Margin-at-Risk (short: MaR) is a quantity used to manage short-term liquidity risks due to variation of margin requirements, i.e. it is a financial risk occurring when trading commodities. Similar
Stochastic calculus
Stochastic calculus is a branch of mathematics that operates on stochastic processes. It allows a consistent theory of integration to be defined for integrals of stochastic processes with respect to s
Johansen test
In statistics, the Johansen test, named after Søren Johansen, is a procedure for testing cointegration of several, say k, I(1) time series. This test permits more than one cointegrating relationship s
Liquidity at risk
The Liquidity-at-Risk (short: LaR) is a measure of the liquidity risk exposure of a financial portfolio. It may be defined as the net liquidity drain which can occur in the portfolio in a given risk s
Carr–Madan formula
In financial mathematics, the Carr–Madan formula of Peter Carr and Dilip B. Madan shows that the analytical solution of the European option price can be obtained once the explicit form of the characte
Roll's critique
Roll's critique is a famous analysis of the validity of empirical tests of the capital asset pricing model (CAPM) by Richard Roll. It concerns methods to formally test the statement of the CAPM, the e
Cheyette model
In mathematical finance, the Cheyette Model is a quasi-Gaussian, quadratic volatility model of interest rates intended to overcome certain limitations of the Heath-Jarrow-Morton framework. By imposing
Financial correlation
Financial correlations measure the relationship between the changes of two or more financial variables over time. For example, the prices of equity stocks and fixed interest bonds often move in opposi
Markov switching multifractal
In financial econometrics (the application of statistical methods to economic data), the Markov-switching multifractal (MSM) is a model of asset returns developed by Laurent E. Calvet and Adlai J. Fis
Alpha (finance)
Alpha is a measure of the active return on an investment, the performance of that investment compared with a suitable market index. An alpha of 1% means the investment's return on investment over a se
Stochastic drift
In probability theory, stochastic drift is the change of the average value of a stochastic (random) process. A related concept is the drift rate, which is the rate at which the average changes. For ex
Black–Scholes equation
In mathematical finance, the Black–Scholes equation is a partial differential equation (PDE) governing the price evolution of a European call or European put under the Black–Scholes model. Broadly spe
Statistical arbitrage
In finance, statistical arbitrage (often abbreviated as Stat Arb or StatArb) is a class of short-term financial trading strategies that employ mean reversion models involving broadly diversified portf
Beta (finance)
In finance, the beta (β or market beta or beta coefficient) is a measure of how an individual asset moves (on average) when the overall stock market increases or decreases. Thus, beta is a useful meas
Intertemporal CAPM
Within mathematical finance, the Intertemporal Capital Asset Pricing Model, or ICAPM, is an alternative to the CAPM provided by Robert Merton. It is a linear factor model with wealth as state variable
Maximum Downside Exposure
In financial investment, the Maximum downside exposure (MDE) values the maximum downside to an investment portfolio. In other words, it states the most that the portfolio could lose in the event of a
The numéraire (or numeraire) is a basic standard by which value is computed. In mathematical economics it is a tradable economic entity in terms of whose price the relative prices of all other tradabl
Forward measure
In finance, a T-forward measure is a pricing measure absolutely continuous with respect to a risk-neutral measure, but rather than using the money market as numeraire, it uses a bond with maturity T.
Over-the-counter (finance)
Over-the-counter (OTC) or off-exchange trading or pink sheet trading is done directly between two parties, without the supervision of an exchange. It is contrasted with exchange trading, which occurs
Intertemporal budget constraint
In economics and finance, an intertemporal budget constraint is a constraint faced by a decision maker who is making choices for both the present and the future. The term intertemporal is used to desc
Negative probability
The probability of the outcome of an experiment is never negative, although a quasiprobability distribution allows a negative probability, or quasiprobability for some events. These distributions may
Arizona Financial Text System (AZFinText) is a textual-based quantitative financial prediction system written by Robert P. Schumaker of University of Texas at Tyler and Hsinchun Chen of the University
High frequency data
High frequency data refers to time-series data collected at an extremely fine scale. As a result of advanced computational power in recent decades, high frequency data can be accurately collected at a
SKEW is the ticker symbol for the CBOE Skew Index, a measure of the perceived tail risk of the distribution of S&P 500 investment returns over a 30-day horizon.The index values are calculated and publ
Pricing kernel
No description available.
