The uncertain volatility model has long ago attracted the attention of practitioners as it provides worst-case pricing scenario for the sell-side. The valuation of a financial derivative based on this model requires solving a fully non-linear PDE. One can rely on finite difference schemes only...

We revisit the so-called Bergomi-Guyon expansion (Bergomi and Guyon, Stochastic volatility's orderly smiles, Risk, May 2012). The expansion provides the smile of implied volatility at second order in the volatility of volatility for general stochastic volatility models, including variance curve...

In this paper, we introduce a new GARCH model with an infinitely divisible distributed innovation, referred to as the rapidly decreasing tempered stable (RDTS) GARCH model. This model allows the description of some stylized empirical facts observed for stock and index returns, such as volatility...

In this paper we will introduce a hybrid option pricing model that combines the classical tempered stable model and regime switching by a hidden Markov chain. This model allows the description of some stylized phenomena about asset return distributions that are well documented in financial...

We consider general stochastic volatility models with no local volatility component and derive the general expression of the volatility smile at order two in volatility-of-volatility. We show how, at this order, the smile only depends on three dimensionless numbers whose precise expressions as...

Following previous work on calibration of multi-factor local stochastic volatility models to market smiles, we show how to calibrate exactly any such models. Our approach, based on McKean's particle method, extends to hybrid models, for which we provide a Malliavin representation of the...

In this paper, we combine modern portfolio theory and option pricing theory so that a trader who takes a position in a European option contract and the underlying assets can construct an optimal portfolio such that at the moment of the contract's maturity the contract is perfectly hedged. We...

We derive sharp bounds for the prices of VIX futures using the full information of S&P 500 smiles. To that end, we formulate the model-free sub/superreplication of the VIX by trading in the S&P 500 and its vanilla options as well as the forward-starting log-contracts. A dual problem of...

So far, path-dependent volatility models have drawn little attention from both practitioners and academics compared to local volatility and stochastic volatility models. This is unfair: in this article we show that they combine benefits from both. Like the local volatility model, they are...

We investigate a systemic risk measure known as CoVaR that represents the value-at-risk (VaR) of a financial system conditional on an institution being under distress. For characterizing and estimating CoVaR, we use the copula approach and introduce the normal tempered stable (NTS) copula based...