Application of Quasi Monte Carlo and Global Sensitivity Analysis to Option Pricing and Greeks

48 Pages Posted: 6 Feb 2017

See all articles by Stefano Scoleri

Stefano Scoleri

Iason Ltd.

Marco Bianchetti

Intesa Sanpaolo - Financial and Market Risk Management; University of Bologna

Sergei Kucherenko

Imperial College London - Faculty of Engineering

Date Written: February 5, 2017

Abstract

Quasi Monte Carlo (QMC) and Global Sensitivity Analysis (GSA) techniques are applied for pricing and hedging representative financial instruments of increasing complexity. We compare standard Monte Carlo (MC) vs QMC results using Sobol' low discrepancy sequences, different sampling strategies, and various analyses of performance.

We find that QMC outperforms MC in most cases, including the highest-dimensional simulations, showing faster and more stable convergence. Regarding greeks computation, we compare standard approaches, based on finite differences (FD) approximations, with adjoint methods (AAD) providing evidences that, when the number of greeks is small, the FD approach combined with QMC can lead to the same accuracy as AAD, thanks to increased convergence rate and stability, thus saving a lot of implementation effort while keeping low computational cost. Using GSA, we are able to fully explain our findings in terms of reduced effective dimension of QMC simulation, allowed in most cases, but not always, by Brownian bridge discretization or PCA construction.

We conclude that, beyond pricing, QMC is a very efficient technique also for computing risk measures, greeks in particular, as it allows to reduce the computational effort of high dimensional Monte Carlo simulations typical of modern risk management.

Keywords: derivative, option, European, Asian, barrier, knock-out, cliquet, greeks, Monte Carlo, Quasi Monte Carlo, random, pseudo random, quasi random, low discrepancy, Sobol', convergence, speed-up, Brownian bridge, global sensitivity analysis, principal component analysis, AAD

JEL Classification: C63, G12, G13

Suggested Citation

Scoleri, Stefano and Bianchetti, Marco and Kucherenko, Sergei, Application of Quasi Monte Carlo and Global Sensitivity Analysis to Option Pricing and Greeks (February 5, 2017). Available at SSRN: https://ssrn.com/abstract=2911698 or http://dx.doi.org/10.2139/ssrn.2911698

Stefano Scoleri

Iason Ltd. ( email )

7th Floor, Hume House
Ballsbridge
Dublin 4
Ireland

Marco Bianchetti (Contact Author)

Intesa Sanpaolo - Financial and Market Risk Management ( email )

Piazza P. Ferrari 10
Milan, 20121
Italy

University of Bologna ( email )

Piazza Scaravilli 2
Bologna, 40100
Italy

Sergei Kucherenko

Imperial College London - Faculty of Engineering ( email )

United Kingdom

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