Quantitative Finance Glossary

A comprehensive glossary of terms used in quantitative finance to aid those new to the field.

TL; DR
A glossary providing definitions for complex quantitative finance terms.
Designed to help individuals with limited financial knowledge understand the jargon.
Includes terms like Arbitrage, Beta, CAPM, Derivative, and more.
Each term is explained with a brief summary and formulae where applicable.

Quantitative Finance Glossary

Quantitative finance can be daunting with its complex models and financial jargon. This glossary aims to demystify the terms commonly used in the field, making it more accessible to those new to finance.

Arbitrage

Arbitrage refers to the simultaneous purchase and sale of an asset to profit from a difference in the price. It is a trade that profits by exploiting the price differences of identical or similar financial instruments on different markets or in different forms.

Beta (β)

Beta is a measure of the volatility, or systematic risk, of a security or a portfolio in comparison to the market as a whole. It is used in the capital asset pricing model (CAPM), which calculates the expected return of an asset based on its beta and expected market returns. $\beta = \frac{Cov(r_a, r_m)}{Var(r_m)}$ where $r_a$ is the asset return and $r_m$ is the market return.

Capital Asset Pricing Model (CAPM)

The CAPM is a model that describes the relationship between systematic risk and expected return for assets, particularly stocks. It is used to determine a theoretically appropriate required rate of return of an asset, if that asset is to be added to an already well-diversified portfolio, given that asset's non-diversifiable risk. $E(r_i) = r_f + \beta_i (E(r_m) - r_f)$ where $E(r_i)$ is the expected return of the investment, $r_f$ is the risk-free rate, $\beta_i$ is the beta of the investment, and $E(r_m)$ is the expected return of the market.

Derivative

A derivative is a financial security with a value that is reliant upon or derived from, an underlying asset or group of assets—a benchmark. The derivative itself is a contract between two or more parties, and the derivative derives its price from fluctuations in the underlying asset.

Efficient Market Hypothesis (EMH)

The EMH is an investment theory that states it is impossible to "beat the market" because stock market efficiency causes existing share prices to always incorporate and reflect all relevant information. According to the EMH, stocks always trade at their fair value, making it impossible for investors to either purchase undervalued stocks or sell stocks for inflated prices.

Financial Engineering

Financial engineering is the use of mathematical techniques to solve financial problems. It uses tools and knowledge from the fields of computer science, statistics, economics, and applied mathematics to address current financial issues as well as to devise new and innovative financial products.

Greeks

In options trading, the "Greeks" are the variables denoted by Greek letters that quantify the sensitivity of the option's price to changes in underlying parameters. The most common ones are Delta, Gamma, Theta, Vega, and Rho.

Hedge

A hedge is an investment to reduce the risk of adverse price movements in an asset. Normally, a hedge consists of taking an offsetting position in a related security, such as a futures contract.

Implied Volatility

Implied volatility is the market's forecast of a likely movement in a security's price. It is often used to price options contracts. High implied volatility results in higher option premiums.

Jensen's Alpha

Jensen's Alpha is a risk-adjusted performance measure that represents the average return on a portfolio or investment above or below that predicted by the CAPM, given the portfolio's or investment's beta and the average market return. This is the portfolio's excess return. $\alpha = r_i - (r_f + \beta_i (r_m - r_f))$ where $\alpha$ is Jensen's Alpha, $r_i$ is the actual return, $r_f$ is the risk-free rate, $\beta_i$ is the beta of the investment, and $r_m$ is the expected market return.

Kurtosis

Kurtosis is a statistical measure that defines how heavily the tails of a distribution differ from the tails of a normal distribution. In finance, kurtosis is used as a measure of financial risk.

Leverage

Leverage is the use of various financial instruments or borrowed capital—such as margin—to increase the potential return of an investment. It can also refer to the amount of debt used to finance assets.

Monte Carlo Simulation

Monte Carlo simulations are used to model the probability of different outcomes in a process that cannot easily be predicted due to the intervention of random variables. It is a technique used to understand the impact of risk and uncertainty in prediction and forecasting models.

Net Present Value (NPV)

NPV is the difference between the present value of cash inflows and the present value of cash outflows over a period of time. In finance, NPV is used to determine the value of an investment. $NPV = \sum_{t=1}^{T} \frac{C_t}{(1+r)^t} - C_0$ where $C_t$ is the cash flow at time $t$ , $r$ is the discount rate, and $C_0$ is the initial investment.

Option

An option is a contract that gives the buyer the right, but not the obligation, to buy or sell an underlying asset at a specified price on or before a certain date. Options are a form of derivative.

Portfolio Optimization

Portfolio optimization is the process of selecting the best portfolio (asset distribution), out of the set of all portfolios being considered, according to some objective. The objective typically maximizes factors such as expected return, and minimizes costs like financial risk.

Quantitative Analysis

Quantitative analysis is a technique that seeks to understand behavior by using mathematical and statistical modeling, measurement, and research. In finance, it aims to represent a given reality in terms of a numerical value.

Risk-Adjusted Return

Risk-adjusted return refines an investment's return by measuring how much risk is involved in producing that return. It is calculated by taking the return of the investment, subtracting the risk-free rate, and dividing this result by the investment's standard deviation.

Sharpe Ratio

The Sharpe ratio is used to help investors understand the return of an investment compared to its risk. The ratio is the average return earned in excess of the risk-free rate per unit of volatility or total risk. $Sharpe\ Ratio = \frac{R_p - R_f}{\sigma_p}$ where $R_p$ is the return of the portfolio, $R_f$ is the risk-free rate, and $\sigma_p$ is the standard deviation of the portfolio's excess return.

Time Value of Money (TVM)

The time value of money is the concept that money available at the present time is worth more than the same amount in the future due to its potential earning capacity. This core principle of finance holds that, provided money can earn interest, any amount of money is worth more the sooner it is received.

Utility Function

A utility function is an economic term that describes whether or not a consumer prefers one good or service over another. In finance, it can also refer to the total satisfaction received from consuming a good or service.

Value at Risk (VaR)

Value at Risk is a statistical technique used to measure and quantify the level of financial risk within a firm, portfolio, or position over a specific time frame. This metric is most commonly used by investment and commercial banks to determine the extent and occurrence ratio of potential losses in their institutional portfolios.

Warrant

A warrant is a derivative that confers the right, but not the obligation, to buy or sell a security – typically an equity – at a certain price before expiration. The price at which the underlying security can be bought or sold is referred to as the exercise price or strike price.

Exotic Option

An exotic option is an option that differs from common American or European options in terms of the underlying asset, the calculation of how or when the investor receives a certain payoff, or the structure of the option. These options are usually traded in the over-the-counter (OTC) market.

Yield Curve

The yield curve is a line that plots the interest rates, at a set point in time, of bonds having equal credit quality but differing maturity dates. The most frequently reported yield curve compares the three-month, two-year, five-year, and thirty-year U.S. Treasury debt.

Zero-Coupon Bond

A zero-coupon bond is a bond that does not pay interest during its life and is instead sold at a deep discount from its face value. The buyer of the bond receives the rate of return by the gradual appreciation of the security, which is redeemed at face value on a specified maturity date.

This glossary provides a foundational understanding of quantitative finance terms, which is essential for anyone looking to delve into the field or understand the complex models and strategies used by financial professionals.

Last updated 10 months ago