Semistatic Variance-Optimal Hedging with Self-Exciting Jumps

• 成果类型: Article; Early Access
• 署名作者: Callegaro, Giorgia; Di Tella, Paolo; Ongarato, Beatrice; Sgarra, Carlo
• 署名单位: University of Padua; Technische Universitat Dresden; Universita degli Studi di Bari Aldo Moro
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2024.0804
• 发表日期: 2025
• 关键词: affine; options; MODEL

摘要

The aim of this paper is to investigate a quadratic, that is, variance-optimal, semistatic hedging problem in an incomplete market model where the underlying log-asset price is driven by a diffusion process with stochastic volatility and a self-exciting jump process of the Hawkes type. More precisely, we aim at hedging a claim at time T > 0 by using a portfolio of available contingent claims so as to minimize the variance of the residual hedging error at time T. In order to improve the replication of the claim, we look for a hybrid hedging strategy of the semistatic type in which some assets are continuously rebalanced (the dynamic hedging component), and for some other assets, a buy-and-hold strategy (the static component) is performed. We discuss in detail a specific example in which the approach proposed is applied, that is, a variance swap hedged by means of European options, and we provide a numerical illustration of the results obtained.