Delta Hedging

The strategy undertaken by grantors of options to manage their exposure. The delta is the mechanism or mathematical formula used by option participants to measure the amount of gold to be bought or sold in order to hedge the exposure. The ‘delta variable’ is a measure of the probability of an option being exercised against the grantor and therefore dictates how much an option grantor must hedge to be covered or ‘delta neutral’.

The delta hedge is calculated on a basic model taking into account changes in the spot price, the time to expiry and the difference between the strike and spot prices. As the delta changes, so the grantor will either buy or sell metal.

.	PUTS			.	CALLS
	PUTS				CALLS
	IMMEDIATE ACTION	SUBSEQUENT ACTION			IMMEDIATE ACTION	SUBSEQUENT ACTION
	.	PRICE RISES	PRICE FALLS		.	PRICE RISES	PRICE FALLS
HOLDERS/ BUYERS	BUY	.	BUY		.	.	BUY
HOLDERS/ BUYERS	.	SELL	.		SELL	SELL	.
.					.
.					.
	IMMEDIATE ACTION	SUBSEQUENT ACTION			IMMEDIATE ACTION	SUBSEQUENT ACTION
.	.	PRICE RISES	PRICE FALLS		.	PRICE RISES	PRICE FALLS
GRANTORS/ WRITERS	.	BUY	.		BUY	BUY
GRANTORS/ WRITERS	SELL	.	SELL		.	.	SELL
.	PUTS				CALLS
.	PUTS				CALLS

Source: Merrill Lynch, London

The delta varies between 0 and 1. Deeply in-the-money options have a delta close to or equal to 1 because they are likely to be exercised; by contrast, the delta of a deeply out-of-the-money option will be close or equal to 0 as the option has little or no intrinsic value. The further out-of-the-money the options are at the time of granting, therefore, the lower the delta variable and the less the initial delta hedging. The closer into-the-money, the greater the delta hedging, with 50 per cent of the gold hedged if options are at-the-money.

In practice, how does it work? If an options dealer grants 100,000 ounces of out-of-the-money puts at a strike price of $275 when spot gold is $300, he will have sold the holder the right to sell him gold at $275. Potentially the dealer is long and must hedge. If the delta is 0.3, the dealer will immediately sell 30 per cent or 30,000 ounces into the market either spot or through a futures contract. He is now delta neutral.

If the spot price then fell, increasing the likelihood of the options being exercised, the delta might rise to 0.35, calling for a further sale of 5,000 ounces. If the spot price fell below the strike price, the put options would be in-the-money and the full 100,000 ounces should then have been sold. Conversely, if the price rose after the initial sale of 30,000 ounces, the options grantor would progressively buy back that gold as the puts fell further out-of-the-money.

Delta hedging on calls works in reverse, with the options grantor progressively buying if the calls look like being in-the-money. Thus the grantor of both put and call options will be a buyer of gold into price rallies and a seller into price falls to remain delta neutral. The increase in options volume has meant that delta hedging can have considerable impact on the gold price.

On the other side of this exchange, the option buyer need not necessarily delta hedge because the potential loss is limited to the premium paid for the original option. However, where a large options book is being run, the dealer himself will often be both a grantor and buyer of a range of options. Since the options are being bought not so much for price protection as for exposure to price volatility, the buyer will delta hedge. His/her action will be a mirror image of hedging by the options grantor.