Pricing and hedging American options in incomplete markets

Purpose – This paper sets out to consider the problem that the initial value of the American option is less than its fair price; this implies that the replication portfolio does not exist in the market. Design/methodology/approach – The paper develops an optimization model whose solution provides an optimal strategy for the writer to minimize the expected loss for this problem. Findings – The numerical results reveal that loaning money to construct a replication portfolio may not be an optimal strategy for the writer. Practical implications – The solution of the minimum expected loss model provides an optimal strategy to construct a lower expected loss portfolio. Originality/value – The numerical results reveal that loaning money to construct a replication portfolio may not be an optimal strategy for the writer.