## An easy computable upper bound for the price of an arithmetic Asian option.(English)Zbl 0964.91021

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 [M. J. Goovaerts and 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.

### MSC:

 91G20 Derivative securities (option pricing, hedging, etc.) 60E15 Inequalities; stochastic orderings 62P05 Applications of statistics to actuarial sciences and financial mathematics

### Keywords:

Asian options; stop-loss order; comonotonicity

Zbl 0942.60008
Full Text:

### References:

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