Optimal hedging of stock options in Brazil

We consider the problem of hedging the market risk of options portfolios. There are several alternatives to this problem. Three possibilities are: stop-loss strategies, covered positions and dynamic hedging strategies (including delta hedging, delta–gamma hedging, delta–gamma–vega hedging, etc.). In this work we propose a dynamic hedging strategy that obtains the minimum-variance hedge using mixed-integer programming. We use as our case study the problem of hedging exotic stock options sold by a Brazilian financial institution. Mainly due to the huge volatility of the Brazilian stock and fixed-income markets, simple hedging approaches (such as delta hedging) are not recommended in the local market. Moreover, since there is a small number of liquid exchange-traded options, the hedging strategies available for Brazilian traders and risk managers are very limited. We comment on these as well as other operational difficulties when hedging options portfolios in Brazil.