# European and Asian Greeks for exponential L\'evy processes

@inproceedings{Hudde2016EuropeanAA, title={European and Asian Greeks for exponential L\'evy processes}, author={Anselm Hudde and L. Ruschendorf}, year={2016} }

In this paper we give easy-to-implement closed expressions for European and Asian Greeks for general L-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 an continuous payoff function, a combination of Malliavin Monte Carlo Greeks and the finite difference method has a… Expand

#### Figures and Tables from this paper

#### References

SHOWING 1-10 OF 12 REFERENCES

Malliavin Calculus in Lévy spaces and Applications to Finance.

- Mathematics
- 2007

The main goal of this paper is to generalize the results of Fournie et al. [7] for markets generated by Levy processes. For this reason we extend the theory of Malliavin calculus to provide the tools… Expand

Malliavin Monte Carlo Greeks for jump diffusions

- Mathematics
- 2006

In recent years efficient methods have been developed for calculating derivative price sensitivities using Monte Carlo simulation. Malliavin calculus has been used to transform the simulation problem… Expand

Canonical Lévy process and Malliavin calculus

- Mathematics
- 2007

A suitable canonical Levy process is constructed in order to study a Malliavin calculus based on a chaotic representation property of Levy processes proved by Ito using multiple two-parameter… Expand

Applications of Malliavin calculus to Monte Carlo methods in finance

- Computer Science
- Finance Stochastics
- 1999

An original probabilistic method for the numerical computations of Greeks in finance, based on the Greeks formulae, which is compared to the Monte Carlo finite difference approach and turns out to be very efficient in the case of discontinuous payoff functionals. Expand

Computation of option greeks under hybrid stochastic volatility models via Malliavin calculus

- Economics, Mathematics
- 2018

This study introduces computation of option sensitivities (Greeks) using the Malliavin calculus under the assumption that the underlying asset and interest rate both evolve from a stochastic… Expand

Efficient calculation of the Greeks for exponential Lévy processes: an application of measure valued differentiation

- Economics
- 2016

Monte Carlo simulation methods have become more and more important in the financial sector in the past years. In this paper, we introduce a new simulation method for the estimation of the derivatives… Expand

numderiv: Accurate numerical derivatives [Computer software manual

- 2015

Efficient simulation of Greeks of multiasset European and Asian style options by Malliavin calculus and quasi-Monte Carlo methods

- Mathematics, Computer Science
- Appl. Math. Comput.
- 2014

Simulation of sensitivities or Greeks of multiasset European and Asian style options by Malliavin calculus combined with Monte Carlo and quasi-Monte Carlo methods and results show the advantages of Malliavine calculus method to the finite difference method for options with nonsmooth payoffs. Expand

Computation of Greeks using Malliavin ’ s calculus in jump type market models

- 2006

We use the Malliavin calculus for Poisson processes in order to compute sensitivities for European and Asian options with underlying following a jump type diffusion. The main point is to settle an… Expand

Calculation of the greeks for jumpdiffusions

- Financial and Actuarial Mathematics
- 2005