Constant Elasticity of Variance Model
In mathematical finance, the CEV or Constant Elasticity of Variance model is a stochastic volatility model, which attempts to capture stochastic volatility and the leverage effect. The model is widely used by practitioners in the financial industry, especially for modelling equities and commodities. It was developed by John Cox in 1975
The CEV model describes a process which evolves according to the following stochastic differential equation:
The constant parameters satisfy the conditions .
The parameter γ controls the relationship between volatility and price, and is the central feature of the model. When γ < 1 we see the so-called leverage effect, commonly observed in equity markets, where the volatilty of a stock increases as its price falls. Conversely, in commodity markets, we often observe γ > 1, the so-called inverse leverage effect, whereby the volatilty of the price of a commodity tends to increase as its price increases.
- ^ Cox, J. “Notes on Option Pricing I: Constant Elasticity of Diffusions.” Unpublished draft, Stanford University, 1975.
- ^ Emanuel, D.C., and J.D. MacBeth, 1982. “Further Results of the Constant Elasticity of Variance Call Option Pricing Model.” Journal of Financial and Quantitative Analysis, 4 : 533–553
- ^ Geman, H, and Shih, YF. 2009. “Modeling Commodity Prices under the CEV Model.” The Journal of Alternative Investments 11 (3): 65-84. doi:10.3905/JAI.2009.11.3.065
- Asymptotic Approximations to CEV and SABR Models
- Price and implied volatility of European options in CEV Model delamotte-b.fr
Derivatives market OptionsTermsVanilla options Swaps Forwards and Futures Other derivatives Market issues Volatility Modelling volatility Trading volatility
Wikimedia Foundation. 2010.
Look at other dictionaries:
Productivity model — Productivity in economics is the ratio of what is produced to what is required to produce. Productivity is the measure on production efficiency. Productivity model is a measurement method which is used in practice for measuring productivity.… … Wikipedia
Cobweb model — The cobweb model or cobweb theory is an economic model that explains why prices might be subject to periodic fluctuations in certain types of markets. It describes cyclical supply and demand in a market where the amount produced must be chosen… … Wikipedia
CEV — may stand for: Certified Video Engineer, a professional title regulated by the Society of Broadcast Engineers Chemins de fer électriques Veveysans, a Swiss railway company Contemporary English Version, a translation of the Bible into English Crew … Wikipedia
Power transform — In statistics, the power transform is a family of transformations that map data from one space to another using power functions. This is a useful data (pre)processing technique used to reduce data variation, make the data more normal distribution … Wikipedia
Modern portfolio theory — Portfolio analysis redirects here. For theorems about the mean variance efficient frontier, see Mutual fund separation theorem. For non mean variance portfolio analysis, see Marginal conditional stochastic dominance. Modern portfolio theory (MPT) … Wikipedia
Ideal chain — An ideal chain (or freely jointed chain) is the simplest model to describe a polymer. It only assumes a polymer as a random walk and neglects any kind of interactions among monomers. Although it is simple, its generality gives us some insights… … Wikipedia
Greeks (finance) — The Greeks redirects here. For the ethnic group, see Greeks. In mathematical finance, the Greeks are the quantities representing the sensitivities of the price of derivatives such as options to a change in underlying parameters on which the value … Wikipedia
List of mathematics articles (A) — NOTOC A A Beautiful Mind A Beautiful Mind (book) A Beautiful Mind (film) A Brief History of Time (film) A Course of Pure Mathematics A curious identity involving binomial coefficients A derivation of the discrete Fourier transform A equivalence A … Wikipedia
analysis — /euh nal euh sis/, n., pl. analyses / seez /. 1. the separating of any material or abstract entity into its constituent elements (opposed to synthesis). 2. this process as a method of studying the nature of something or of determining its… … Universalium
atom — /at euhm/, n. 1. Physics. a. the smallest component of an element having the chemical properties of the element, consisting of a nucleus containing combinations of neutrons and protons and one or more electrons bound to the nucleus by electrical… … Universalium