An easy computable upper bound for the price of an arithmetic Asian option (Q1584514)

In an arbitrage-free complete market, the price of an arithmetic Asian option with \(n\) averaging dates is of the form \( E[ ( {1\over n} \sum_{i=1}^n S_{t_i} - K)^+ ] \). This is bounded from above by the price of a portfolio of European call options, namely \( {1\over n} \sum_{i=1}^n E[ ( S_{t_i} - k_i)^+ ] \), for any choice of \(k_i\) summing to \(nK\). By using results from [\textit{M. J. Goovaerts} and \textit{J. Dhaene}, Insur. Math. Econ. 24, 281-290 (1999; Zbl 0942.60008)] on comonotone random variables, this paper provides explicit formulae for the optimal choice of \(k_i\) in terms of the marginal distributions \(F_i\) of \(S_{t_i}\). In comparison to prices computed by simulation, the resulting bounds in the Black-Scholes model seem to be rather sharp.