Dynamic hedging of conditional value-at-risk

• Published in: Insurance, mathematics & economics Vol. 51; no. 1; pp. 182 - 190
• Main Authors: Melnikov, Alexander, Smirnov, Ivan
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.07.2012; North Holland Publ. Co; Elsevier Sequoia S.A
• Subjects: Conditional value-at-risk; Contracts; Dynamic hedging; Hedging; IB10; IM01; IM10; IM53; Insurance; Investment strategies; Life insurance; Mathematical methods; Portfolio management; Put & call options; Quantile hedging; Risk assessment; Stochastic modeling; Stochastic models; Studies; Unit-linked contracts; IM53; IM10; Conditional value-at-risk; Quantile hedging; G22; IM01; G13; Dynamic hedging; IB10; Stochastic modeling; C61; Unit-linked contracts
• ISSN: 0167-6687; 1873-5959
• DOI: 10.1016/j.insmatheco.2012.03.011

In this paper, the problem of partial hedging is studied by constructing hedging strategies that minimize conditional value-at-risk (CVaR) of the portfolio. Two dual versions of the problem are considered: minimization of CVaR with the initial wealth bounded from above, and minimization of hedging costs subject to a CVaR constraint. The Neyman–Pearson lemma approach is used to deduce semi-explicit solutions. Our results are illustrated by constructing CVaR-efficient hedging strategies for a call option in the Black–Scholes model and also for an embedded call option in an equity-linked life insurance contract. ► We construct CVaR-optimal hedges subject to constraints on the initial wealth. ► We also discuss how to minimize hedging costs subject to a CVaR constraint. ► The approach is illustrated by deriving closed-form solutions in the Black–Scholes model. ► A practical application: CVaR-hedging a unit-linked life insurance contract.