Delta hedging
With delta hedging or delta hedging refers to a hedging strategy that allows you an option position against price changes of the underlying hedged. To do this, a position is built up in the base value, the changes in value of which are exactly the opposite of the changes in value of the option position when the price moves.
The delta of an option position indicates how much the price of an option changes in absolute terms if the price of the underlying changes by 1 EUR. Holds an investor for example, 1,000 put options on a particular stock with a delta of 0.6 (with a subscription ratio 1: 1), so his options position loses 600 EUR in value when the underlying stock gains 1 EUR in value. The amount of −600 EUR is the product of the delta of −0.6, the business volume of 1000 shares and the price change of 1 EUR.
If the investor now buys 600 shares of the underlying share, the change in value exactly compensates for the change in the value of the option position. The investor has a delta hedge (“delta hedge”); its position is called delta-neutral.
The investor's counterparty - the option writer - has a positive delta of 0.6. He has to sell 600 stocks short for a delta hedge . In general, the following applies (see also long and short positions ):
- Purchase of a call option or sell a put option : Positive delta, delta hedge through short sales (short position) of the underlying
- Selling a call option or acquiring a put option: negative delta, delta hedging by buying (long position) the underlying
In addition to buying or selling the underlying asset on the cash market , delta hedging can also be carried out with a futures contract or a forward on the futures market .
With the procedure described, however, the investor has only hedged against small price changes in the underlying, since the delta of an option depends, among other things, on the price of the underlying (see gamma ). With the change in the delta of his option position, the investor must constantly adjust his delta hedging by buying or selling the underlying. This is why delta hedging is known as local or dynamic hedging.
For the seller of an option (writer) costs arise from the delta hedge: He must buy the underlying asset when its price has increased and sell it again when its price has decreased. This fact is synonymous with the fact that the gamma is negative for the writer (in financial jargon "short gamma"). For this, the writer received the option premium. Conversely, the option buyer earns profits from the delta hedge, but has paid the option premium for this.
literature
- John C. Hull : Options, Futures, and Other Derivatives. 9th edition, global edition. Prentice Hall International, Upper Saddle River NJ, 2018, ISBN 1-292-21289-6 , pp. 424-431.
- Wendy Pirie: Derivatives. John Wiley & Sons, Inc, Hoboken, New Jersey, 2017, ISBN 978-1-119-38181-5 , pp. 490-500.