id: 05662710
dt: j
an: 05662710
au: Becker, Martin
ti: Exact simulation of final, minimal and maximal values of Brownian motion
    and jump-diffusions with applications to option pricing.
so: Comput. Manag. Sci. 7, No. 1, 1-17 (2010).
py: 2010
pu: Springer, Heidelberg
la: EN
cc: 
ut: Brownian motion; Monte Carlo simulation; jump-diffusions; double barrier
    options; importance sampling
ci: 
li: doi:10.1007/s10287-007-0065-9
ab: Summary: We introduce a method for generating
    $(W_{x,T}^{(μ,σ)},m_{x,T}^{(μ,σ)},M_{x,T}^{(μ,σ)})$, where
    $W_{x,T}^{(μ,σ)}$ denotes the final value of a Brownian motion
    starting in $x$ with drift $μ$ and volatility $σ$ at some final time
    $T, m_{x,T}^{(μ,σ)} = {\inf}_{0\leq t \leq T}W_{x,t}^{(μ,σ)}$ and
    $M_{x,T}^{(μ,σ)} = {\sup}_{0\leq t \leq T} W_{x,t}^{(μ,σ)}$. By
    using the trivariate distribution of
    $(W_{x,T}^{(μ,σ)},m_{x,T}^{(μ,σ)},M_{x,T}^{(μ,σ)})$, we obtain a
    fast method which is unaffected by the well-known random walk
    approximation errors. The method is extended to jump-diffusion models.
    As sample applications we include Monte Carlo pricing methods for
    European double barrier knock-out calls with continuous reset
    conditions under both models. The proposed methods feature simple
    importance sampling techniques for variance reduction.
rv: