We work in the Uncertain Volatility Model setting of Avellaneda, Levy, Paras [1] and Lyons [10] (cf. also [11]). We first look at European options in a market with no interest rate and focus on theextreme case where the volatility has a lower bound but no upper bound. We show that the smallest...

The aim of this work is to introduce a new stochastic volatility model for equity derivatives. To overcome some of the well-known problems of the Heston model, and more generally of the affine models, we define a new specification for the dynamics of the stock and its volatility. Within this...

We develop a dynamic version of the SSVI parameterisation for the total implied variance, ensuring that European vanilla option prices are martingales, hence preventing the occurrence of arbitrage, both static and dynamic. Insisting on the constraint that the total implied variance needs to be...

The rough Bergomi model introduced by Bayer, Friz and Gatheral has been outperforming conventional Markovian stochastic volatility models by reproducing implied volatility smiles in a very realistic manner, in particular for short maturities. We investigate here the dynamics of the VIX and the...

The aim of this work is to introduce a new stochastic volatility model for equity derivatives. To overcome some of the well-known problems of the Heston model, and more generally of the affine models, we define a new specification for the dynamics of the stock and its volatility. Within this...

We observe that a European Call option with strike $L K$ can be seen as a Call option with strike $L-K$ on a Call option with strike $K$. Under no arbitrage assumptions, this yields immediately that the prices of the two contracts are the same, in full generality. We study in detail the...

Central clearing counterparty houses (CCPs) play a fundamental role in mitigating the counterparty risk for exchange traded options. CCPs cover for possible losses during the liquidation of a defaulting member's portfolio by collecting initial margins from their members. In this article we...

Implied volatility is at the very core of modern finance, notwithstanding standard option pricing models continue to derive option prices starting from the joint dynamics of the underlying asset price and the spot volatility. These models often cause difficulties: no closed formulas for prices,...

We study the term structure of the implied volatility in a situation where the smile is symmetric. Starting from the result by Tehranchi that a symmetric smile generated by a continuous martingale necessarily comes from a mixture of normal distributions, we derive representation formulae for the...