This paper demonstrates the simple incorporation of any shape of risk aversion into an asset allocation framework. Indeed, the relevant literature about risk aversion shows mixed evidence regarding the shape of this important but subjective variable. Our setting builds on, and can be compared...

The paper considers the asymptotic behavior of the implied volatility in stochastic asset price models with atoms. In such models, the asset price distribution has a singular component at zero. Examples of models with atoms include the constant elasticity of variance (CEV) model, jump-to-default...

In this article, we derive a new most-likely-path (MLP) approximation for implied volatility in terms of local volatility, based on time-integration of the lowest order term in the heat-kernel expansion. This new approximation formula turns out to be a natural extension of the well-known formula...

We introduce a class of randomly time-changed fast mean-reverting stochastic volatility (TC-FMR-SV) models. Using spectral theory and singular perturbation techniques, we derive an approximation for the price of any European option in the TC-FMR-SV setting. Three examples of random time-changes...

In this paper, we study the asymptotic behavior of the implied volatility in stochastic asset price models. We provide necessary and sufficient conditions for the validity of asymptotic equivalence in Lee's moment formulas, and obtain new asymptotic formulas for the implied volatility in asset...

We study the term structure of the implied volatility in the presence of a symmetric smile. Exploiting the result by Tehranchi (2009) that a symmetric smile generated by a continuous martingale necessarily comes from a mixture of normal distributions, we derive representation formulae for the...