Mean-variance hedging strategies in discrete time and continuous state space

Resumo

In this paper we consider the mean-variance hedging problem of a continuous state space financial model with the rebalancing strategies for the hedging portfolio taken at discrete times. An expression is derived for the optimal self-financing mean-variance hedging strategy problem, considering any given payoff in an incomplete market environment. To some extent, the paper extends the work of Černý [1] to the case in which prices may assume any value within a continuous state space, a situation that more closely reflects real market conditions. An expression for the 'fair hedging price' for a derivative with any given payoff is derived. Closed-form solutions for both the 'fair hedging price' and the optimal control for the case of a European call option are obtained. Numerical results indicate that the proposed method is consistently better than the Black and Scholes approach, often adopted by practitioners.

Ficha do documento

Tipo

Artigo científico

Ano

2006

Instituição

Fundação Getulio Vargas

Fonte

Repositório da FGV

Idioma

Inglês

Acesso

Acesso aberto

DOI

10.2495/CF060111

Identificador

oai:repositorio.fgv.br:10438/25242

Palavras-chave

Discrete-time mean-variance hedgingOptimal controlOptions pricingComputer simulationOptimal control systemsProblem solvingState space methodsDiscrete time control systemsHedge (Finanças)Ativos (Contabilidade)Derivativos (Finanças)