{"paper":{"title":"Small-time expansions of the distributions, densities, and option prices of stochastic volatility models with L\\'evy jumps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"q-fin.PR","authors_text":"C. Houdr\\'e, J. E. Figueroa-L\\'opez, R. Gong","submitted_at":"2010-09-21T20:54:08Z","abstract_excerpt":"We consider a stochastic volatility model with L\\'evy jumps for a log-return process $Z=(Z_{t})_{t\\geq 0}$ of the form $Z=U+X$, where $U=(U_{t})_{t\\geq 0}$ is a classical stochastic volatility process and $X=(X_{t})_{t\\geq 0}$ is an independent L\\'evy process with absolutely continuous L\\'evy measure $\\nu$. Small-time expansions, of arbitrary polynomial order, in time-$t$, are obtained for the tails $\\bbp(Z_{t}\\geq z)$, $z>0$, and for the call-option prices $\\bbe(e^{z+Z_{t}}-1)_{+}$, $z\\neq 0$, assuming smoothness conditions on the {\\PaleGrey density of $\\nu$} away from the origin and a small-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4211","kind":"arxiv","version":5},"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"}