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A General Approach to Hedging Options: Applications to Barrier and Partial Barrier Options

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  • Hans‐Peter Bermin

Abstract

In this paper we consider a Black and Scholes economy and show how the Malliavin calculus approach can be extended to cover hedging of any square integrable contingent claim. As an application we derive the replicating portfolios of some barrier and partial barrier options.

Suggested Citation

  • Hans‐Peter Bermin, 2002. "A General Approach to Hedging Options: Applications to Barrier and Partial Barrier Options," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 199-218, July.
    • Handle: RePEc:bla:mathfi:v:12:y:2002:i:3:p:199-218
    DOI: 10.1111/1467-9965.02007
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    Cited by:

    1. D'Auria, Bernardo & Salmerón Garrido, José Antonio, 2022. "An anticipative Markov modulated market," DES - Working Papers. Statistics and Econometrics. WS 34083, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. Leão, Dorival & Ohashi, Alberto, 2012. "Weak Approximations for Wiener Functionals," Insper Working Papers wpe_276, Insper Working Paper, Insper Instituto de Ensino e Pesquisa.
    3. Jér^me Detemple & Marcel Rindisbacher, 2005. "Closed‐Form Solutions For Optimal Portfolio Selection With Stochastic Interest Rate And Investment Constraints," Mathematical Finance, Wiley Blackwell, vol. 15(4), pages 539-568, October.
    4. Salmerón Garrido, José Antonio & Nunno, Giulia Di & D'Auria, Bernardo, 2022. "Before and after default: information and optimal portfolio via anticipating calculus," DES - Working Papers. Statistics and Econometrics. WS 35411, Universidad Carlos III de Madrid. Departamento de Estadística.
    5. Jos'e A. Salmer'on & Giulia Di Nunno & Bernardo D'Auria, 2022. "Before and after default: information and optimal portfolio via anticipating calculus," Papers 2208.07163, arXiv.org, revised May 2023.
    6. Yuji Hishida & Kenji Yasutomi, 2009. "Asymptotic behavior of prices of path dependent options," Papers 0911.5579, arXiv.org.
    7. Leão, Dorival & Ohashi, Alberto, 2010. "Weak Approximations for Wiener Functionals," Insper Working Papers wpe_215, Insper Working Paper, Insper Instituto de Ensino e Pesquisa.
    8. Tebaldi, Claudio, 2005. "Hedging using simulation: a least squares approach," Journal of Economic Dynamics and Control, Elsevier, vol. 29(8), pages 1287-1312, August.
    9. Bernardo D'Auria & Jos'e A. Salmer'on, 2021. "Anticipative information in a Brownian-Poissonmarket: the binary information," Papers 2111.01529, arXiv.org.
    10. Lim, Andrew E.B. & Wong, Bernard, 2010. "A benchmarking approach to optimal asset allocation for insurers and pension funds," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 317-327, April.
    11. D'Auria, Bernardo & Salmerón Garrido, José Antonio, 2021. "Anticipative information in a Brownian-Poisson market: the binary information," DES - Working Papers. Statistics and Econometrics. WS 33624, Universidad Carlos III de Madrid. Departamento de Estadística.

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