VIX AND EUROPEAN OPTIONS WITH JUMPS IN THE SHORT-MATURITY REGIME

Battle Count: 81

Highly relevant for practitioners trading VIX derivatives and European options in jump-diffusion frameworks. The closed-form asymptotic formulas enable fast pricing and calibration for short-maturity options. The results clarify when jumps dominate (OTM) vs. when diffusion dominates (ATM), which is critical for hedging strategies. However, the short-maturity restriction limits direct applicability to longer-dated trading strategies. The paper is more theoretical/analytical than directly implementable for trading systems.

The asymptotic formulas involve integrals over jump size distributions (some closed-form, some requiring numerical quadrature), hypergeometric functions (Gauss 2F1), and Black-Scholes-type functions. The Eraker model predictions are relatively straightforward. The Kou-type model requires case distinctions based on log-moneyness. MC simulation validation requires Euler discretization of the jump-diffusion SDEs. The mathematical derivation is complex but the final formulas are tractable for implementation.

The paper provides complete mathematical derivations in the appendix, explicit model parameters in tables, and detailed MC simulation settings (number of paths, time steps, Euler scheme). All three jump models (Eraker, Kou-type, folded normal) are fully specified with parameter values. However, no code repository is provided.