Exact Barrier Option Valuation with Arbitrary Functions for the Volatility

Autores

  • Estevão Rosalino Jr.
  • Allan Jonathan Silva
  • Jack Baczynski Laboratório Nacional de Computação Científica - LNCC
  • Dorival Leão

DOI:

https://doi.org/10.5540/tema.2015.016.01.0061

Resumo

Focus, in the past four decades, has been obtaining closed-form expressions for the no-arbitrage prices and hedges of modified versions of the Europeanoptions, allowing the dynamic of the underlying assets to have non-constant pa-rameters.In this paper, we obtain a closed-form expression for the price and hedge of an up-and-out European barrier option, assuming that the volatility in the dynamicof the risky asset is an arbitrary deterministic function of time. Setting a con-stant volatility, the formulas recover the Black and Scholes results, which suggestsminimum computational effort.We introduce a novel concept of relative standard deviation for measuring the ex-posure of the practitioner to risk (enforced by a strategy). The notion that is found in the literature is different and looses the correct physical interpreta-tion. The measure serves aiding the practitioner to adjust the number of rebalancesduring the option’s lifetime.

Biografia do Autor

Jack Baczynski, Laboratório Nacional de Computação Científica - LNCC

Coordenação de Sistemas e Controle - CSCLaboratório Nacional de Computação Científica - LNCC

Referências

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Publicado

2015-05-29

Como Citar

Rosalino Jr., E., Silva, A. J., Baczynski, J., & Leão, D. (2015). Exact Barrier Option Valuation with Arbitrary Functions for the Volatility. Trends in Computational and Applied Mathematics, 16(1), 61–70. https://doi.org/10.5540/tema.2015.016.01.0061

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Artigo Original