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A closed form approach to valuing and hedging basket options

Author

Listed:
  • Svetlana Borovkova

    () (Delft Institute of Applied Mathematics Delft University of Technology)

  • Ferry Permana

    (Delft University of Technology)

Abstract

We develop a new approach to valuing and hedging basket options. We consider baskets of assets with potentially negative portfolio weights (spread options are a subclass of such basket options). The basket distribution is approximated using a generalized family of log-normal distributions. This approximation copes with negative basket values as well as negative skewness of the basket distribution, and it provides closed formulae for the option price and greeks. Numerical simulations show our approach provides a very close approximation of the option price, and performs remarkably well in terms of the hedging error. We analyze the option price sensitivities with respect to the assets' volatilities and correlations; and explain the seemingly paradoxical phenomenon of negative volatility vegas

Suggested Citation

  • Svetlana Borovkova & Ferry Permana, 2006. "A closed form approach to valuing and hedging basket options," Computing in Economics and Finance 2006 54, Society for Computational Economics.
  • Handle: RePEc:sce:scecfa:54
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    More about this item

    Keywords

    basket options; log-normal approximation; closed formula; hedging; greeks; correlation; vega risk;

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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