Constant elasticity of variance model
In mathematical finance, the constant elasticity of variance model (CEV) is a stochastic volatility model, although technically it would be classed more precisely as a local volatility model, that 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
Overview
In mathematical finance, the constant elasticity of variance model (CEV) is a stochastic volatility model, although technically it would be classed more precisely as a local volatility model, that 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 is a stochastic 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
{\displaystyle \mathrm {d} S_{t}=\mu S_{t}\mathrm {d} t+\sigma S_{t}^{\gamma }\mathrm {d} W_{t}}
in which S is the spot price, t is time, and μ is a parameter characterising the drift, σ and γ are volatility parameters, and W is a Brownian motion. It is a special case of a general local volatility model, written as
d
S
t
See also
Volatility (finance) Stochastic volatility Local volatility SABR volatility model CKLS process
External links
Asymptotic Approximations to CEV and SABR Models Price and implied volatility under CEV model with closed formulas, Monte-Carlo and Finite Difference Method Price and implied volatility of European options in CEV Model delamotte-b.fr
Wikipedia contributors · Constant elasticity of variance model · revision 1334911322 · CC BY-SA 4.0 · Plain text extracted and formatting adapted; tags derived from linked topics.