AN ANALYTICAL APPROXIMATION FOR THE ASSET-OR-NOTHING PUT OPTION

British asset-or-nothing put options are financial derivatives with an early exercise feature through which on payoff, the holder receives the best prediction of the European asset-or-nothing put payoff under the hypothesis that the true drift of the stock price is equal to a contract drift. In this paper, we develop simple analytic approximations for the optimal exercise boundary and also the option valuation, valid for short times to expiry — which is a very common feature of most options that are traded in the market. The approximations are in the form of series solutions in which explicit formulae for the coefficients are provided. This then efficiently yields rapid results. Empirical results demonstrate that the approximations provide accurate results for expiries at least up to 3 months.