Financial engineering
Financial engineering is a multidisciplinary field involving financial theory, methods of engineering, tools of mathematics and the practice of programming. It has also been defined as the application
Cointegration is a statistical property of a collection (X1, X2, ..., Xk) of time series variables. First, all of the series must be integrated of order d (see Order of integration). Next, if a linear
Index arbitrage
Index arbitrage is a subset of statistical arbitrage focusing on index components. An index (such as S&P 500) is made up of several components (in the case of the S&P 500, 500 large US stocks picked b
Fokker–Planck equation
In statistical mechanics, the Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of the velocity of a particle under the in
Variance swap
A variance swap is an over-the-counter financial derivative that allows one to speculate on or hedge risks associated with the magnitude of movement, i.e. volatility, of some underlying product, like
Affine term structure model
An affine term structure model is a financial model that relates zero-coupon bond prices (i.e. the discount curve) to a spot rate model. It is particularly useful for deriving the yield curve – the pr
Financial modeling
Financial modeling is the task of building an abstract representation (a model) of a real world financial situation. This is a mathematical model designed to represent (a simplified version of) the pe
Volatility (finance)
In finance, volatility (usually denoted by σ) is the degree of variation of a trading price series over time, usually measured by the standard deviation of logarithmic returns. Historic volatility mea
ExMark is a term describing the relationship between a fund's return and the market index. The usual designation for this concept is R-squared, but John C. Bogle coined this expression to highlight th
Implied volatility
In financial mathematics, the implied volatility (IV) of an option contract is that value of the volatility of the underlying instrument which, when input in an option pricing model (such as Black–Sch
Bjerksund and Stensland
No description available.
Earnings response coefficient
In financial economics, finance, and accounting, the earnings response coefficient, or ERC, is the estimated relationship between equity returns and the unexpected portion of (i.e., new information in
Stochastic partial differential equation
Stochastic partial differential equations (SPDEs) generalize partial differential equations via random force terms and coefficients, in the same way ordinary stochastic differential equations generali
Modified Dietz method
The modified Dietz method is a measure of the ex post (i.e. historical) performance of an investment portfolio in the presence of external flows. (External flows are movements of value such as transfe
Current yield
The current yield, interest yield, income yield, flat yield, market yield, mark to market yield or running yield is a financial term used in reference to bonds and other fixed-interest securities such
Jamshidian's trick
Jamshidian's trick is a technique for one-factor asset price models, which re-expresses an option on a portfolio of assets as a portfolio of options. It was developed by Farshid Jamshidian in 1989. Th
Margrabe's formula
In mathematical finance, Margrabe's formula is an option pricing formula applicable to an option to exchange one risky asset for another risky asset at maturity. It was derived by William Margrabe (Ph
Volatility tax
The volatility tax is a mathematical finance term, formalized by hedge fund manager Mark Spitznagel, describing the effect of large investment losses (or volatility) on compound returns. It has also b
Returns-based style analysis
Returns-based style analysis is a statistical technique used in finance to deconstruct the returns of investment strategies using a variety of explanatory variables. The model results in a strategy's
Enterprise value
Enterprise value (EV), total enterprise value (TEV), or firm value (FV) is an economic measure reflecting the market value of a business (i.e. as distinct from market price). It is a sum of claims by
Accumulation function
The accumulation function a(t) is a function defined in terms of time t expressing the ratio of the value at time t (future value) and the initial investment (present value). It is used in . Thus a(0)
Stochastic discount factor
The concept of the stochastic discount factor (SDF) is used in financial economics and mathematical finance. The name derives from the price of an asset being computable by "discounting" the future ca
No free lunch with vanishing risk
No free lunch with vanishing risk (NFLVR) is a no-arbitrage argument. We have free lunch with vanishing risk if by utilizing a sequence of time self-financing portfolios, which converge to an arbitrag
Variance risk premium
Variance risk premium is a phenomenon on the variance swap market, of the variance swap strike being greater than the realized variance on average. For most trades, the buyer of variance ends up with
Multi-curve framework
No description available.
Jensen's alpha
In finance, Jensen's alpha (or Jensen's Performance Index, ex-post alpha) is used to determine the abnormal return of a security or portfolio of securities over the theoretical expected return. It is
Walk forward optimization
Walk forward optimization is a method used in finance to determine the optimal parameters for a trading strategy. The trading strategy is optimized with in-sample data for a time window in a data seri
Equity value
Equity value is the value of a company available to owners or shareholders. It is the enterprise value plus all cash and cash equivalents, short and long-term investments, and less all short-term debt
Sonkin enterprise multiple
The Sonkin enterprise multiple (Sonkin ratio) was named after by , a graduate of Columbia Business School. This ratio can be used when Value investing, and can be calculated using the following formul
Volume-weighted average price
In finance, volume-weighted average price (VWAP) is the ratio of the value of a security or financial asset traded to the total volume of transactions during a trading session. It is a measure of the
Value investing
Value investing is an investment paradigm that involves buying securities that appear underpriced by some form of fundamental analysis. The various forms of value investing derive from the investment
Implied repo rate
Implied repo rate (IRR) is the rate of return of borrowing money to buy an asset in the spot market and delivering it in the futures market where the notional is used to repay the loan.
