Monte Carlo simulation is playing an increasingly important role in the pricing and hedging of complex, path dependent financial instruments. Low discrepancy simulation methods offer the potential to provide faster rates of convergence than those of standard Monte Carlo methods; however, in high dimensional problems special methods are required to ensure that the faster convergence rates hold. Indeed, Ninomiya and Tezuka (1996) have shown highdimensional examples, in which low discrepancy methods perform worse than Monte Carlo methods. The principal component construction introduced by Acworth et al. (1998) provides one solution to this problem. However, the computational effort required to generate each path grows quadratically with the dimension of the problem. This article presents two new methods that offer accuracy equivalent, in terms of explained variability, to the principal components construction with computational requirements that are linearly related to the problem dimension. One method is to take into account knowledge about the payoff function, which makes it more flexible than the Brownian Bridge construction. Numerical results are presented that show the benefits of such adjustments. The different methods are compared for the case of pricing mortgage backed securities using the Hull-White term structure model.Monte Carlo simulation, quasi-Monte Carlo, mortgage backed securities, Brownian bridge, principal component decomposition, option pricing
Purpose In patients who underwent virtual planning and guided flapless implant surgery for teeth missing in the anterior maxilla, we compared buccal bone loss between those treated with and without autogenous bone augmentation. Methods Of 22 patients with teeth missing because of trauma or aplasia, 10 (18 implant sites) were reconstructed with buccally placed bone graft harvested from the mandibular ramus, and 12 were non-reconstructed (16 sites). Baseline cone-beam computed tomography allowed for implant planning using the NobelClinician® software and was performed again at 1 year after functional loading. The marginal bone level was assessed radiographically at post-implant baseline and at follow-up. Results At follow-up, buccal bone loss differed significantly between groups at the central level of the implant (p = 0.0005) but not at the coronal level (p = 0.329). The mean marginal bone level change was 0.6 mm, with no significant between-group difference (p = 0.876). The actual implant position often deviated in the vertical or sagittal plane by an average of 0.3–0.6 mm from the planned position. Conclusion Compared with non-reconstructed patients, reconstructed patients experienced significantly more buccal bone loss at the central level of implants. The groups did not differ at the coronal level or in marginal bone loss, possibly because of the more augmented bone at the central level among reconstructed patients. Differences between planned versus actual implant positions should be considered in situations of limited bone volume at the planned implant site.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.