We introduce the formalism of generalized Fourier transforms in the context of risk management. We develop a general framework in which to efficiently compute the most popular risk measures, value-at-risk and expected shortfall (also known as conditional value-at-risk). The only ingredient...

The presence of non linear instruments is responsible for the emergence of non Gaussian features in the price changes distribution of realistic portfolios, even for Normally distributed risk factors. This is especially true for the benchmark Delta Gamma Normal model, which in general exhibits...

In this work we afford the statistical characterization of a linear Stochastic Volatility Model featuring Inverse Gamma stationary distribution for the instantaneous volatility. We detail the derivation of the moments of the return distribution, revealing the role of the Inverse Gamma law in the...

In this work we detail the application of a fast convolution algorithm computing high dimensional integrals to the context of multiplicative noise stochastic processes. The algorithm provides a numerical solution to the problem of characterizing conditional probability density functions at...

In this work we afford the statistical characterization of a linear Stochastic Volatility Model featuring Inverse Gamma stationary distribution for the high frequency volatility. We detail the derivation of the moments of the return distribution, revealing the role of the Inverse Gamma law in...

In this work we afford the statistical characterization of a linear Stochastic Volatility Model featuring Inverse Gamma stationary distribution for the high frequency volatility. We detail the derivation of the moments of the return distribution, revealing the role of the Inverse Gamma law in...

We propose a novel algorithm which allows to sample paths from an underlying price process in a local volatility model and to achieve a substantial variance reduction when pricing exotic options. The new algorithm relies on the construction of a discrete multinomial tree. The crucial feature of...

We derive an analytic relation between equity risk premium and the term structure of variance risk premium (VRP). Motivated by this result, we estimate the VRP term structure using a general and fully analytical discrete-time option pricing framework featuring multiple volatility components and...

In financial markets, the order flow, defined as the process assuming value one for buy market orders and minus one for sell market orders, displays a very slowly decaying autocorrelation function. Since orders impact prices, reconciling the persistence of the order flow with market efficiency...