TY - JOUR
T1 - An introduction to multilevel Monte Carlo for option valuation
AU - Higham, Desmond J.
N1 - This is an Accepted Manuscript of an article published by Taylor & Francis in International Journal of Computer Mathematics on 11/09/2015, available online: http://www.tandfonline.com/10.1080/00207160.2015.1077236
PY - 2015/9/11
Y1 - 2015/9/11
N2 - Monte Carlo is a simple and flexible tool that is widely used in computational finance. In this context, it is common for the quantity of interest to be the expected value of a random variable defined via a stochastic differential equation. In 2008, Giles proposed a remarkable improvement to the approach of discretizing with a numerical method and applying standard Monte Carlo. His multilevel Monte Carlo method offers a speed up of Ο(ε-1), where ε is the required accuracy. So computations can run 100 times more quickly when two digits of accuracy are required. The 'multilevel philosophy' has since been adopted by a range of researchers and a wealth of practically significant results has arisen, most of which have yet to make their way into the expository literature. In this work, we give a brief, accessible, introduction to multilevel Monte Carlo and summarize recent results applicable to the task of option evaluation.
AB - Monte Carlo is a simple and flexible tool that is widely used in computational finance. In this context, it is common for the quantity of interest to be the expected value of a random variable defined via a stochastic differential equation. In 2008, Giles proposed a remarkable improvement to the approach of discretizing with a numerical method and applying standard Monte Carlo. His multilevel Monte Carlo method offers a speed up of Ο(ε-1), where ε is the required accuracy. So computations can run 100 times more quickly when two digits of accuracy are required. The 'multilevel philosophy' has since been adopted by a range of researchers and a wealth of practically significant results has arisen, most of which have yet to make their way into the expository literature. In this work, we give a brief, accessible, introduction to multilevel Monte Carlo and summarize recent results applicable to the task of option evaluation.
KW - computational complexity
KW - control variate
KW - Euler–Maruyama
KW - Monte Carlo
KW - option value
KW - stochastic differential equation
KW - variance reduction
UR - http://www.scopus.com/inward/record.url?scp=84941248561&partnerID=8YFLogxK
UR - http://www.tandfonline.com/loi/gcom
U2 - 10.1080/00207160.2015.1077236
DO - 10.1080/00207160.2015.1077236
M3 - Article
VL - 92
SP - 2347
EP - 2360
JO - International Journal of Computer Mathematics
JF - International Journal of Computer Mathematics
SN - 0020-7160
IS - 12
ER -