# Copula

A function used to combine many univariate distributions to make a single multivariate distribution. Often used to model relationships between many underlying in credit derivatives. See page 229.

# Correlation

Covariance between two random variables divided by both of their standard deviations. It is a number between (and including) minus one and plus one that measures the amount of linear relationship between the two variables. Correlation is a parameter in most option-pricing models in which there are two or more random factors. However, the parameter is often highly unstable.

# CQF

Certificate in Quantitative Finance, a part-time qualification offered by Wilmott and 7city Learning which teaches the more practical aspects of quantitative finance, including modelling, data analysis, implementation of the models and, crucially, focuses on which models are good and which aren't.

# Default probability

The probability of an entity defaulting or going bankrupt. A concept commonly used in credit risk modelling where it is assumed that default is a probabilistic concept, rather than a business decision. Pricing credit instruments then becomes an exercise in modelling probability of default, and recovery rates. See page 448.

# Delta

The sensitivity of an option to the underlying asset. See page 78.

# Digital

An option with a discontinuous payoff. See page 472.

# Dispersion

The amount by which asset, typically equity, returns are independent. A dispersion trade involves a basket of options on single stocks versus the opposite position in an option on a basket of stocks (an index).

# Duration

The sensitivity of a bond to an interest rate or yield. It can be related to the average life of the bond.

# Exotic

A contract that is made to measure, or bespoke, for a client and which does not exist as an exchange-traded instrument. Since it is not traded on an exchange it must be priced using some mathematical model. See pages 459-482.

# Expected loss

The average loss once a specified threshold has been breached. Used as a measure of Value at Risk. See page 52.

# Finite difference

A numerical method for solving differential equations wherein derivatives are approximated by differences. The differential equation thus becomes a difference equation which can be solved numerically, usually by an iterative process.

# Gamma

The sensitivity of an option s delta to the underlying. Therefore it is the second derivative of an option price with respect to the underlying. See page 79.

# GARCH

Generalized Auto Regressive Conditional Het-eroskedasticity, an econometric model for volatility in which the current variance depends on the previous random increments.

# Hedge

To reduce risk by exploiting correlations between financial instruments. See page 77.

# Hybrid

An instrument that exhibits both equity and fixed-income characteristics, and even credit risk. An example would be a convertible bond. Pricing such instruments requires knowledge of models from several different areas of quantitative finance.

# Implied

Used as an adjective about financial parameters meaning that they have been deduced from traded prices. For example, what volatility when put into the Black-Scholes formula gives a theoretical price that is the same as the market price? This is the implied volatility. Intimately related to calibration.

# Levy

A probability distribution, also known as a stable distribution. It has the property that sums of independent identically distributed random variables from this distribution have the same distribution. The normal distribution is a special case. The Levy distribution is of interest in finance because returns data matches this distribution quite well. See page 383.