Financial risk modeling is the use of formal
mathematical
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
and
econometric
Econometrics is the application of statistical methods to economic data in order to give empirical content to economic relationships. M. Hashem Pesaran (1987). "Econometrics," '' The New Palgrave: A Dictionary of Economics'', v. 2, p. 8 p. 8 ...
techniques to measure, monitor and control the
market risk
Market risk is the risk of losses in positions arising from movements in market variables like prices and volatility.
There is no unique classification as each classification may refer to different aspects of market risk. Nevertheless, the most ...
,
credit risk
A credit risk is 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 ...
, and
operational risk on a firm's
balance sheet
In financial accounting, a balance sheet (also known as statement of financial position or statement of financial condition) is a summary of the financial balances of an individual or organization, whether it be a sole proprietorship, a business ...
, on a bank's
trading book
The Fundamental Review of the Trading Book (FRTB), is a set of proposals by the Basel Committee on Banking Supervision for a new market risk-related capital requirement for banks.
Background
The reform, which is part of Basel III, is one of th ...
, or re a
fund manager Fund may refer to:
* Funding is the act of providing resources, usually in form of money, or other values such as effort or time, for a project, a person, a business, or any other private or public institution
** The process of soliciting and gathe ...
's portfolio value; see
Financial risk management
Financial risk management is the practice of protecting economic value in a firm by using financial instruments to manage exposure to financial risk - principally operational risk, credit risk and market risk, with more specific variants as liste ...
.
Risk modeling is one of many subtasks within the broader area of
financial modeling
Financial modeling is the task of building an abstract representation (a model) of a real world financial situation. This is a mathematical model designed to represent (a simplified version of) the performance of a financial asset or portfolio o ...
.
Application
Risk modeling uses a variety of techniques including
market risk
Market risk is the risk of losses in positions arising from movements in market variables like prices and volatility.
There is no unique classification as each classification may refer to different aspects of market risk. Nevertheless, the most ...
,
value at risk
Value at risk (VaR) is a measure of the risk of loss for investments. It estimates how much a set of investments might lose (with a given probability), given normal market conditions, in a set time period such as a day. VaR is typically used by ...
(VaR),
historical simulation (HS), or
extreme value theory
Extreme value theory or extreme value analysis (EVA) is a branch of statistics dealing with the extreme deviations from the median of probability distributions. It seeks to assess, from a given ordered sample of a given random variable, the pr ...
(EVT) in order to analyze a portfolio and make forecasts of the likely losses that would be incurred for a variety of risks. As above, such risks are typically grouped into
credit risk
A credit risk is 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 ...
,
market risk
Market risk is the risk of losses in positions arising from movements in market variables like prices and volatility.
There is no unique classification as each classification may refer to different aspects of market risk. Nevertheless, the most ...
,
model risk
In finance, model risk is the risk of loss resulting from using insufficiently accurate models to make decisions, originally and frequently in the context of valuing financial securities. However, model risk is more and more prevalent in activitie ...
,
liquidity risk
Liquidity risk is a financial risk that for a certain period of time a given financial asset, security or commodity cannot be traded quickly enough in the market without impacting the market price.
Types
Market liquidity – An asset cannot be so ...
, and
operational risk categories.
Many large financial intermediary firms use risk modeling to help portfolio managers assess the amount of
capital reserves to maintain, and to help guide their purchases and sales of various classes of
financial assets
A financial asset is a non-physical asset whose value is derived from a contractual claim, such as bank deposits, bonds, and participations in companies' share capital. Financial assets are usually more liquid than other tangible assets, such as ...
.
Formal risk modeling is required under the
Basel II
Basel II is the second of the Basel Accords, which are recommendations on banking laws and regulations issued by the Basel Committee on Banking Supervision. It is now extended and partially superseded by Basel III.
The Basel II Accord was publis ...
proposal for all the major international banking institutions by the various national depository institution regulators. In the past, risk analysis was done qualitatively but now with the advent of powerful computing software, quantitative risk analysis can be done quickly and effortlessly.
Criticism
Modeling the changes by distributions with finite variance is now known to be inappropriate.
