Multilevel Monte Carlo Quadrature of Discontinuous Payoffs in the Generalized Heston Model Using Malliavin Integration by Parts | Zendy

Martin Altmayer | Zendy; Andreas Neuenkirch | Zendy

Open Access

Multilevel Monte Carlo Quadrature of Discontinuous Payoffs in the Generalized Heston Model Using Malliavin Integration by Parts

Author(s) -

Martin Altmayer,

Andreas Neuenkirch

Publication year - 2015

Publication title -

siam journal on financial mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.251

H-Index - 33

ISSN - 1945-497X

DOI - 10.1137/130933629

Subject(s) - numerical integration , estimator , mathematics , malliavin calculus , quadrature (astronomy) , stochastic volatility , monte carlo method , quasi monte carlo method , heston model , stochastic game , monte carlo integration , volatility (finance) , hybrid monte carlo , mathematical economics , mathematical analysis , sabr volatility model , markov chain monte carlo , econometrics , partial differential equation , statistics , physics , stochastic partial differential equation , optics

In this article, we establish an integration by parts formula for the quadrature of discontinuous payoffs in a multidimensional Heston model. For its derivation we use Malliavin calculus techniques and work under mild integrability conditions on the payoff and under the assumption of a strictly positive volatility. The integration by parts procedure smoothes the original functional, and thus our formula in combination with a payoff splitting allows us to construct efficient multilevel Monte Carlo estimators. This is confirmed by our numerical analysis and is illustrated by several numerical examples.

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