Weak approximations for arithmetic means of geometric Brownian motions and applications to Basket options

Romain Bompis ()
Additional contact information
Romain Bompis: Crédit Agricole - Crédit Agricole

Working Papers from HAL

Abstract: In this work we derive new analytical weak approximations for arithmetic means of geometric Brownian motions using a scalar log-normal Proxy with an averaged volatility. The key features of the approach are to keep the martingale property for the approximations and to provide new integration by parts formulas for geometric Brownian motions. Besides, we also provide tight error bounds using Malliavin calculus, estimates depending on a suitable dispersion measure for the volatilities and on the maturity. As applications we give new price and implied volatility approximation formulas for basket call options. The numerical tests reveal the excellent accuracy of our results and comparison with the other known formulas of the literature show a valuable improvement.

Keywords: Weak approximation; Geometric Brownian motion; Arithmetic mean; Malliavin calculus; Basket options (search for similar items in EconPapers)
Date: 2017-04-06
Note: View the original document on HAL open archive server: https://hal.science/hal-01502886
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://hal.science/hal-01502886/document (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hal:wpaper:hal-01502886

Access Statistics for this paper

More papers in Working Papers from HAL
Bibliographic data for series maintained by CCSD ().