Derivatives Models on Models

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Option Pricing and Hedging from Theory to Practice: Know Your Weapon III^*

I sometimes wonder why people still use the Black-Scholes formula, since it is based on such simple assumptions – unrealistic simple assumptions.

Fischer Black 1990

For an option trader an option formula can be seen as a weapon, it is a great tool if you know how to handle it. To really know how to handle it you need to know its ins and outs, its weakness and strengths. Here I will share my current knowledge on some of the most important aspects on option pricing and hedging. I will explain why the very basic option formula is so popular among option traders. I will take you on a journey from the “ancient” past to the present, and from theory to practice. In the end I will take you on a helicopter ride, so hopefully you also can see the forest for the trees. Let's go:

In an idealized fantasy world dynamic delta hedging removes all the risk all the time, but what about the real world? This chapter takes a look at the history as well as the robustness of option pricing and dynamic delta hedging. As we will see the Black-Scholes-Merton idea of dynamic delta hedging is far from robust in practice. Does this mean dynamic delta hedging is dead? Not at all, as I will show dynamic delta hedging is removing a lot of risk compared to not hedging at all. However options are extremely risky instruments, and even after removing a lot of risk there is more than enough risk left. That is in practice dynamic delta hedging ...