Valuation of Variable Annuities with Equity Protection Swaps under Jumps and Default Risks

2026-05-25

AI Summary

This study addresses the pricing and hedging challenges of equity protection swaps (EPS) under joint exposure to market jump risk and counterparty default risk by proposing a unified framework that integrates the Merton jump-diffusion model with Szimayer’s independent stochastic time default model. Within this framework, the authors derive closed-form solutions for European options and establish the corresponding put-call parity relationship. They introduce a default-adjusted definition of the initial premium and quantify the residual unhedgeable loss arising from the interaction of jumps and default. Numerical experiments demonstrate that both jump intensity and default risk substantially affect hedging costs and premium levels, thereby confirming the necessity and effectiveness of jointly modeling financial crisis-induced jumps and credit risk for robust EPS risk management.

Abstract

This paper examines the valuation and hedging of standard equity protection swap (EPS) products proposed by Xu et al.. To account for financial crises and counterparty default risk, we develop pricing frameworks based on Merton's jump-diffusion model and Szimayer's independent random time default model, under which closed-form valuation formulas and put-call parity relations for European options are derived. Hedging strategies for EPS products are analysed under jump and default risks. While static hedging remains effective in the absence of default, counterparty default risk leads to residual losses that cannot be fully hedged. These losses are quantified and used to define default-adjusted initial premiums under both Black-Scholes and jump-diffusion settings. Numerical results illustrate the effects of jump characteristics and default intensity on hedging costs and premiums, highlighting the importance of incorporating crisis and credit risks in EPS pricing and risk management.

Problem

• Variable Annuities
• Equity Protection Swaps
• Jump Risk
• Default Risk
• Valuation

Innovation

• jump-diffusion model
• default risk
• equity protection swap
• static hedging
• closed-form pricing