{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/application-of-simplest-random-walk","title":"Application of simplest random walk algorithms for pricing barrier options","arxiv_id":"1211.5726","date":"2012-11-25","proceeding":null,"authors":["M. Krivko","M. V. Tretyakov"],"abstract":"We demonstrate effectiveness of the first-order algorithm from [Milstein,\nTretyakov. Theory Prob. Appl. 47 (2002), 53-68] in application to barrier\noption pricing. The algorithm uses the weak Euler approximation far from\nbarriers and a special construction motivated by linear interpolation of the\nprice near barriers. It is easy to implement and is universal: it can be\napplied to various structures of the contracts including derivatives on\nmulti-asset correlated underlyings and can deal with various type of barriers.\nIn contrast to the Brownian bridge techniques currently commonly used for\npricing barrier options, the algorithm tested here does not require knowledge\nof trigger probabilities nor their estimates. We illustrate this algorithm via\npricing a barrier caplet, barrier trigger swap and barrier swaption.","url_abs":"http://arxiv.org/abs/1211.5726v1","url_pdf":"http://arxiv.org/pdf/1211.5726v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"application-of-simplest-random-walk","repo_url":"https://github.com/Jefzhang/Barrier-options-pricing","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"application-of-simplest-random-walk","repo_url":"https://github.com/segis95/MCProject","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}