Pricing American Options under High-Dimensional Models with Recursive Adaptive Sparse Expectations.
We introduce a novel numerical framework for pricing American options in high dimensions. Our scheme manages to alleviate the problem of dimension scaling through the use of adaptive sparse grids. We approximate the value function with a low number of points and recursively apply fast approximations...
| Publicado en: | Journal of Financial Econometrics Vol. 19; no. 2; pp. 258 - 291 |
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| Autores principales: | , |
| Formato: | Artículo |
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Oxford University Press / USA
Spring2021
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| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=ssf&AN=151759539&site=ehost-live header: @attributes: shortDbName: ssf uiTerm: 151759539 longDbName: Social Sciences Full Text (H.W. Wilson) uiTag: AN controlInfo: bkinfo: jinfo: jid: 14798409 T2Y jtl: Journal of Financial Econometrics issn: 14798409 maglogo: N pubinfo: dt: Spring2021 vid: 19 iid: 2 pid: 622 pub: Oxford University Press / USA artinfo: ui: 151759539 10.1093/jjfinec/nby024 ppf: 258 ppct: 33 formats: tig: atl: Pricing American Options under High-Dimensional Models with Recursive Adaptive Sparse Expectations. aug: au: Scheidegger, Simon Treccani, Adrien affil: University of Lausanne University of Zurich su: Prices Monte Carlo method Hedging (Finance) Finite differences Parallel programming sug: subj: Prices Monte Carlo method Hedging (Finance) Finite differences Parallel programming ab: We introduce a novel numerical framework for pricing American options in high dimensions. Our scheme manages to alleviate the problem of dimension scaling through the use of adaptive sparse grids. We approximate the value function with a low number of points and recursively apply fast approximations of the expectation operator from an exercise period to the previous period. Given that available option databases gather several thousands of prices, there is a clear need for fast approaches in empirical work. Our method processes an entire cross section of options in a single execution and offers an immediate solution to the estimation of hedging coefficients through finite differences. It thereby brings valuable advantages over Monte Carlo simulations, which are usually considered to be the tool of choice in high dimensions, and satisfies the need for fast computation in empirical work with current databases containing thousands of prices. We benchmark our algorithm under the canonical model of Black and Scholes and the stochastic volatility model of Heston, the latter in the presence of discrete dividends. We illustrate the massive improvement of complexity scaling over dense grids with a basket option study including up to eight underlying assets. We show how the high degree of parallelism of our scheme makes it suitable for deployment on massively parallel computing units to scale to higher dimensions or further speed up the solution process. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: N holdings: @attributes: islocal: N |
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