Quant Common Probability Distributions Flashcards
Asian call option
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
Back simulation
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
Bernoulli random variable
A random variable having outcomes 0 and 1
Bernoulli Trial
An experiment that can produce one of two outcomes
Binomial model
A model for pricing options which the underlying price can move to only one of two possible new prices
Binomial random variable
The number of successes in n Bernoulli trials for which the probability of success is constant for all trials and trials are independent
Binomial tree
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)
Continuous random variable
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)
Continuous time
Time thought of as advancing in extremely small increments
Continuously compounded return
The natural logarithm of 1 plus the holding period return, or equivalently, the natural logarithm of the ending price over the beginning price
Cumulative distribution function
A function giving the probability that a random variable is less than or equal to a specified value
Discrete random variable
A random variable that can take on at most a countable number of possible values
Down transition probability
The probability that an asset’s value moves down in a model of asset price dynamics
European option
An option that can only be exercised on its expiration date
European style
Said of an option contract that can only be exercised on the options expiration date
Financial risk
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
Historical simulation
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
Independently and identically distributed (IID)
With respect to random variables, the property of random variables that are independent of each other but follow the identical probability distribution
Mean-variance analysis
An approach to portfolio analysis using expected means, variances and covariances of asset returns
Monte Carlo simulations
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
Multivariate distribution
A probability distribution that specifies the probabilities for a group of related random variables
Multivariate normal distribution
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
Node
Each value on a binomial tree from which successive moves or outcomes branch
Price relative
A ratio of ending price over a beginning price; it is equal to 1 plus the holding period return on the asset
Probability density function
A function with non-negative values such that probability can be described by areas under the curve graphing function
Probability distribution
A distribution that specifies the probability of a random variables possible outcomes
Probability function
A function that specifies the probability that the random variable takes on a specific value
Pseudo-random numbers
Numbers produced by random number generators
Random number
An observation drawn from a uniform distribution
Random number generator
An algorithm that produces uniformly distributed random numbers between 0 and 1
Random Variable
A quantity whose future outcomes are uncertain
Safety-First Rules
Rules for portfolio selection that focus on the risk that portfolio value will fall below some minimum acceptable level over some time horizon
Scenario Anlysis
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
Shortfall risk
The risk that portfolio value will fall below some minimum acceptable level over some time horizon
Simulation trial
A complete pass through the steps of a simulation
Standard normal distribution
The normal density with mean(u) equal to 0 and standard deviation (o) equal to 1’
Standardizing
A transformation that involves subtracting the mean and dividing the result by the standard deviation
Stress testing
A specific type of scenario analysis that estimates losses in rare and extremely unfavorable combinations of events or scenarios
Unit normal distribution
The normal density with mean (u) equal to 0 and standard deviation (o) equal to 1
Univariate distribution
A distribution that specifies the probabilities for a single random variable
Up transition probability
The probability that an assets value moves up
Value at risk
A money measure of the minimum value of losses expected during a specified time period at a given level of probability
Volatility
As used In option pricing, the standard deviation of the continuously compounded returns on the underlying asset
