European and Asian Greeks for Exponential Lévy Processes

Anselm Hudde () and Ludger Rüschendorf ()
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Anselm Hudde: Frankfurt University of Applied Sciences
Ludger Rüschendorf: University of Freiburg

Methodology and Computing in Applied Probability, 2023, vol. 25, issue 1, 1-24

Abstract: Abstract 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 Lévy process model with nonvanishing Brownian motion part. The results are based on Hilbert space valued Malliavin Calculus and extend previous results from the literature. Numerical experiments suggest, that in the case of a continuous payoff function, a combination of Malliavin Monte Carlo Greeks and the finite difference method has a better convergence behavior, whereas in the case of discontinuous payoff functions, the Malliavin Monte Carlo method clearly is the superior method compared to the finite difference approach, for first- and second order Greeks. Reduction arguments from the literature based on measure change imply that the expressions for the Greeks in this paper also hold true for generalized Asian options in particular for fixed and floating strike Asian options.

Keywords: Malliavin Calculus; Asian Greeks; Jump Diffusions (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11009-023-10014-5

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