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| | 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<ref>Cox, J. "Notes on Option Pricing I: Constant Elasticity of Diffusions." Unpublished draft, Stanford University, 1975.</ref> |
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| | The '''CEV''' model describes a process which evolves according to the following [[stochastic differential equation]]: |
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| | :<math>dS_t=\mu S_t dt + \sigma S_t ^ \gamma dW_t</math> |
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| | The constant parameters <math>\sigma,\;\gamma</math> satisfy the conditions <math>\sigma\geq 0,\;\gamma\geq 0</math>. |
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| | The parameter <math>\gamma</math> controls the relationship between volatility and price, and is the central feature of the model. When <math>\gamma < 1</math> we see the so-called leverage effect, commonly observed in equity markets, where the volatility of a stock increases as its price falls. Conversely, in commodity markets, we often observe <math>\gamma > 1</math>, the so-called inverse leverage effect,<ref>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</ref><ref>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}}</ref> whereby the volatility of the price of a commodity tends to increase as its price increases. |
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| | ==See also== |
| | *[[Volatility (finance)]] |
| | *[[Stochastic volatility]] |
| | *[[SABR volatility model]] |
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| | ==References== |
| | {{Reflist}} |
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| | ==External links== |
| | *[http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1850709 Asymptotic Approximations to CEV and SABR Models] |
| | *[http://www.serdarsen.somee.com/CEV.aspx Price and implied volatility under CEV model with closed formulas, Monte-Carlo and Finite Difference Method] |
| | *[http://www.delamotte-b.fr/CEV.aspx Price and implied volatility of European options in CEV Model] delamotte-b.fr |
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| | {{Derivatives market}} |
| | {{Volatility}} |
| | {{Stochastic processes}} |
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| | [[Category:Mathematical finance]] |
| | [[Category:Options (finance)]] |
| | [[Category:Derivatives (finance)]] |
| | [[Category:Finance theories]] |
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]
Dynamics
The CEV model describes a process which evolves according to the following stochastic differential equation:
The constant parameters satisfy the conditions .
The parameter controls the relationship between volatility and price, and is the central feature of the model. When we see the so-called leverage effect, commonly observed in equity markets, where the volatility of a stock increases as its price falls. Conversely, in commodity markets, we often observe , the so-called inverse leverage effect,[2][3] whereby the volatility of the price of a commodity tends to increase as its price increases.
See also
References
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External links
Template:Derivatives market
Template:Volatility
Template:Stochastic processes
- ↑ 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. 21 year-old Glazier James Grippo from Edam, enjoys hang gliding, industrial property developers in singapore developers in singapore and camping. Finds the entire world an motivating place we have spent 4 months at Alejandro de Humboldt National Park.