Benoît Mandelbrot
Benoit B. Mandelbrot (20 November 1924 – 14 October 2010) was a Polish-born French-American mathematician and polymath with broad interests in the practical sciences, especially regarding what he labeled as "the art of roughness" of phy ...
found in the 1960s that changes in prices in financial markets do not follow a
Gaussian distribution, but are rather modeled better by
Lévy stable distributions. The scale of change, or volatility, depends on the length of the time interval to a
power
Power most often refers to:
* Power (physics), meaning "rate of doing work"
** Engine power, the power put out by an engine
** Electric power
* Power (social and political), the ability to influence people or events
** Abusive power
Power may a ...
a bit more than 1/2. Large changes up or down, also called ''
fat tails
A fat-tailed distribution is a probability distribution that exhibits a large skewness or kurtosis, relative to that of either a normal distribution or an exponential distribution. In common usage, the terms fat-tailed and heavy-tailed are someti ...
'', are more likely than what one would calculate using a Gaussian distribution with an estimated
standard deviation
In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while ...
.
corporate scandals
A corporate collapse typically involves the insolvency or bankruptcy of a major business enterprise. A corporate scandal involves alleged or actual unethical behavior by people acting within or on behalf of a corporation. Many recent corporate col ...
in the past few years (most notably, Enron
Enron Corporation was an American energy, commodities, and services company based in Houston, Texas. It was founded by Kenneth Lay in 1985 as a merger between Lay's Houston Natural Gas and InterNorth, both relatively small regional companies. ...
), Basel II
Basel II is the second of the Basel Accords, which are recommendations on banking laws and regulations issued by the Basel Committee on Banking Supervision. It is now extended and partially superseded by Basel III.
The Basel II Accord was publis ...
, the revised FAS 123R and the Sarbanes–Oxley Act
The Sarbanes–Oxley Act of 2002 is a United States federal law that mandates certain practices in financial record keeping and reporting for corporations.
The act, (), also known as the "Public Company Accounting Reform and Investor Protecti ...
, and for their failure to predict the financial crash of 2008.[ From The Economist print edition.]
Rapid development of financial innovations lead to sophisticated models that are based on a set of assumptions. These models are usually prone to model risk
In finance, model risk is the risk of loss resulting from using insufficiently accurate models to make decisions, originally and frequently in the context of valuing financial securities. However, model risk is more and more prevalent in activitie ...
. There are several approaches to deal with model uncertainty. Jokhadze and Schmidt (2018) propose practical model risk measurement framework based on Bayesian calculation.
See also
* Black–Scholes model
The Black–Scholes or Black–Scholes–Merton model is a mathematical model for the dynamics of a financial market containing derivative investment instruments. From the parabolic partial differential equation in the model, known as the Blac ...
* Financial risk management
Financial risk management is the practice of protecting economic value in a firm by using financial instruments to manage exposure to financial risk - principally operational risk, credit risk and market risk, with more specific variants as liste ...
* Knightian uncertainty
In economics, Knightian uncertainty is a lack of any quantifiable knowledge about some possible occurrence, as opposed to the presence of quantifiable risk (e.g., that in statistical noise or a parameter's confidence interval). The concept acknow ...
* Financial modeling
Financial modeling is the task of building an abstract representation (a model) of a real world financial situation. This is a mathematical model designed to represent (a simplified version of) the performance of a financial asset or portfolio o ...
* Value-at-Risk
Value at risk (VaR) is a measure of the risk of loss for investments. It estimates how much a set of investments might lose (with a given probability), given normal market conditions, in a set time period such as a day. VaR is typically used by ...
Bibliography
*
* Machina, Mark J., and Michael Rothschild (1987). "Risk," '' The New Palgrave: A Dictionary of Economics'', v. 4, pp. 201–206.
*
References
External links
Risk World
is a web site devoted to risk, with a collection of books.
A Stochastic Processes toolkit for Risk Management
at SSNR.com is a tutorial paper by Damiano Brigo Damiano Brigo (born Venice, Italy 1966) is an applied mathematician and Chair in Mathematical Finance at Imperial College London. He is known for research in filtering theory and mathematical finance.
Main results
Brigo started his work with the ...
, Antonio Dalessandro, Matthias Neugebauer and Fares Triki, explaining how to use different stochastic processes for risk measurement.
{{Financial risk
Actuarial science