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^{[1]}
Contents
Dynamics
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 socalled 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 socalled inverse leverage effect^{[2]}^{[3]}, whereby the volatilty of the price of a commodity tends to increase as its price increases.
See also
References
 ^ 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 Unpublished draft, Stanford University, 1975.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): 6584. doi:10.3905/JAI.2009.11.3.065
External links
 Asymptotic Approximations to CEV and SABR Models
 Price and implied volatility of European options in CEV Model delamotteb.fr
Volatility Modelling volatility Trading volatility Volatility arbitrage · Straddle · Volatility swap · IVX · VIX
Categories: Mathematical finance
 Options
 Derivatives (finance)
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