We focus our work here on some very recent results obtained by Cherny and Madan on risk measures. They developed a rigorous mathematical framework for the study of coherent risk measures. The first sections mainly review the existing literature. We present it here for sake of completeness as...

We investigate the links between various no-arbitrage conditions and the existence of pricing functionals in general markets, and prove the Fundamental Theorem of Asset Pricing therein. No-arbitrage conditions, either in this abstract setting or in the case of a market consisting of European...

We revisit the foundational Moment Formula proved by Roger Lee fifteen years ago. We show that when the underlying stock price martingale admits finite log-moments E[|log (S)|^q] for some positive q, the arbitrage-free growth in the left wing of the implied volatility smile is less constrained...

In this short note, we prove by an appropriate change of variables that the SVI implied volatility parameterization presented in Gatheral's book and the large-time asymptotic of the Heston implied volatility agree algebraically, thus confirming a conjecture from Gatheral as well as providing a...

We provide a thorough analysis of the path-dependent volatility model introduced by Guyon proving existence and uniqueness of a strong solution, characterising its behaviour at boundary points, providing asymptotic closed-form option prices as well as deriving small-time behaviour estimates

We propose a hybrid quantum-classical algorithm, originated from quantum chemistry, to price European and Asian options in the Black-Scholes model. Our approach is based on the equivalence between the pricing partial differential equation and the Schrodinger equation in imaginary time. We devise...

We consider here the fractional version of the Heston model originally proposed by Comte, Coutin and Renault. Inspired by some recent ground-breaking work by Gatheral, Jaisson and Rosenbaum, who showed that fractional Brownian motion with short memory allows for a better calibration of the...

We study how the introduction of carbon taxes in a closed economy propagate in a credit portfolio and precisely describe how carbon taxes dynamics affect the firm value and credit risk measures such as probability of default, expected and unexpected losses.We adapt a stochastic multisectoral...

We construct a deep learning-based numerical algorithm to solve path-dependent partial differential equations arising in the context of rough volatility. Our approach is based on interpreting the PDE as a solution to an SPDE, building upon recent insights by Bayer, Qiu and Yao, and on...