Given the price of a call or put option, the Black-Scholes implied volatility is the unique
volatility parameter for which the Black-Scholes formula recovers the option price. This …

Building upon the ideas introduced in their previous book, Derivatives in Financial Markets
with Stochastic Volatility, the authors study the pricing and hedging of financial derivatives …

In this paper, we present a comprehensive survey of continuous stochastic volatility models,
discussing their historical development and the key stylized facts that have driven the field …

In this paper we use Malliavin calculus techniques to obtain an expression for the short-time
behavior of the at-the-money implied volatility skew for a generalization of the Bates model …

In this paper we propose to use a combination of regular and singular perturbations to
analyze parabolic PDEs that arise in the context of pricing options when the volatility is a …

A general class of stochastic volatility models with jumps is considered and an asymptotic
expansion for European option prices around the Black–Scholes prices is validated in the …

The use of the Heston model is still challenging because it has a closed formula only when
the parameters are constant [S. Heston, Rev. Financ. Stud., 6 (1993), pp. 327–343] or …

The Black–Scholes implied volatility skew at the money of SPX options is known to obey a
power law with respect to the time to maturity. We construct a model of the underlying asset …

In a continuous-time economy, we investigate the asset allocation problem among a risk-
free asset and two risky assets with an ambiguous correlation between the two risky assets …

We develop a closed-form bivariate expansion of the shape characteristics of the implied
volatility surface generated by a stochastic volatility model with jumps in returns. We use the …