Combined Custom Hedging: Optimal Design, Noninsurable Exposure, and Operational Risk Management
Forthcoming in Operations Research
83 Pages Posted: 2 Feb 2021
Date Written: November 30, 2020
We develop a normative framework for the optimal design, value assessment, and risk management integration of combined custom contingent claims. A risk averse ﬁrm faces a mix of ﬁnancially insurable and noninsurable risk. The ﬁrm seeks optimal positioning in a pair of custom claims, one written on the insurable term, and another written on any listed index correlated to the noninsurable term. We prove that a unique optimum always exists unless the index is redundant, and show that the optimal payoﬀ schedules satisfy a design integral equation. We assess the ﬁrm’s incremental beneﬁt in terms of both an indiﬀerence value and an eﬃciency rating: this beneﬁt increases with the correlation of the index to the noninsurable term, and it decreases with the correlation of the index to the insurable term. Our hedge proves empirically relevant for a highly risk averse ﬁrm facing a market shock (COVID-19 pandemic). In the context of a newsvendor model featuring random price and demand, we show that: (i) integrating our optimal combined custom hedge with the corresponding optimal procurement policy allows the ﬁrm to obtain a signiﬁcant improvement in both risk and return; (ii) this gain may be traded oﬀ for a substantial enhancement in operational ﬂexibility.
Keywords: Integrated risk management, Noninsurable risk, Financial product design, COVID-19 pandemic
JEL Classification: C44, G22, G23, G32, D81
Suggested Citation: Suggested Citation