Quant Common Probability Distributions

Question 1

Asian call option

Answer 1

A European style option with a value at maturity equal to the difference between the stock price at maturity and the average stock price during the life of the option, or $0, whichever is greater

Question 2

Back simulation

Answer 2

Another term for the historical method of estimating VaR. This term is somewhat misleading in that the method involved not a simulation of the past but rather what actually happened in the past, sometimes adjusted to reflect your fact that a different portfolio may have existed in the past than is planned for the future

Question 3

Bernoulli random variable

Answer 3

A random variable having outcomes 0 and 1

Question 4

Bernoulli Trial

Answer 4

An experiment that can produce one of two outcomes

Question 5

Binomial model

Answer 5

A model for pricing options which the underlying price can move to only one of two possible new prices

Question 6

Binomial random variable

Answer 6

The number of successes in n Bernoulli trials for which the probability of success is constant for all trials and trials are independent

Question 7

Binomial tree

Answer 7

The graphical representation of a model of asset price dynamics in which at each period, the asset moves up with probability p or down with probability (1-p)

Question 8

Continuous random variable

Answer 8

A random variable for which the range of possible outcomes is the real line (all real numbers between -infinite and infinite or some subset of the real line)

Question 9

Continuous time

Answer 9

Time thought of as advancing in extremely small increments

Question 10

Continuously compounded return

Answer 10

The natural logarithm of 1 plus the holding period return, or equivalently, the natural logarithm of the ending price over the beginning price

Question 11

Cumulative distribution function

Answer 11

A function giving the probability that a random variable is less than or equal to a specified value

Question 12

Discrete random variable

Answer 12

A random variable that can take on at most a countable number of possible values

Question 13

Down transition probability

Answer 13

The probability that an asset’s value moves down in a model of asset price dynamics

Question 14

European option

Answer 14

An option that can only be exercised on its expiration date

Question 15

European style

Answer 15

Said of an option contract that can only be exercised on the options expiration date

Question 16

Financial risk

Answer 16

The risk that environmental social or governance risk factors will result in significant costs or other losses to a company and its shareholders; the risk arising from a companies obligation to meet required payments under its financing agreements

Question 17

Historical simulation

Answer 17

Another term for the historical method of estimating VaR. This term is somewhat misleading in that the method involves not a simulation of the past but rather what actually happened in the past, sometimes adjusted to reflect the fact that a different portfolio may have existed in the past than is planned for the future

Question 18

Independently and identically distributed (IID)

Answer 18

With respect to random variables, the property of random variables that are independent of each other but follow the identical probability distribution

Question 19

Mean-variance analysis

Answer 19

An approach to portfolio analysis using expected means, variances and covariances of asset returns

Question 20

Monte Carlo simulations

Answer 20

An approach to estimating a probability distribution of outcomes to examine what might happen if particular risks are faced. This method is widely used in the sciences as well as in business to study a variety of problems

Question 21

Multivariate distribution

Answer 21

A probability distribution that specifies the probabilities for a group of related random variables

Question 22

Multivariate normal distribution

Answer 22

A probability distribution for a group of random variables that is completely defined by the means and variances of the variables plus all the correlations between pairs of variables

Question 23

Node

Answer 23

Each value on a binomial tree from which successive moves or outcomes branch

Question 24

Price relative

Answer 24

A ratio of ending price over a beginning price; it is equal to 1 plus the holding period return on the asset

Question 25

Probability density function

Answer 25

A function with non-negative values such that probability can be described by areas under the curve graphing function

Question 26

Probability distribution

Answer 26

A distribution that specifies the probability of a random variables possible outcomes

Question 27

Probability function

Answer 27

A function that specifies the probability that the random variable takes on a specific value

Question 28

Pseudo-random numbers

Answer 28

Numbers produced by random number generators

Question 29

Random number

Answer 29

An observation drawn from a uniform distribution

Question 30

Random number generator

Answer 30

An algorithm that produces uniformly distributed random numbers between 0 and 1

Question 31

Random Variable

Answer 31

A quantity whose future outcomes are uncertain

Question 32

Safety-First Rules

Answer 32

Rules for portfolio selection that focus on the risk that portfolio value will fall below some minimum acceptable level over some time horizon

Question 33

Scenario Anlysis

Answer 33

Analysis that shows the changes in key financial quantities that result from given (economic) events, such as the loss of customers, the loss of a supply source, or a catastrophic event; a risk management technique involving examination of the performance of a portfolio under the specified situations. Closely related to stress testing

Question 34

Shortfall risk

Answer 34

The risk that portfolio value will fall below some minimum acceptable level over some time horizon

Question 35

Simulation trial

Answer 35

A complete pass through the steps of a simulation

Question 36

Standard normal distribution

Answer 36

The normal density with mean(u) equal to 0 and standard deviation (o) equal to 1’

Question 37

Standardizing

Answer 37

A transformation that involves subtracting the mean and dividing the result by the standard deviation

Question 38

Stress testing

Answer 38

A specific type of scenario analysis that estimates losses in rare and extremely unfavorable combinations of events or scenarios

Question 39

Unit normal distribution

Answer 39

The normal density with mean (u) equal to 0 and standard deviation (o) equal to 1

Question 40

Univariate distribution

Answer 40

A distribution that specifies the probabilities for a single random variable

Question 41

Up transition probability

Answer 41

The probability that an assets value moves up

Question 42

Value at risk

Answer 42

A money measure of the minimum value of losses expected during a specified time period at a given level of probability

Question 43

Volatility

Answer 43

As used In option pricing, the standard deviation of the continuously compounded returns on the underlying asset