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.

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.