Volatility Models: Constant elasticity of variance model
As we see above price volatility is non-constant. The second observed feature of stock volatility is cor-relation between volatility and
price levels. Loosely speaking market expects the volatility to rise as the price falls. This is so called leverage effect. In this way
leverage introduce negative correlation be-tween price and volatility. This argument provides introduction of constant elasticity of
variance (CEV) model.
(3.7)
which is a particular case of local volatility model (3.1), CEV model has a several desirable feature. Firstly it catches leverage effect,
secondly as in the all local volatility models the market is complete this means that non-arbitrage argument alone enough to define
unique option price, thirdly equation (3.7) analytically tractable.
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