Optimal market completion through financial derivatives with applications to volatility risk

TL;DR

This paper develops a simulation-based method to identify optimal derivatives for completing stochastic volatility markets, showing strangle options and volatility index derivatives as effective choices for market completeness.

Contribution

It introduces a new simulation approach for optimal derivative selection in stochastic volatility models and demonstrates the effectiveness of specific options for market completion.

Findings

Strangle options are optimal for equity market completion.

Volatility index derivatives can substitute long-term equity options effectively.

The proposed method accurately approximates optimal derivative strategies.

Abstract

This paper investigates the optimal choices of financial derivatives to complete a financial market in the framework of stochastic volatility (SV) models. We introduce an efficient and accurate simulation-based method, applicable to generalized diffusion models, to approximate the optimal derivatives-based portfolio strategy. We build upon the double optimization approach (i.e. expected utility maximization and risk exposure minimization) proposed in Escobar-Anel et al. (2022); demonstrating that strangle options are the best choices for market completion within equity options. Furthermore, we explore the benefit of using volatility index derivatives and conclude that they could be more convenient substitutes when only long-term maturity equity options are available.