ABSTRACT
This chapter focuses on risk management and hedging – two key reasons why financial mathematics is crucial to the financial industry markets. Unlike other textbooks which organize hedging strategies within different chapters based on the assets being hedged and the different hedging vehicles, this book organizes hedging strategies in this chapter according to two approaches: unit-value hedging and return-based hedging. Commonly used hedging strategies such as systematic risk (beta) hedging and duration hedging are return-based hedging. However, Greek letter hedging of options is based on unit-value hedging. Due to the underlying mathematics, the hedge ratio formulas are very similar: the portfolio’s target risk (e.g., beta, duration or Greek letter) minus the portfolio’s existing risk is in the numerator, while the hedging vehicle’s risk is in the denominator. Another similarity between the hedging approaches is that the calculation of duration and Greek letters both use partial derivatives. However, due to the different approaches mentioned above, Greek letter hedging weights are expressed as units of options, while duration hedging weights are expressed as percentages of the dollar value relative to the total dollar value. The chapter includes a project to practice constructing a hedge and to practice additional simulation.
