December 2019
Beginner
912 pages
28h 36m
English
Content preview from Derivatives
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CHAPTER 27Delta Hedging
Aims
- To demonstrate simple delta hedging of calls and puts and the need for rebalancing.
- To show how dynamic delta hedging is used to protect the value of an options portfolio from (small) changes in the price of the underlying asset.
- To show that after dynamic delta hedging, you can close out your positions at any time and you will have neither gained nor lost money.
27.1 DELTA
A portfolio can be constructed so that any gain or loss from a small change in the option price (over a short interval of time) is offset by changes in the price of the underlying asset – this is delta hedging. Delta hedging applies to all kinds of options, where the underlying 
can be a stock price, stock index, commodity price, exchange rate, futures price, or an interest rate. The delta of a long call (which is written on one stock) is defined as:
Hence:
The delta of a long call 
is positive because a rise in the stock price leads to a rise in the call premium (Figure 27.1). Consider delta hedging a position in European call options. The value V of a portfolio consisting of
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