Abstract

In Chapter 2, we have seen that options and derivative instruments present non-linear risks that are more difficult to assess and measure than for a long-only portfolio of stocks or bonds. Moreover, those financial instruments are traded in OTC markets, meaning that their market value is not known with certainty. These issues imply that the current value is a mark-to-model price and the risk factors depend on the pricing model and the underlying assumptions. The pricing problem is then at the core of the risk management of derivative instruments. However, risk management of such financial products cannot be reduced to a pricing problem. Indeed, the main difficulty lies in managing dynamically the hedging of the option in order to ensure that the replication cost is equal to the option price. In this case, the real challenge is the model risk and concerns three levels: the model risk of pricing the option, the model risk of hedging the option and the discrepancy risk between the pricing model and the hedging model. Therefore, this chapter cannot be just a catalogue of pricing models, but focuses more on pricing errors and hedging uncertainties.