The super-replication problem via probabilistic methods
This paper deals with finding the minimal investment that is needed, in the presence of transaction costs, to super-replicate options using their underlying financial assets. The goal is to select, from all the portfolios that have values exceeding the payoff associated with the option, the one with the smallest initial value. Exclusively probabilistic methods are used. Both exotic and path-independent European and American options are considered. The main idea is that if an investor can super-replicate an option in a continuous-time model with transaction costs, then it is possible with even smaller initial investment to hedge a perpetual discrete-time related option in a market which is free of transaction costs where prices are martingales. The method is to study in a discrete-time shadow market that is free of transaction costs, where the options are perpetual. The advantage of the approach is that any trading strategies restrictions related to the bankruptcy condition are not imposed. Hedging with unlimited borrowing is allowed and still the best policy is buy-and-hold.
scientific article; zbMATH DE number 2005176