## Chapter 8. Optimal Hedging

After discussing the theoretical background in the previous chapters, we will now focus on some practical problems of derivatives trading.

Derivatives pricing, as detailed in *Daróczi et al. (2013)*, Chapter 6, *Derivatives Pricing*, is based on the availability of a replicating portfolio that consists of traded securities that offer the same cash flow as the derivative asset. In other words, the risk of a derivative can be perfectly hedged by holding a certain number of underlying assets and riskless bonds. Forward and futures contracts can be hedged statically, while the hedging of options needs a rebalancing of the portfolio from time to time. The perfect dynamic hedge presented by the **Black-Scholes-Merton (BSM)** model (*Black and Scholes, 1973*, *Merton, 1973*) has several limitations in reality.

In this chapter, we are going to go into the details of the hedging of derivatives in a static as well as a dynamic setting. The effects of discrete time trading and the presence...