 Very fast algorithms for implied barriers and moving-barrier options pricingYu-Ming Lu and Yuh-Dauh Lyuu Mathematics and Computers in Simulation (MATCOM), 2023, vol. 205, issue C, 251-271 Abstract: Two closely related O(nlogn)-time tree algorithms under the Black–Scholes model are presented, where n denotes the tree’s number of time steps. The first finds the implied step barrier that matches the barrier-hitting probabilities exactly. In the constant-barrier case, the implied barrier is surprisingly accurate even for small ns; indeed, n=1 gives good results in typical situations. The second prices options with a time-dependent barrier (i.e., moving-barrier options). In practice, both algorithms are one to three orders faster than the standard algorithms even when n is moderate. As a consequence, large portfolios or datasets can finally be studied in a timely manner. Both algorithms can be easily tailored to handle barriers that are continuously monitored, discretely monitored, a mixture of both, or even when the model parameters are all time varying. Keywords: Implied barrier; Option pricing; Algorithm; Moving-barrier option; Fast Fourier transform; Translation invariance (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:205:y:2023:i:c:p:251-271 DOI: 10.1016/j.matcom.2022.09.018 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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