{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,25]],"date-time":"2026-10-25T07:37:08Z","timestamp":1792913828903,"version":"4.5.0"},"posted":{"date-parts":[[2024]]},"group-title":"SSRN","reference-count":39,"publisher":"Elsevier BV","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>We consider the Fourier-Laplace transforms of a broad class of polynomial Ornstein-Uhlenbeck (OU) volatility models, including the well-known Stein-Stein, Sch\u00f6bel-Zhu, one-factor Bergomi, and the recently introduced Quintic OU models motivated by the SPX-VIX joint calibration problem. We show the connection between the joint Fourier-Laplace functional of the log-price and the integrated variance, and the solution of an infinite dimensional Riccati equation. Next, under some non- vanishing conditions of the Fourier-Laplace transforms, we establish an existence result for such Riccati equation and we provide a discretized approximation of the joint characteristic functional that is exponentially entire. On the practical side, we develop a numerical scheme to solve the stiff infinite dimensional Riccati equations and demonstrate the efficiency and accuracy of the scheme for pricing SPX options and volatility swaps using Fourier and Laplace inversions, with specific examples of the Quintic OU and the one-factor Bergomi models and their calibration to real market data.<\/jats:p>","DOI":"10.2139\/ssrn.4816314","type":"posted-content","created":{"date-parts":[[2024,5,7]],"date-time":"2024-05-07T11:07:13Z","timestamp":1715080033000},"source":"Crossref","is-referenced-by-count":3,"title":["Fourier-Laplace Transforms in Polynomial Ornstein-Uhlenbeck Volatility Models"],"prefix":"10.2139","author":[{"given":"Eduardo","family":"Abi Jaber","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shaun (Xiaoyuan)","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xuyang","family":"Lin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"issue":"12","key":"ref1","doi-asserted-by":"crossref","first-page":"1995","DOI":"10.1080\/14697688.2019.1615113","article-title":"Lifting the Heston model","volume":"19","author":"Eduardo Abi","year":"2019","journal-title":"Quantitative Finance"},{"issue":"4","key":"ref2","doi-asserted-by":"crossref","first-page":"733","DOI":"10.1007\/s00780-022-00489-4","article-title":"The characteristic function of Gaussian stochastic volatility models: an analytic expression","volume":"26","author":"Eduardo Abi","year":"2022","journal-title":"Finance and Stochastics"},{"issue":"3","key":"ref3","doi-asserted-by":"crossref","first-page":"785","DOI":"10.1137\/23M1558847","article-title":"Reconciling rough volatility with jumps","volume":"15","author":"Eduardo Abi","year":"2024","journal-title":"SIAM Journal on Financial Mathematics"},{"issue":"2","key":"ref4","doi-asserted-by":"crossref","first-page":"606","DOI":"10.1137\/24M1636952","article-title":"Signature volatility models: pricing and hedging with Fourier","volume":"16","author":"Eduardo Abi","year":"2025","journal-title":"SIAM Journal on Financial Mathematics"},{"key":"ref5","doi-asserted-by":"crossref","first-page":"796","DOI":"10.1111\/mafi.12463","article-title":"Volatility models in practice: rough, pathdependent","volume":"35","author":"Eduardo Abi","year":"2025","journal-title":"or Markovian? 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