Maturity Risk for Variational Hedge with Composed Risk Measure

Maturity Risk for Variational Hedge with Composed Risk Measure

• Autor
• João Ramos Jungblut
• Co-autores
• Marcelo Brutti Righi
• Resumo

• We study the maturity risk of contingent claims based on convex risk measures combined with utility functions, allowing the solution of an optimal hedging problem equivalent to the dual of a decision under variational preferences. Our analysis starts from the construction of the Profit-and-Loss of the hedged contract over time, defined as the financial result of the difference between a self-financing portfolio and the derivative price, quantifying the residual risk that cannot be eliminated even under the optimal strategy. The proposed approach formalizes this by including a temporal dimension in addition to its spatial nature; we analyze the properties, its induced acceptance set, and obtain its dual representation. For numerical estimation, we solve the optimal hedging problem and introduce a version of the stochastic maximum principle applied to risk measures. We conduct a numerical analysis for the construction of the maturity risk surfaces by magnitude, moneyness, and time.

• Palavras-chave
• maturity risk; optimal hedging; composed risk measures; stochastic control; market incompletness.
• Modalidade
• Comunicação oral
• Área Temática
• Engenharia Financeira

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