We propose a hybrid CEV Exponential L\'evy model whose volatility, L\'evy measure, and killing rate are all state-dependence. In this setting we find a closed form solution for the price of any European-style option. Additionally, for a certain sub-class of models, we find a closed-form expression for the  implied volatility smile  .
We propose a class of equity models whose volatility, L\'evy measure, and killing rate all have local stochastic state-dependence. In this framework we find a closed form solution for the price of any European-style option. Additionally, for a certain sub-class of models, we find an exact expression for the induced implied volatility smile . To illustrate our framework, we perform specific computations for hybrid CEV/L\'evy model (which we christen as the "C\'EV" model) .
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hybrid CEV Exponential L\'evy model
class of equity models
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are all
all have local stochastic
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setting
framework
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a closed-form
an exact
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induced
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. To illustrate our framework, we perform specific computations for hybrid CEV/L\'evy model (which we christen as the "C\'EV" model)