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We discuss the class of "Quadratic Normal Volatility" models, which have drawn much attention in the financial industry due to their analytic tractability and flexibility. We characterize these models as the ones that can be obtained from…

In this paper we give easy-to-implement closed-form expressions for European and Asian Greeks for general L2-payoff functions and underlying assets in an exponential L\'evy process model with nonvanishing Brownian motion part. The results…

We introduce a Multifractal Random Walk (MRW) defined as a stochastic integral of an infinitely divisible noise with respect to a dependent fractional Brownian motion. Using the techniques of the Malliavin calculus, we study the existence…

In this paper, we establish a probabilistic representation as well as some integration by parts formulae for the marginal law at a given time maturity of some stochastic volatility model with unbounded drift. Relying on a perturbation…

Pricing of high-dimensional options is one of the most important problems in Mathematical Finance. The objective of this manuscript is to present an original self-contained treatment of the multidimensional pricing. During the past decades…

This study developed a novel formulation of conditional expectations within the framework of a jump-diffusion mean-field stochastic differential equation. We introduce an integrated approach that combines unconditioned expectations with…

The question of the volatility roughness is interpreted in the framework of a data-reconstructed fractional volatility model, where volatility is driven by fractional noise. Some examples are worked out and also, using Malliavin calculus…

This paper develops a flexible and computationally efficient multivariate volatility model, which allows for dynamic conditional correlations and volatility spillover effects among financial assets. The new model has desirable properties…

Consider stochastic functional differential equations, whose coefficients depend on past histories. The solution determines a non-Markov process. In the present paper, we shall obtain the existence of smooth densities for joint…

We consider the problem of Hurst index estimation for solutions of stochastic differential equations driven by an additive fractional Brownian motion. Using techniques of the Malliavin calculus, we analyze the asymptotic behavior of the…

In this paper we provide a comprehensive analysis of a structural model for the dynamics of prices of assets traded in a market originally proposed in [1]. The model takes the form of an interacting generalization of the geometric Brownian…

We present a new numerical method to price vanilla options quickly in time-changed Brownian motion models. The method is based on rational function approximations of the Black-Scholes formula. Detailed numerical results are given for a…

We introduce a flexible method to simultaneously infer both the drift and volatility functions of a discretely observed scalar diffusion. We introduce spline bases to represent these functions and develop a Markov chain Monte Carlo…

Financial markets have long since been modeled using stochastic methods such as Brownian motion, and more recently, rough volatility models have been built using fractional Brownian motion. This fractional aspect brings memory into the…

This paper considers a portfolio optimization problem in which asset prices are represented by SDEs driven by Brownian motion and a Poisson random measure, with drifts that are functions of an auxiliary diffusion 'factor' process. The…

We study the obtainment of closed-form formulas for the distribution of the jumps of a doubly-stochastic Poisson process. The problem is approached in two ways. On the one hand, we translate the problem to the computation of multiple…

In this paper, we develop a novel method based on Malliavin calculus to find an approximation for the convexity adjustment for various classical interest rate products. Malliavin calculus provides a simple way to get a template for the…

We consider a stochastic volatility model where the dynamics of the volatility are described by a linear function of the (time extended) signature of a primary process which is supposed to be a polynomial diffusion. We obtain closed form…

This article is the second one in a series on the use of scaling invariance in finance. In the first article (cond-mat/9906048), we introduced a new formalism for the pricing of derivative securities, which focusses on tradable objects…

This study presents a long-term alternative formula for stock price variation described by a geometric Brownian motion on the basis of median instead of mean or expected values. The proposed method is motivated by the observation made in…