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hat do we mean by Dynamic Hedging?

One of the most important concepts in quantitative finance is that of "dynamic hedging". Dynamic Hedging is also the title of Nassim Taleb's best selling textbook on trading and risk management of vanilla and exotic options.

Black-Scholes option pricing model tells us that a portfolio consisting of one option and minus delta shares at any point in time is risk neutral and should yield the risk free rate of interest. This is the principle of delta hedging. If we are long a call option then delta hedging means selling shares and if we are long a put option then delta hedging means buying shares (minus delta for put means buying shares because delta of a put is itself negative). In practice, of course, we cannot have minus delta shares to hedge an option at all times. Since stock prices change continuously we'll have to adjust the number of shares in our portfolio continuously, which is not possible (very frequent rebalancing of portfolio will anyway cost us a lot of money and we'll have to incur losses). Therefore, option traders rebalance their portfolio, i.e. delta hedge at discrete points in time only. This process is known as dynamic hedging.

1. de Weert, Frans, Exotic Options Trading (John Wiley & Sons, 2008)
2. Taleb, Nassim, Dynamic Hedging (John Wiley & Sons, 1999)

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