Portfolio Sensitivity to the Changes in the Maximum and the Maximum Drawdown

In this article, we define new “Greeks” for financial derivatives: sensitivities to the running maximum and the running maximum drawdown of an underlying asset. Some types of portfolios, such as the net asset value of a hedge fund or performance fees are sensitive to these parameters. In order to illustrate the concept of the new “Greeks”, we derive probabilistic representations of sensitivities for two classes of financial contracts: forwards on the maximum drawdown and lookback options. These results allow us to interpret the delta-hedge of the contracts in a novel way.