Dynamic hedging

Price risk on a security can be lowered through the use of derivatives. A long position in a certain stock be thus be hedged by taking a short position in a forward contract on the same stock. Since both deltas sum up to 0, delta equal to 1 for the stock and -1 for the forward, there is no change in the overall portfolio value when price changes in direction to whatever extent. Price risk can also be hedged through the means of options. In this case for example by selling call option. However, the delta of a call option is most likely not being equal to 1, except if it is very deep in the money. Therefore, it is needed to calculated the call option delta as explained in the greeks section. Thereafter, an amount of call options need to be sold until the total portfolio delta equals 0.

The effect of gamma

In contrast to forwards, option deltas change with respect to the underlying price. This is because the gamma which changes the delta of options. As a result of the gamma, the portfolio can become over or underhedged. Therefore, the option portfolio delta needs to be periodically recalculated and the exposure needs to be adjusted accordingly. Because of the required periodical rebalancing, the action of buying and selling options to make a whole portfolio delta neutral is called dynamic hedging. Specifically dynamic hedging means that when a stock increases in price, the option delta increases as well. When a long stock is hedged with short call, then it is required to buy back some calls in order to reduce the overall option portfolio delta. in contrast when a stock declines in value, more call options need to be sold such that the overall option portfolio delta equals -1.