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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 Unpublished draft, Stanford University, 1975.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>
| | Частное предприятие «Илигран»<br>220073, г. [http://iligran.by/%d0%b0%d0%b2%d1%82%d0%be%d0%b2%d1%8b%d1%88%d0%ba%d0%b8/ аренда автовышки Минск], ул. Кальварийская, дом 25, офис 424<br>Телефоны:<br><br>+375 44 545-67-00<br><br>+375 29 379-91-88<br>+375 17 204 42 28 (факс)<br>+375 17 204 42 26 (факс)<br>+375 17 204 01 72<br>Email: 2044228@mail.ru<br><br>http://iligran.by |
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| == Dynamics ==
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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==
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| *[[Volatility (finance)]]
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| *[[Stochastic volatility]]
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| *[[SABR volatility model]]
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| ==References==
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| {{Reflist}}
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| ==External links==
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| *[http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1850709 Asymptotic Approximations to CEV and SABR Models]
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| *[http://www.serdarsen.somee.com/CEV.aspx Price and implied volatility under CEV model with closed formulas, Monte-Carlo and Finite Difference Method]
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| *[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}}
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| {{Volatility}}
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| {{Stochastic processes}}
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| [[Category:Mathematical finance]]
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| [[Category:Options (finance)]]
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| [[Category:Derivatives (finance)]]
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| [[Category:Finance theories]]
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Частное предприятие «Илигран»
220073, г. аренда автовышки Минск, ул. Кальварийская, дом 25, офис 424
Телефоны:
+375 44 545-67-00
+375 29 379-91-88
+375 17 204 42 28 (факс)
+375 17 204 42 26 (факс)
+375 17 204 01 72
Email: 2044228@mail.ru
http://iligran.by