Beyond Lognormal Sums: A Four-Moment Probability Framework for Basket and Spread Option Pricing

Battle Count: 74

The paper is directly relevant to quantitative trading desks that price and hedge basket and spread options, particularly in energy markets (crack spreads). The analytical formulas enable fast repeated valuation across strikes and maturities, which is essential for real-time pricing and risk management. However, the reliance on lognormal assumptions and historical (rather than implied) parameters limits direct applicability to live trading without calibration. The framework is most useful as a fast approximation layer within a broader derivatives pricing system.

The analytical formulas are explicit and closed-form once parameters are recovered. However, implementation requires: (1) solving nonlinear systems for four-moment matching (two equations for positive sums, one equation for signed proxy), (2) implementing admissibility checks and root-selection rules, (3) handling edge cases (p near 0 or 1, zero skewness), (4) computing high-order moments of correlated lognormal sums (up to fourth-order tensor products), and (5) numerical stability considerations (Cardano formula, floating-point cancellation). The core pricing formula is straightforward, but robust parameter recovery across diverse inputs requires careful numerical engineering.

The paper provides complete analytical formulas, explicit parameter tables for all six standard-basket benchmarks, detailed crack-spread inputs (volatilities, correlations, weights), and a clear step-by-step procedure. Monte Carlo benchmarks with standard errors are reported. However, no code repository is provided, and the nonlinear root-finding procedure requires careful implementation. Yahoo Finance data is publicly available but the exact extraction date and processing steps for the April 2020 anomaly are described but not fully automated.