{"paper":{"title":"On the Heston Model with Stochastic Volatility: Analytic Solutions and Complete Markets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"B\\'en\\'edicte Alziary, Peter Tak\\'a\\v{c}","submitted_at":"2017-11-13T11:48:51Z","abstract_excerpt":"We study the Heston model for pricing European options on stocks with stochastic volatility. This is a Black\\--Scholes\\--type equation whose spatial domain for the logarithmic stock price $x\\in \\RR$ and the variance $v\\in (0,\\infty)$ is the half\\--plane $\\HH = \\RR\\times (0,\\infty)$. The {\\it volatility\\/} is then given by $\\sqrt{v}$. The diffusion equation for the price of the European call option $p = p(x,v,t)$ at time $t\\leq T$ is parabolic and degenerates at the boundary $\\partial \\HH = \\RR\\times \\{0\\}$ as $v\\to 0+$. The goal is to hedge with this option against volatility fluctuations, i.e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.04536","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}