A recursive formula for the nth survival function and the nth first passage time distribution for jump and diffusion processes. Applications to the pricing of nth-to-default CDS.

A recursive formula for the nth survival function and the nth first passage time distribution for jump and diffusion processes. Applications to the pricing of nth-to-default CDS. | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article A recursive formula for the n th survival function and the n th first passage time distribution for jump and diffusion processes. Applications to the pricing of n th -to-default CDS. Alessio Lapolla This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7646734/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract We derive some rather general, but combinatorially challenging, formulae to compute the survival function and the first passage time distribution of the n th coordinate of a many-body stochastic process in the presence of a killing barrier. First we will study the case of two coordinates and then we will generalize the results to three or more coordinates. Even if the results are difficult to implement, we will provide examples of their use applying them to a physical system, the single file diffusion, and to the financial problem of pricing a n th -to-default credit default swap (n th -CDS). MSC Classification: 60J70 , 60J25 , 60J27 , 60K35 , 82C31 , 91G20 survival function first passage time problem order statistics many-body system nth-to-default CDS single file diffusion multivariate Poisson process Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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