Constant elasticity of variance model - Alchetron, the free social encyclopedia

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

Dynamic

The CEV model describes a process which evolves according to the following stochastic differential equation:

d S t = μ S t d t + σ S t γ d W t

The constant parameters σ , γ satisfy the conditions σ ≥ 0 , γ ≥ 0 .

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 volatility 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 volatility of the price of a commodity tends to increase as its price increases.

References

Constant elasticity of variance model Wikipedia

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