Choquet-based European option pricing with stochastic (and fixed) strikes

This paper develops closed-form formulae for pricing European exchange options involving stochastic (and fixed) strikes under uncertainty based on the Choquet expected utility. We extend the benchmark models of Margrabe (J Financ 33:177–186, 1978) and Merton (Bell J Econ Manag Sci 4:141–183, 1973) using a modified pricing kernel and derive option “Greeks” and other option characteristics in an incomplete market with Choquet ambiguity. The Margrabe–Merton–Black–Scholes (MMBS) classical formulae are seen as special cases (under risk-neutrality) of our generalized framework under ambiguity/ignorance, suggesting that there could be multiple martingale-based option prices in the economy characterizing abnormally uncertain markets. We further show how standard option pricing properties (under risk) should be adjusted to account for investor ambiguity attitudes and heterogeneous beliefs (i.e., ambiguity aversion and seeking) and how such beliefs and attitudes can be extracted from observed option prices.