Credit riskCredit risk is the possibility of losing a lender holds due to a risk of default on a debt that may arise from a borrower failing to make required payments. In the first resort, the risk is that of the lender and includes lost principal and interest, disruption to cash flows, and increased collection costs. The loss may be complete or partial. In an efficient market, higher levels of credit risk will be associated with higher borrowing costs.
Pareto distributionThe Pareto distribution, named after the Italian civil engineer, economist, and sociologist Vilfredo Pareto, is a power-law probability distribution that is used in description of social, quality control, scientific, geophysical, actuarial, and many other types of observable phenomena; the principle originally applied to describing the distribution of wealth in a society, fitting the trend that a large portion of wealth is held by a small fraction of the population.
Estimation theoryEstimation theory is a branch of statistics that deals with estimating the values of parameters based on measured empirical data that has a random component. The parameters describe an underlying physical setting in such a way that their value affects the distribution of the measured data. An estimator attempts to approximate the unknown parameters using the measurements.
Credit derivativeIn finance, a credit derivative refers to any one of "various instruments and techniques designed to separate and then transfer the credit risk" or the risk of an event of default of a corporate or sovereign borrower, transferring it to an entity other than the lender or debtholder. An unfunded credit derivative is one where credit protection is bought and sold between bilateral counterparties without the protection seller having to put up money upfront or at any given time during the life of the deal unless an event of default occurs.
Beta prime distributionIn probability theory and statistics, the beta prime distribution (also known as inverted beta distribution or beta distribution of the second kind) is an absolutely continuous probability distribution. If has a beta distribution, then the odds has a beta prime distribution. Beta prime distribution is defined for with two parameters α and β, having the probability density function: where B is the Beta function. The cumulative distribution function is where I is the regularized incomplete beta function.
Heavy-tailed distributionIn probability theory, heavy-tailed distributions are probability distributions whose tails are not exponentially bounded: that is, they have heavier tails than the exponential distribution. In many applications it is the right tail of the distribution that is of interest, but a distribution may have a heavy left tail, or both tails may be heavy. There are three important subclasses of heavy-tailed distributions: the fat-tailed distributions, the long-tailed distributions, and the subexponential distributions.
Bond credit ratingIn investment, the bond credit rating represents the credit worthiness of corporate or government bonds. It is not the same as an individual's credit score. The ratings are published by credit rating agencies and used by investment professionals to assess the likelihood the debt will be repaid. Credit rating is a highly concentrated industry with the "Big Three" credit rating agencies – Fitch Ratings, Moody's and Standard & Poor's (S&P) – controlling approximately 95% of the ratings business.
ParameterA parameter (), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when identifying the system, or when evaluating its performance, status, condition, etc. Parameter has more specific meanings within various disciplines, including mathematics, computer programming, engineering, statistics, logic, linguistics, and electronic musical composition.
Statistical parameterIn statistics, as opposed to its general use in mathematics, a parameter is any measured quantity of a statistical population that summarises or describes an aspect of the population, such as a mean or a standard deviation. If a population exactly follows a known and defined distribution, for example the normal distribution, then a small set of parameters can be measured which completely describes the population, and can be considered to define a probability distribution for the purposes of extracting samples from this population.
Log-logistic distributionIn probability and statistics, the log-logistic distribution (known as the Fisk distribution in economics) is a continuous probability distribution for a non-negative random variable. It is used in survival analysis as a parametric model for events whose rate increases initially and decreases later, as, for example, mortality rate from cancer following diagnosis or treatment. It has also been used in hydrology to model stream flow and precipitation, in economics as a simple model of the distribution of wealth or income, and in networking to model the transmission times of data considering both the network and the software.
Merton modelThe Merton model, developed by Robert C. Merton in 1974, is a widely used "structural" credit risk model. Analysts and investors utilize the Merton model to understand how capable a company is at meeting financial obligations, servicing its debt, and weighing the general possibility that it will go into credit default. Under this model, the value of stock equity is modeled as a call option on the value of the whole company – i.e.
Probability of defaultProbability of default (PD) is a financial term describing the likelihood of a default over a particular time horizon. It provides an estimate of the likelihood that a borrower will be unable to meet its debt obligations. PD is used in a variety of credit analyses and risk management frameworks. Under Basel II, it is a key parameter used in the calculation of economic capital or regulatory capital for a banking institution. PD is closely linked to the expected loss, which is defined as the product of the PD, the loss given default (LGD) and the exposure at default (EAD).
Credit bureauA credit bureau is a data collection agency that gathers account information from various creditors and provides that information to a consumer reporting agency in the United States, a credit reference agency in the United Kingdom, a credit reporting body in Australia, a credit information company (CIC) in India, Special Accessing Entity in the Philippines, and also to private lenders. It is not the same as a credit rating agency. A consumer reporting agency is an organization providing information on individuals' borrowing and bill-paying habits.
Municipal bondA municipal bond, commonly known as a muni, is a bond issued by state or local governments, or entities they create such as authorities and special districts. In the United States, interest income received by holders of municipal bonds is often, but not always, exempt from federal and state income taxation. Typically, only investors in the highest tax brackets benefit from buying tax-exempt municipal bonds instead of taxable bonds. Taxable equivalent yield calculations are required to make fair comparisons between the two categories.
Poisson point processIn probability, statistics and related fields, a Poisson point process is a type of random mathematical object that consists of points randomly located on a mathematical space with the essential feature that the points occur independently of one another. The Poisson point process is often called simply the Poisson process, but it is also called a Poisson random measure, Poisson random point field or Poisson point field.
Bayesian probabilityBayesian probability (ˈbeɪziən or ˈbeɪʒən ) is an interpretation of the concept of probability, in which, instead of frequency or propensity of some phenomenon, probability is interpreted as reasonable expectation representing a state of knowledge or as quantification of a personal belief. The Bayesian interpretation of probability can be seen as an extension of propositional logic that enables reasoning with hypotheses; that is, with propositions whose truth or falsity is unknown.
Credit default swapA credit default swap (CDS) is a financial swap agreement that the seller of the CDS will compensate the buyer in the event of a debt default (by the debtor) or other credit event. That is, the seller of the CDS insures the buyer against some reference asset defaulting. The buyer of the CDS makes a series of payments (the CDS "fee" or "spread") to the seller and, in exchange, may expect to receive a payoff if the asset defaults.
Bond marketThe bond market (also debt market or credit market) is a financial market where participants can issue new debt, known as the primary market, or buy and sell debt securities, known as the secondary market. This is usually in the form of bonds, but it may include notes, bills, and so on for public and private expenditures. The bond market has largely been dominated by the United States, which accounts for about 39% of the market.
Compound Poisson processA compound Poisson process is a continuous-time stochastic process with jumps. The jumps arrive randomly according to a Poisson process and the size of the jumps is also random, with a specified probability distribution. To be precise, a compound Poisson process, parameterised by a rate and jump size distribution G, is a process given by where, is the counting variable of a Poisson process with rate , and are independent and identically distributed random variables, with distribution function G, which are also independent of When are non-negative integer-valued random variables, then this compound Poisson process is known as a stuttering Poisson process.
High-yield debtIn finance, a high-yield bond (non-investment-grade bond, speculative-grade bond, or junk bond) is a bond that is rated below investment grade by credit rating agencies. These bonds have a higher risk of default or other adverse credit events, but offer higher yields than investment-grade bonds in order to compensate for the increased risk. As indicated by their lower credit ratings, high-yield debt entails more risk to the investor compared to investment grade bonds.
