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...