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

Roger Mercken (), Lisette Motmans () and Ghislain Houben ()
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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

EuroEconomica, 2010, issue 24, 64-71

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.

Keywords: investments; stock; Black-Scholes; volatility (search for similar items in EconPapers)
Date: 2010
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