Derivatives

CHAPTER 18Stock Options and Stock Index Options

Aims

• To examine stock options and stock index options.
• To show how you can provide a minimum (floor) value for a portfolio of stocks but also be able to capture most of the ‘upside’ if stock prices rise – this is a protective put.
• To show how you can hedge a portfolio of stocks using dynamic delta hedging.
• To show how several options (on the same underlying asset) can be combined to give a risk-free portfolio – this is a ratio spread.
• To demonstrate how you can make a profit from mispriced options, while hedging any changes in market risk.

We have seen in Chapter 17 that investors can use stock options to speculate on the direction of stock price changes and on changes in the volatility of stock returns. Investors can also insure or hedge a cash market position consisting of stocks held in a specific firm (e.g. 50,000 stocks in AT&T) or in certain specific industries (e.g. oil industry) or in a ‘market portfolio’ (e.g. S&P 500) by using various types of stock index options. First we discuss hedging using options on individual stocks and then using stock index options.

18.1 OPTIONS ON STOCKS

If you hold a number of stocks in one particular company (e.g. AT&T) you can alter or eliminate the (market and specific) risk, using options on this stock.

18.1.1 Static Hedge: Covered Call

A static hedge assumes the initial options positions are held to maturity. Suppose an investor holds AT&T stocks. She can offset some of the downside ...