The role of dynamic hedging

Most of the time, replication is a dynamic strategy. You should do more or less trading almost continuously during the lifetime of the derivatives. Haug (2007b) shows that the hedging error of non-continuous hedging could be significant even for plain vanilla options. Anyway, continuous hedging is a huge effort, which is often not seen explicitly in the pricing formulas; however, most pricing functions are based on the assumption that dynamic hedging should be done in the background properly all the time. This is also the case whenever we talk about risk-neutral world or the risk-neutral pricing. For further references, see Wilmott (2006).

Luckily, no matter how hard dynamic hedging could be, running an option book is at least a scalable business; hedging thousands of options is not much more difficult than hedging just a couple of them. All options can be decomposed into certain sensitivities, the so-called Greek letters (or simply Greeks). This nickname came...