can anyone help me in implementing a mean reverting and geometric brownian bridge?the only thing i can find is the standard brownian motion case of a wiener process, which is easy.but let';s say we have a vasicek model and we want to interpolate between two known points , say r_s and r_u , we want to find r_t (where s<t<u)standard brownian bridge gives: r_t = (u-t) /(u-s) r_s + (t-s) /(u-s) r_u + sqrt((t-s)(u-t) /(u-s) ) Zwhich (i think) fails to capture the mean reverting characteristic, anyone who knows if the mean reverting case is done differently ? the same question for the gemetric brownian bridge case....

windcloud: nice question.Paul: perhaps we should move this to the technical forum.This is how I'd do it - maybe others have different ideas.First, express r_u in terms of r_s:Notice the exponential decay function in the integrand. Effectively the mean reversion dampens the effect of earlier noise on later rate observations. To overcome this, make time 'accelerate':and define so that X is Brownian motion with respect to the time measure \tau. You can apply the standard bridging results to X, using the time measure \tau.Now using r_s and r_u and you can observe and . Finally express r_t asand use the bridge results for X.Also, check my mathematics. I rushed this off after work, so there may be some algebraic mistakes - but the intuition is there