geometric brownian bridge

quentin · August 22nd, 2006, 9:52 am

Hello,I need to simulate a process of the kindbetween times 0 and T, for a Monte-Carlo pricer. f0 and fT are given positive constants.Using brownians bridges or backward simulation is fine as long as the volatility is constant, or even time-dependent. In that case you can find the value of both bounds of your brownian bridge by inverting the formulaDoes anyone know how to simulate this process when the volatility is spot-dependent (Dupire local vol)?

tigerbill · August 30th, 2006, 2:26 am

I havent implemented this yet, but Peter Jackel's book 'monte carlo methods in finance' has a short description on this, see page 122--124.

frontofficequant · October 18th, 2006, 3:34 pm

You wno't find any good answers to that question in a book. Simulating a conditioned (or tied-down ) diffusion is in general a very difficult problem which has only been very recently addressed in the literature in a satisfactory way. When the process is a Brownian motion (or a transformation of one) then we can use well known Brownian bridge results. The following paper addresses the problem in a quite general setting: http://www.stats.uwaterloo.ca/stats_nav ... 06-12.pdfI hope this helps.