Quasi-Monte Carlo Methods for Calculating Derivatives Sensitivities on the GPU

```@article{Bilokon2022QuasiMonteCM,
title={Quasi-Monte Carlo Methods for Calculating Derivatives Sensitivities on the GPU},
author={Paul Bilokon and Sergei S. Kucherenko and Casey Williams},
journal={SSRN Electronic Journal},
year={2022}
}```
• Published 22 September 2022
• Computer Science
• SSRN Electronic Journal
The calculation of option Greeks is vital for risk management. Traditional pathwise and ﬁnite-difference methods work poorly for higher-order Greeks and options with discontinuous payoff functions. The Quasi-Monte Carlo-based conditional pathwise method (QMC-CPW) for options Greeks allows the payoff function of options to be effectively smoothed, allowing for increased efﬁciency when calculating sensitivities. Also demonstrated in literature is the increased computational speed gained by…

References

SHOWING 1-10 OF 31 REFERENCES

• Economics
Quantitative Finance
• 2019
This paper generalizes the traditional pathwise method to calculate the first- and high-order Greeks by taking a conditional expectation, and the discontinuous integrand is smoothed, so the interchange of expectation and differentiation is proved to be possible.
This paper discusses the three main approaches to computing Greeks: finite dierence, likelihood ratio method (LRM) and pathwise sensitivity calculation, and a new idea is presented to address these limitations by combining the adjoint pathwise approach for the stochastic path evolution with LRM for the payo evaluation.
• Computer Science
• 2015
Quasi Monte Carlo is a very promising technique also for computing risk figures, greeks in particular, as it allows to reduce the computational effort of high-dimensional Monte Carlo simulations typical of modern risk management.
• Mathematics
Finance Stochastics
• 2011
A new but simple mathematical formulation is built so that formulas of Greeks for a broad class of derivative securities can be derived systematically and these formulas are the first in the literature.
Monte Carlo is one of the most versatile and widely used numerical methods. Its convergence rate, O(N−1/2), is independent of dimension, which shows Monte Carlo to be very robust but also slow. This
We show how the benefits of the pathwise sensitivity approach to computing Monte Carlo Greeks can be extended to discontinuous payoff functions through a combination of the pathwise approach and the
• Mathematics
• 1996
Simulation has proved to be a valuable tool for estimating security prices for which simple closed form solutions do not exist. In this paper we present two direct methods, a pathwise method and a
• A. Owen
• Computer Science
J. Complex.
• 1998
This paper shows that scrambled ( t ,  m,  s )-nets enjoy the same properties as scrambled (0,  m ,  s)-nets, except the sampling variance is guaranteed only to be below b t [( b +1)/( b −1)] s times the Monte Carlo variance for a least-favorable integrand and finite n.