Valuation of options
In finance, a price (premium) is paid or received for purchasing or selling options. This article discusses the calculation of this premium in general. For further detail, see: Mathematical finance §
Replicating portfolio
In mathematical finance, a replicating portfolio for a given asset or series of cash flows is a portfolio of assets with the same properties (especially cash flows). This is meant in two distinct sens
Stochastic volatility jump
In mathematical finance, the stochastic volatility jump (SVJ) model is suggested by Bates. This model fits the observed implied volatility surface well. The model is a Heston process for stochastic vo
Time-weighted return
The time-weighted return (TWR) is a method of calculating investment return. To apply the time-weighted return method, combine the returns over sub-periods by compounding them together, resulting in t
Financial Modelers' Manifesto
The Financial Modelers' Manifesto was a proposal for more responsibility in risk management and quantitative finance written by financial engineers Emanuel Derman and Paul Wilmott. The manifesto inclu
Correlation swap
A correlation swap is an over-the-counter financial derivative that allows one to speculate on or hedge risks associated with the observed average correlation, of a collection of underlying products,
Theory of fructification
In economics, the theory of fructification is a theory of the interest rate which was proposed by French economist and finance minister Anne Robert Jacques Turgot. The term theory of fructification is
Forward volatility
Forward volatility is a measure of the implied volatility of a financial instrument over a period in the future, extracted from the term structure of volatility (which refers to how implied volatility
QuantLib is an open-source software library which provides tools for software developers and practitioners interested in financial instrument valuation and related subjects. QuantLib is written in C++
Modigliani risk-adjusted performance
Modigliani risk-adjusted performance (also known as M2, M2, Modigliani–Modigliani measure or RAP) is a measure of the risk-adjusted returns of some investment portfolio. It measures the returns of the
Consumer math
Consumer math comprises practical mathematical techniques used in commerce and everyday life. In the United States, consumer math is typically offered in high schools, some elementary schools, or in s
Convexity (finance)
In mathematical finance, convexity refers to non-linearities in a financial model. In other words, if the price of an underlying variable changes, the price of an output does not change linearly, but
Profit at risk
Profit-at-Risk (PaR) is a risk management quantity most often used for electricity portfolios that contain some mixture of generation assets, trading contracts and end-user consumption. It is used to
Frictionless market
In economic theory a frictionless market is a financial market without transaction costs. Friction is a type of market incompleteness. Every complete market is frictionless, but the converse does not
Quantitative behavioral finance
Quantitative behavioral finance is a new discipline that uses mathematical and statistical methodology to understand behavioral biases in conjunction with valuation. The research can be grouped into t
Stochastic volatility
In statistics, stochastic volatility models are those in which the variance of a stochastic process is itself randomly distributed. They are used in the field of mathematical finance to evaluate deriv
Adjusted current yield
The adjusted current yield is a financial term used in reference to bonds and other fixed-interest securities. It is closely related to the concept of current yield. The adjusted current yield is give
Skewness risk
Skewness risk in financial modeling is the risk that results when observations are not spread symmetrically around an average value, but instead have a skewed distribution. As a result, the mean and t
Lattice model (finance)
In finance, a lattice model is a technique applied to the valuation of derivatives, where a discrete time model is required. For equity options, a typical example would be pricing an American option,
Alternative beta
Alternative beta is the concept of managing volatile "alternative investments", often through the use of hedge funds. Alternative beta is often also referred to as "alternative risk premia". Researche
Vanna–Volga pricing
The Vanna–Volga method is a mathematical tool used in finance. It is a technique for pricing first-generation exotic options in foreign exchange market (FX) derivatives.
Indifference price
In finance, indifference pricing is a method of pricing financial securities with regard to a utility function. The indifference price is also known as the reservation price or private valuation. In p
No description available.
