Pricing Derivatives Under a Gains Tax Regime:New Impacts

Three years after the seminal work of Black and Scholes [3] on the pricing of European options,Scholes [18] presented a paper in which the impact of taxation on the value of an option is analyzed.We restart this discussion in a simple binomial setting emphasizing the economic principlesof replicating strategies under taxation. Two perspectives will be introduced. The first one focuseson replicating payoff structures if the underlying assets are taxed. The second one discusses the influenceof a tax system on a given contract specification. The limit results lead to a pricing formulain closed form suggesting a modification of the partial differential equation derived by Scholes [18].We claim that the value of the option is influenced by taxation even if gains of all relevant assets aretaxed with the same rate. Furthermore, we demonstrate that the difference between numerical andclosed form solutions are negligible in acceptable computing time. Thus the algorithmic schemescan be used as a base for pricing of complex options under taxation.