Dynamic hedging with stocastic differential utility
Data(s) |
17/11/2014
17/11/2014
22/05/2003
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Resumo |
In this paper we study the dynamic hedging problem using three different utility specifications: stochastic differential utility, terminal wealth utility, and we propose a particular utility transformation connecting both previous approaches. In all cases, we assume Markovian prices. Stochastic differential utility, SDU, impacts the pure hedging demand ambiguously, but decreases the pure speculative demand, because risk aversion increases. We also show that consumption decision is, in some sense, independent of hedging decision. With terminal wealth utility, we derive a general and compact hedging formula, which nests as special all cases studied in Duffie and Jackson (1990). We then show how to obtain their formulas. With the third approach we find a compact formula for hedging, which makes the second-type utility framework a particular case, and show that the pure hedging demand is not impacted by this specification. In addition, with CRRA- and CARA-type utilities, the risk aversion increases and, consequently the pure speculative demand decreases. If futures price are martingales, then the transformation plays no role in determining the hedging allocation. We also derive the relevant Bellman equation for each case, using semigroup techniques. |
Identificador | |
Idioma(s) |
en_US |
Publicador |
Escola de Pós-Graduação em Economia da FGV |
Relação |
Seminários de pesquisa econômica da EPGE |
Direitos |
Todo cuidado foi dispensado para respeitar os direitos autorais deste trabalho. Entretanto, caso esta obra aqui depositada seja protegida por direitos autorais externos a esta instituição, contamos com a compreensão do autor e solicitamos que o mesmo faça contato através do Fale Conosco para que possamos tomar as providências cabíveis. |
Palavras-Chave | #Stochastic Control #Recursive Utility #Hedging #Bellman Equation #Hedging (Finanças) #Equações diferenciais estocásticas |
Tipo |
Working Paper |