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

Joanna Goard ()
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Joanna Goard: School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW 2522, Australia

International Journal of Theoretical and Applied Finance (IJTAF), 2025, vol. 28, issue 01n02, 1-12

Abstract: 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.

Keywords: British asset-or-nothing options; analytic approximations; optimal exercise boundary; free boundary problems (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0219024925500098

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