Three options are roughly enough - Variance-optimal semi-static hedging in the rough Heston model

By Paolo Di Tella, Martin Keller-Ressel, Beatrice Ongarato

Rating

1818
Battle Count: 50

Relevance

8/10
Highly relevant for derivatives desks and risk managers dealing with variance swaps and stochastic volatility products. The finding that 'three options are roughly enough' has direct practical implications for reducing transaction costs and operational complexity in hedging.

Implementation Complexity

9/10
High complexity. Requires implementing Volterra stochastic differential equations, Riccati-Volterra equations, Fourier inversion techniques, and multifactor approximations. Numerical stability and accuracy require careful tuning of discretization parameters.

Reproducibility

3/5
The paper provides detailed mathematical derivations, parameter tables (Table 1, Table 2), and specifies the numerical methods (Euler scheme, Monte Carlo, quadrature rules, specific Python packages like pymittagleffler). However, no public code repository URL is provided in the text.

Abstract

This paper studies semi-static variance-optimal hedging of variance swaps in the rough Heston model under a risk-neutral measure. We combine dynamic trading in the underlying asset with static positions in a finite basket of European options, with the aim of minimizing the variance of the residual hedging error. Exploiting the Markovian lift provided by the forward variance curve, the Fourier representations of the claims and the Laplace transform characterization of the log-price, we derive semi-explicit formulas for the optimal strategies and the hedging error. We then study the optimal claim selection problem, investigating numerically how the choice of static instruments depends on the Hurst index. Under standard parametrization, we discover that "three options are roughly enough", i.e. adding three static vanilla options reduces the hedging error by more than 95% relative to the purely dynamic hedge for all considered roughness regimes H= 0.1, 0.3, 0.5.

Links

arXiv:2610.13543 ยท Paper rankings

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