Recovering Risk-Neutral Moments from Options

Battle Count: 50

Highly relevant for quantitative trading in derivatives markets. The projection method provides a practical, model-free way to estimate risk-neutral moments (variance, skewness, kurtosis, covariance, correlation) from traded options, which are essential inputs for: (1) VIX/SVIX-based trading strategies, (2) cross-currency tail risk hedging, (3) multi-asset portfolio construction, (4) equity premium estimation, and (5) central bank event-driven trading. The 28% reduction in out-of-sample hedging error vs. CM and the ability to work with sparse strike grids (5 strikes) make it directly applicable to OTC FX options trading. The contagion decomposition framework is useful for macro-event trading strategies.

The univariate projection is straightforward: construct the payoff design matrix, solve weighted least squares, and price using observed option prices. The multivariate extension requires handling change-of-numeraire for cross-currency options, constructing the joint state grid, and managing the larger basis. The VG calibration adds complexity. The constrained least-squares variant (for non-negative variance estimates) requires a convex QP solver. The ridge function spanning conditions and FTAP proofs are theoretical and not needed for implementation. Overall, a competent quantitative developer could implement the core method in 1-2 weeks, but the full multivariate FX application with proper numeraire handling and VG calibration would take longer.

The paper provides detailed mathematical formulations, algorithmic steps, and simulation parameters (AFT model calibration in Table 4). However, the empirical application relies on proprietary Bloomberg OTC FX option data and OptionMetrics S&P 500 options data. The Internet Appendix contains full proofs and additional simulation details. The projection method itself is straightforward to implement (weighted least squares), but the VG calibration and multivariate implementation require careful attention. No code repository is mentioned.