Rate of return
In finance, return is a profit on an investment. It comprises any change in value of the investment, and/or cash flows (or securities, or other investments) which the investor receives from that inves
Rate of return on a portfolio
The rate of return on a portfolio is the ratio of the net gain or loss (which is the total of net income, foreign currency appreciation and capital gain, whether realized or not) which a portfolio gen
Financial econometrics
Financial econometrics is the application of statistical methods to financial market data. Financial econometrics is a branch of financial economics, in the field of economics. Areas of study include
Future value
Future value is the value of an asset at a specific date. It measures the nominal future sum of money that a given sum of money is "worth" at a specified time in the future assuming a certain interest
Smith–Wilson method
The Smith–Wilson method is a method for extrapolating forward rates. It is recommended by EIOPA to extrapolate interest rates. It was introduced in 2000 by A. Smith and T. Wilson for .
Delta neutral
In finance, delta neutral describes a portfolio of related financial securities, in which the portfolio value remains unchanged when small changes occur in the value of the underlying security. Such a
Net present value
The net present value (NPV) or net present worth (NPW) applies to a series of cash flows occurring at different times. The present value of a cash flow depends on the interval of time between now and
Exotic option
In finance, an exotic option is an option which has features making it more complex than commonly traded vanilla options. Like the more general exotic derivatives they may have several triggers relati
No description available.
Spoofing (finance)
Spoofing is a disruptive algorithmic trading activity employed by traders to outpace other market participants and to manipulate markets. Spoofers feign interest in trading futures, stocks and other p
Simple Dietz method
The simple Dietz method is a means of measuring historical investment portfolio performance, compensating for external flows into/out of the portfolio during the period. The formula for the simple Die
Scenario optimization
The scenario approach or scenario optimization approach is a technique for obtaining solutions to robust optimization and problems based on a sample of the constraints. It also relates to inductive re
Theoretical Finance
No description available.
Master of Quantitative Finance
A master's degree in quantitative finance concerns the application of mathematical methods to the solution of problems in financial economics. There are several like-titled degrees which may further f
International Association for Quantitative Finance
The International Association for Quantitative Finance (IAQF), formerly the International Association of Financial Engineers (IAFE), is a non-profit professional society dedicated to fostering the fie
Compound interest
Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest. It is the result of reinvesting interest, or adding it
Consistent pricing process
A consistent pricing process (CPP) is any representation of (frictionless) "prices" of assets in a market. It is a stochastic process in a filtered probability space such that at time the component ca
Rational 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
Trinomial tree
The trinomial tree is a lattice-based computational model used in financial mathematics to price options. It was developed by Phelim Boyle in 1986. It is an extension of the binomial options pricing m
In mathematical finance, fugit is the expected (or optimal) date to exercise an American- or Bermudan option. It is useful for hedging purposes here; see Greeks (finance) and Optimal stopping § Option
Edgeworth binomial tree
No description available.
Admissible trading strategy
In finance, an admissible trading strategy or admissible strategy is any trading strategy with wealth almost surely bounded from below. In particular, an admissible trading strategy precludes unhedged
Brace-Gatarek-Musiela model
No description available.
Late fee
A late fee, also known as an overdue fine, late fine, or past due fee, is a charge fined against a client by a company or organization for not paying a bill or returning a rented or borrowed item by i
Credit valuation adjustment
Credit valuation adjustments (CVAs) are accounting adjustments made to reserve a portion of profits on uncollateralized financial derivatives. They are charged by a bank to a risky (capable of default
Holding period return
In finance, holding period return (HPR) is the return on an asset or portfolio over the whole period during which it was held. It is one of the simplest and most important measures of investment perfo
Hawkes process
In probability theory and statistics, a Hawkes process, named after Alan G. Hawkes, is a kind of self-exciting point process. It has arrivals at times where the infinitesimal probability of an arrival
Weighted average return on assets
The weighted average return on assets, or WARA, is the collective rates of return on the various types of tangible and intangible assets of a company. The presumption of a WARA is that each class of a
Korn–Kreer–Lenssen model
The Korn–Kreer–Lenssen model (KKL model) is a discrete trinomial model proposed in 1998 by Ralf Korn, Markus Kreer and Mark Lenssen to model illiquid securities and to value financial derivatives on t
Complete market
In economics, a complete market (aka Arrow-Debreu market or complete system of markets) is a market with two conditions: 1. * Negligible transaction costs and therefore also perfect information, 2.
