Construction and Hedging of Equity Index Options Portfolios

ArXiv ID: 2407.13908 “View on arXiv”

Authors: Unknown

Abstract

This research presents a comprehensive evaluation of systematic index option-writing strategies, focusing on S&P500 index options. We compare the performance of hedging strategies using the Black-Scholes-Merton (BSM) model and the Variance-Gamma (VG) model, emphasizing varying moneyness levels and different sizing methods based on delta and the VIX Index. The study employs 1-minute data of S&P500 index options and index quotes spanning from 2018 to 2023. The analysis benchmarks hedged strategies against buy-and-hold and naked option-writing strategies, with a focus on risk-adjusted performance metrics including transaction costs. Portfolio delta approximations are derived using implied volatility for the BSM model and market-calibrated parameters for the VG model. Key findings reveal that systematic option-writing strategies can potentially yield superior returns compared to buy-and-hold benchmarks. The BSM model generally provided better hedging outcomes than the VG model, although the VG model showed profitability in certain naked strategies as a tool for position sizing. In terms of rehedging frequency, we found that intraday hedging in 130-minute intervals provided both reliable protection against adverse market movements and a satisfactory returns profile.

Keywords: Option Writing, Black-Scholes-Merton, Variance-Gamma Model, Delta Hedging, VIX, Equities (Index Options)

Complexity vs Empirical Score

• Math Complexity: 7.0/10
• Empirical Rigor: 8.5/10
• Quadrant: Holy Grail
• Why: The paper involves advanced mathematics including partial differential equations (BSM), Levy processes (Variance-Gamma), and Fourier transform methods, scoring high on math complexity. It is extremely rigorous empirically, using high-frequency 1-minute data (2018-2023), realistic transaction cost models, specific rehedging intervals (130 minutes), and comparative backtests against benchmarks, making it highly backtest-ready.

  flowchart TD
    A["Research Goal: Evaluate systematic<br>index option-writing strategies"] --> B["Data Collection:<br>S&P500 Options & Index 1-min data<br>2018-2023"]
    B --> C["Model Calibration:<br>BSM & Variance-Gamma Models"]
    C --> D["Hedging Engine:<br>Delta & VIX-based Sizing<br>130-min Rehedging"]
    D --> E{"Performance Benchmarks"}
    E --> F["Buy & Hold"]
    E --> G["Naked Option Writing"]
    D --> H["Cost Integration:<br>Transaction Costs"]
    H --> I["Outcome: Risk-Adjusted Metrics<br>BSM superior hedging<br>VG useful for naked sizing"]