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No more replicating portfolios : a simple convex combination to understand the risk-neutral valuation method for the multi-step binomial valuation of a call option

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  • Roger MERCKEN

    () (Hasselt University, Faculty of Business Economics, KIZOK)

  • Lisette MOTMANS

    () (Hasselt University, Faculty of Business Economics, KIZOK)

  • Ghislain HOUBEN

    () (Hasselt University, Faculty of Business Economics, KIZOK)

Abstract

This paper covers the valuation, from beginning to implementation, of a European call option on a stock using the multi-step binomial model in a risk-neutral world. The aim is to introduce this model in a simple but rather unconventional way. The usual presentation of the risk-neutral valuation, see Hull (2009),among others, relies on replicating portfolios. For most practitioners, this technique looks rather mysterious. We present a new transparent analysis requiring no replicating portfolios. The new finding to understand why the risk-neutral pricing is consistent with investors being risk-averse is the notion of a convex combination.

Suggested Citation

  • Roger MERCKEN & Lisette MOTMANS & Ghislain HOUBEN, 2010. "No more replicating portfolios : a simple convex combination to understand the risk-neutral valuation method for the multi-step binomial valuation of a call option," EuroEconomica, Danubius University of Galati, issue 24, pages 64-71, March.
  • Handle: RePEc:dug:journl:y:2010:i:24:p:64-71
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    File URL: http://journals.univ-danubius.ro/index.php/euroeconomica/article/view/267/250
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    References listed on IDEAS

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    1. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
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    Keywords

    investments; stock; Black-Scholes; volatility;

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