Jumps or Rough Volatility? Identifying Jumps in a Rough Volatility Setting
Author
Jensen, Christian Bang
Term
4. term
Education
Publication year
2024
Submitted on
2024-06-03
Abstract
Dette speciale undersøger, om Aït-Sahalia og Jacods forholdsbaserede hop-test kan skelne mellem egentlige pris-hop og hop-lignende adfærd, der skyldes rough volatilitet, i et high-frequency setup. Først gennemgås centrale kendetegn ved højfrekvente data, herunder asynkronitet og mikrostrukturstøj, samt hvordan realiseret kovarians kan bruges til at estimere den integrerede volatilitet. Derefter præsenteres testen, som sammenligner powervariationer på forskellige samplingfrekvenser, og der introduceres stokastiske forsinkede differentialligninger (SDDE) til at modellere rough volatilitet. En simulationsundersøgelse benchmarker testen på standard Itô-semmartingaler, både med og uden hop, hvor testen i store træk opfører sig som forventet, og vurderer dens adfærd i to rough modeller: log-volatilitet drevet af en SDDE samt den rough fraktionelle stokastiske volatilitet (RFSV) model af Gatheral m.fl. Formålet er at vurdere testens robusthed og dens evne til at skelne mellem hop og rough volatilitet i diskret observerede prisprocesser; detaljerede resultater for de rough modeller fremgår ikke af dette uddrag.
This thesis examines whether the Aït-Sahalia and Jacod ratio jump test can distinguish genuine price jumps from jump-like behavior generated by rough volatility in a high-frequency setting. It first reviews key features of high-frequency market data, including asynchronicity and microstructure noise, and how realized covariation can be used to estimate integrated volatility. The test, which compares power variations across sampling frequencies, is then presented, and stochastic delay differential equations (SDDEs) are introduced to build rough volatility models. A simulation study benchmarks the test on standard Itô semimartingales, with and without jumps, where the test performs largely as expected, and evaluates its behavior under two rough models: log-volatility driven by an SDDE and the rough fractional stochastic volatility (RFSV) model of Gatheral et al. The goal is to assess the test’s robustness and its ability to separate jumps from rough volatility in discretely observed price processes; detailed performance results for the rough models are not provided in this excerpt.
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