Tail Risk Management with Puts and Trend Following: A CVaR Framework for Crashes and Drawdowns

Battle Count: 64

Highly relevant to quantitative trading and institutional risk management. The paper provides a rigorous mathematical framework for combining two widely-used tail-risk hedging technologies (put options and trend following) within a single optimization objective. The CVaR policy-gradient identity enables direct numerical optimization of hedge weights. The four-axis diagnostic framework provides actionable structure for hedge selection. The temporal separation of hedge mechanisms (puts for crashes, trend for drawdowns) is directly applicable to systematic hedging program design. The framework is theory-first but includes implementable numerical methods and a replication script.

High complexity due to: (1) continuous-time stochastic control with jump-diffusion and Heston volatility requiring viscosity solution theory for the HJB equation; (2) augmented Markov state space (wealth, spot, variance, trend signal); (3) marked-to-market option overlay modeling with elasticity and vega loadings; (4) CVaR policy-gradient computation with tail-conditional expectations; (5) Monte Carlo simulation with full-truncation Euler scheme for CIR variance; (6) grid search over hybrid weights with common random numbers. However, the reduced two-parameter policy class and the provided replication script lower the practical barrier for numerical implementation.

The paper includes a companion Python replication script (replication_tail_risk_management.py) implementing the full simulation pipeline including Heston-type variance with full truncation, finite-activity jumps, rolled Black-Scholes put proxies, EWMA trend signals, hybrid weights, CVaR curves, bootstrap standard errors, and projected-gradient illustration. All simulation parameters are explicitly stated in Table 2. However, the paper uses stylized inputs rather than live market data, and the option pricing uses a Black-Scholes proxy rather than full Heston-jump calibration, limiting exact reproducibility of production-level results.