A new perspective for the use of financial derivatives to hedge foreign exchange rate: L-BFGS perspective to assess the strikes and principals of plain vanilla options

The international relationships between nations and economic agents have evolved so rapidly that the services and products are being traded almost instantly. Nevertheless, a great amount of these services and products are quoted in different currencies; thus, it is necessary the use of financial products to trade these products and services without incurring in unnecessary risks. The use of financial derivatives in the financial market has been increasing over the last decade. Moreover, foreign exchange derivatives have become an essential tool for companies to hedge their exposure in a foreign exchange currency. Nonetheless, there has not been enough research about methodologies that emphasize in the mixing of strategies. In this document, we develop a methodology to hedge effectively. Hence, we propose the Limited-memory bfgs in order to find the optimal percentage of the position of the derivative based on simulations created by a garch model. In this paper, we show an example with an exporting Colombian company based on Colombia, which has an exposure in us American Dollars. In this example, we find that the methodology proposed has a lower Value at Risk than a strategy using derivatives operating in isolation.