Andrea Pascucci

University of Bologna

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Stefano Pagliarani

University of Bologna

Matthew Lorig

University of Washington Applied Physics Laboratory

Sergio Polidoro

University of Modena and Reggio Emilia

Anastasia Borovykh

Imperial College London

Paolo Foschi

University of Bologna

Wolfgang J. Runggaldier

University of Padua

Cornelis W. Oosterlee

Centrum Wiskunde & Informatica

A. Pesce

University of Bologna

Alberto Lanconelli

University of Bologna

María del Carmen Calvo-Garrido

Universidade da Coruña

Cooperative Institutions

University of Bologna

University of Padua

Universidade da Coruña

Sapienza University of Rome

Umeå University

Purdue University West Lafayette

University of Modena and Reggio Emilia

Politecnico di Milano

University of Minnesota

University of L'Aquila

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PDE and Martingale Methods in Option Pricing

Bocconi & Springer Series (2011)

Andrea Pascucci

This book offers an introduction to the mathematical, probabilistic and numerical methods used in the modern theory of option pricing. The text is designed for readers with a basic mathematical backgr

Martingale pricing

10.1007/978-88-470-1781-8

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Citations (261)

Stochastic differential equations

Bocconi & Springer Series (2011)

Andrea Pascucci

In this chapter we present some basic results on stochastic differential equations, hereafter shortened to SDEs, and we examine the connection to the theory of parabolic partial differential equations.

10.1007/978-88-470-1781-8_9

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Citations (17)

Well-posedness of McKean-Vlasov kinetic equations by inversion

arXiv (Cornell University) (2025)

Andrea Pascucci Alessio Rondelli

We consider the McKean-Vlasov equation $dX_t = b(t, X_t, [X_t])dt + \sigma(t, X_t, [X_t])dW_t$ where $[X_t]$ is the law of $X_t$. We focus specifically on the "kinetic" case, where the equation is degenerate in the sense that the dimension of the Brownian motion $W$ can be strictly less than the dimension of the solution $X$. Assuming H\"older continuous coefficients and a hypoellipticity condition, we prove the well-posedness of the equation. This result complements the existing literature by addressing the case where the diffusion coefficient $\sigma$ depends on the law $[X_t]$, which have been previously unexplored. Our proof employs a novel technique that offers a simplified and direct argument, eliminating the need for PDEs involving derivatives with respect to the measure argument and exploiting the sub-Riemannian metric structure induced by the corresponding Fokker-Planck operator.

Vlasov Equation

10.48550/arxiv.2501.10987

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Leveraged {ETF} implied volatilities from {ETF} dynamics

RePEc: Research Papers in Economics (2014)

Tim Leung Matthew Lorig Andrea Pascucci

The growth of the exhange-traded fund (ETF) industry has given rise to the trading of options written on ETFs and their leveraged counterparts {(LETFs)}. We study the relationship between the ETF and LETF implied volatility surfaces when the underlying ETF is modeled by a general class of local-stochastic volatility models. A closed-form approximation for prices is derived for European-style options whose payoff depends on the terminal value of the ETF and/or LETF. Rigorous error bounds for this pricing approximation are established. A closed-form approximation for implied volatilities is also derived. We also discuss a scaling procedure for comparing implied volatilities across leverage ratios. The implied volatility expansions and scalings are tested in three well-known settings: CEV, Heston and SABR.

Leverage (statistics)

Stochastic game

Leverage effect

Local volatility

Terminal value

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Explicit implied volatilities for multifactor local-stochastic volatility models

Matthew Lorig Stefano Pagliarani Andrea Pascucci

We consider an asset whose risk-neutral dynamics are described by a general class of local-stochastic volatility models and derive a family of asymptotic expansions for European-style option prices and implied volatilities. Our implied volatility expansions are explicit; they do not require any special functions nor do they require numerical integration. To illustrate the accuracy and versatility of our method, we implement it under five different model dynamics: CEV local volatility, quadratic local volatility, Heston stochastic volatility, $3/2$ stochastic volatility, and SABR local-stochastic volatility.

Local volatility

Heston model

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Pricing Bermudan Options Under Local LLvy Models with Default

SSRN Electronic Journal (2016)

Anastasia Borovykh Andrea Pascucci Cornelis W. Oosterlee

We consider a defaultable asset whose risk-neutral pricing dynamics are described by an exponential Lévy-type martingale. This class of models allows for a local volatility, local default intensity and a locally dependent Lévy measure. We present a pricing method for Bermudan options based on an analytical approximation of the characteristic function combined with the COS method. Due to a special form of the obtained characteristic function the price can be computed using a Fast Fourier Transform-based algorithm resulting in a fast and accurate calculation. The Greeks can be computed at almost no additional computational cost. Error bounds for the approximation of the characteristic function as well as for the total option price are given.

10.2139/ssrn.2771632

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Citations (2)

Opzioni Americane

Unitext (2008)

Andrea Pascucci

10.1007/978-88-470-0601-0_11

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Analysis of a glass-fibre sandwich panel for car body constructions

Composite Structures (1997)

Paolo Gaudenzi Andrea Pascucci R. Barboni Alexander Horoschenkoff

Sandwich panel

10.1016/s0263-8223(97)00077-9

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Citations (11)

Geometric Methods in PDE's: a conference on the occasion of the 65th birthday of Ermanno Lanconelli

Giovanna Citti Sever S Dragomir Bruno Franchi Cristian E. Gutiérrez Annamaria Montanari

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Backward and forward filtering under the weak Hörmander condition

arXiv (Cornell University) (2020)

Andrea Pascucci A. Pesce

We derive the forward and backward filtering equations for a class of degenerate partially observable diffusions, satisfying the weak H\"ormander condition. Our approach is based on the H\"older theory for degenerate SPDEs that allows to pursue the direct approaches proposed by N. V. Krylov and A. Zatezalo, and A. Yu. Veretennikov, avoiding the use of general results from filtering theory. As a by-product we also provide existence, regularity and estimates for the filtering density.

Filtering problem

10.48550/arxiv.2006.13325

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