Abstracts

In this paper, we investigate an optimization problem related to super-replicating strategies for European-type call options written on a weighted sum of asset prices, for example Asian or basket options. Firstly, we proved that in general, the optimal solution is non-unique. This observation is useful since it allows some flexibility to compose the optimal super-replicating strategies in a real market situation, which often has some constraints in trading. Secondly, a generalized optimization problem with random weights has been studied. Using these results, we derived optimal static super-replicating strategies for different kind of options in a stochastic interest rate setting. Thirdly, the co-existence of the comonotonicity property and the martingale property was studied. We have seen that in the case of a single underlying asset, they can co-exist and additionally a linear relationship of the underlying random variables was found in certain situations. However, there can also exist a contradiction between them. For Asian options e.g., the price of the optimal static super-replicating strategies may not be reached by the Asian option price.