Annual percentage rate
The term annual percentage rate of charge (APR), corresponding sometimes to a nominal APR and sometimes to an effective APR (EAPR), is the interest rate for a whole year (annualized), rather than just
Kurtosis risk
In statistics and decision theory, kurtosis risk is the risk that results when a statistical model assumes the normal distribution, but is applied to observations that have a tendency to occasionally
Self-financing portfolio
In financial mathematics, a self-financing portfolio is a portfolio having the feature that, if there is no exogenous infusion or withdrawal of money, the purchase of a new asset must be financed by t
Absorbing barrier (finance)
No description available.
Econophysics is a heterodox interdisciplinary research field, applying theories and methods originally developed by physicists in order to solve problems in economics, usually those including uncertai
Bid–ask matrix
The bid–ask matrix is a matrix with elements corresponding with exchange rates between the assets. These rates are in physical units (e.g. number of stocks) and not with respect to any numeraire. The
Present value
In economics and finance, present value (PV), also known as present discounted value, is the value of an expected income stream determined as of the date of valuation. The present value is usually les
Alpha Profiling
Alpha profiling is an application of machine learning to optimize the execution of large orders in financial markets by means of algorithmic trading. The purpose is to select an execution schedule tha
Crank–Nicolson method
In numerical analysis, the Crank–Nicolson method is a finite difference method used for numerically solving the heat equation and similar partial differential equations. It is a second-order method in
Statistical finance
Statistical finance, is the application of econophysics to financial markets. Instead of the normative roots of finance, it uses a positivist framework. It includes exemplars from statistical physics
Malliavin calculus
In probability theory and related fields, Malliavin calculus is a set of mathematical techniques and ideas that extend the mathematical field of calculus of variations from deterministic functions to
Viscosity solution
In mathematics, the viscosity solution concept was introduced in the early 1980s by Pierre-Louis Lions and Michael G. Crandall as a generalization of the classical concept of what is meant by a 'solut
Rising moving average
The rising moving average is a technical indicator used in stock market trading. Most commonly found visually, the pattern is spotted with a moving average overlay on a stock chart or price series. Wh
(For the sculpture, see Perpetuity (sculpture).) A perpetuity is an annuity that has no end, or a stream of cash payments that continues forever. There are few actual perpetuities in existence. For ex
State price density
No description available.
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, usu
Heston model
In finance, the Heston model, named after Steven L. Heston, is a mathematical model that describes the evolution of the volatility of an underlying asset. It is a stochastic volatility model: such a m
Undervalued stock
An undervalued stock is defined as a stock that is selling at a price significantly below what is assumed to be its intrinsic value. For example, if a stock is selling for $50, but it is worth $100 ba
Convexity correction
No description available.
Implied trinomial tree
No description available.
Separation property (finance)
A separation property is a crucial element of modern portfolio theory that gives a portfolio manager the ability to separate the process of satisfying investing clients' assets into two separate parts
Range accrual
In finance, a range accrual is a type of derivative product very popular among structured note investors. It is estimated that more than US$160 billion of Range Accrual indexed on interest rates only
An X-Value Adjustment (XVA, xVA) is an umbrella term referring to a number of different “valuation adjustments” that banks must make when assessing the value of derivative contracts that they have ent
Mathematical finance
Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling of financial markets. In general, there exis
Quantitative analysis (finance)
Quantitative analysis is the use of mathematical and statistical methods in finance and investment management. Those working in the field are quantitative analysts (quants). Quants tend to specialize
Low-volatility anomaly
In investing and finance, the low-volatility anomaly is the observation that low-volatility stocks have higher returns than high-volatility stocks in most markets studied. This is an example of a stoc
Efficient frontier
In modern portfolio theory, the efficient frontier (or portfolio frontier) is an investment portfolio which occupies the "efficient" parts of the risk–return spectrum. Formally, it is the set of portf
Counterparty credit risk
No description available.
Modified internal rate of return
The modified internal rate of return (MIRR) is a financial measure of an investment's attractiveness. It is used in capital budgeting to rank alternative investments of equal size. As the name implies
VIX is the ticker symbol and the popular name for the Chicago Board Options Exchange's CBOE Volatility Index, a popular measure of the stock market's expectation of volatility based on S&P 500 index o
Incomplete markets
In economics, incomplete markets are markets in which there does not exist an Arrow–Debreu security for every possible state of nature. In contrast with complete markets, this shortage of securities w
Discount points
Discount points, also called mortgage points or simply points, are a form of pre-paid interest available in the United States when arranging a mortgage. One point equals one percent of the loan amount
Time consistency (finance)
Time consistency in the context of finance is the property of not having mutually contradictory evaluations of risk at different points in time. This property implies that if investment A is considere