What is Hedging?
Hedging is a term used in finance to describe the process of eliminating (or minimizing at best) the risk of a position. Typically, the risk referred to is the directional, or price risk, and the hedge is accomplished by taking the opposite view/position in a similar asset (or same asset traded elsewhere).
For example, take Vodafone stock. This is traded on the London Stock Exchange in GBP as Vodafone Group PLC (VOD.L) and also traded on America's NASDAQ in USD as Vodafone Group Public Limited Company (VOD). If you were long VOD in the US you could hedge your exposure to the company's stock price risk by shorting the same notional value of VOD.L in GBP. Your price risk would be reduced but you would now have exposure to currency and dividend risk.
The same concept applies to options when hedging the option delta; you remove the delta (position/price) risk by buying/selling the underlying instrument (stock, future etc).
Hedging Options Using Option Delta
As mentioned, Option Delta represents the relative price movement that an option will experience given a one point move in the underlying. The delta therefore results in a sort of proxy for the underlying stock; that is, the number itself tells you
the proportion of equivalent shares you are long/short.
Example: 10 call options on MSFT, where the option has a delta of 0.25, means you have effectively 250 shares in MSFT (10 * 0.25 * 100). Delta hedging this option position with shares means you would sell 250 MSFT stock to offset the 250 "deltas" of call options.
Example 2: 50 put options on AAPL, where the option delta is 0.85, means your effective position in the stock is short 4,250 shares (50 * -0.85 * 100). As you are short deltas, your hedge would involve buying 4,250 shares of AAPL stock.
The Gamma and the Delta
The tricky part when using the delta of an option to determine the hedge volume is that the actual delta value is always changing. You might sell 500 shares to hedge a delta value 0.50 but after your hedge, the market moves and the delta of the option now becomes 0.60. Now, your total position delta has increased to 100 meaning you will need to sell another 100 shares to square off the delta to zero. Let's go through an example.
1) Buy 10 call options on ABC with a delta of 0.544. Position delta = 544 (10 * 0.544 * 100)