Paper: arXiv 2304.12450
Authors: Carsten H. Chong, Viktor Todorov
Abstract
We derive a nonparametric higher-order asymptotic expansion for small-time changes of conditional characteristic functions of Itô semimartingale increments. The asymptotics setup is of joint type: both the length of the time interval of the increment of the underlying process and the time gap between evaluating the conditional characteristic function are shrinking. The spot semimartingale characteristics of the underlying process as well as their spot semimartingale characteristics appear as leading terms in the derived asymptotic expansions. The analysis applies to a general class of Itô semimartingales that includes in particular Lévy-driven SDEs and time-changed Lévy processes. The asymptotic expansion results are subsequently used to construct a test for whether volatility jumps are of finite or infinite variation. In an application to high-frequency data of options written on the S&P 500 index, we find evidence for infinite variation volatility jumps.
Complexity vs Empirical Score
- Math Complexity: 9.2/10
- Empirical Rigor: 8.0/10
- Quadrant: Holy Grail — high math complexity, high empirical rigor
Why this score: This paper presents a sophisticated theoretical framework for joint asymptotic expansions in Itô semimartingales, backed by rigorous limit theorems. The empirical application to high-frequency S&P 500 option data provides strong statistical testing for the variation type of volatility jumps.
Research Flowchart
flowchart TD
A[Research Goal: Analyze High-Frequency Option Data & Test Volatility Jump Variation] --> B[Data Input: S&P 500 Index High-Frequency Option Data]
B --> C[Methodology: Derive Nonparametric Higher-Order Asymptotic Expansion]
C --> D[Joint Asymptotics Setup: Shrink Time Interval & Time Gap for Itô Semimartingales]
D --> E[Statistical Testing: Construct Test for Finite vs. Infinite Variation Volatility Jumps]
E --> F[Key Outcome: Evidence Found for Infinite Variation Volatility Jumps]