THE PUT OPTION

Using Put Options in Volatility Trades

The long and short volatility trades described in Chapters 4 and 5 used combinations of call options and stock. In almost every exchange traded options market in the world, for every call option there is a put option. Put options can be used in volatility trades just as easily as call options. They have not been mentioned until now in order to keep the descriptions straightforward. In this chapter we introduce the use of put options and show that, to the volatility trader, they are indistinguishable from call options. We show that the price and price sensitivities of put options can be derived directly from those of call options. The prices of puts and calls are inextricably linked. If the price of one instrument becomes disconnected from the price of the other we will show how risk-free arbitrage profits can be generated irrespective of volatility considerations.

6.1 THE PUT OPTION

There are put options on commodities, currencies, stock indexes. futures and interest rates but, as with call options, for simplicity throughout this book we will refer to put options on stocks.

Definition A stock put option gives the right but not the obligation to sell a given quantity of stock at a given price on or before a given date.

The given quantity is fixed and is usually either 100 or 1,000. The given price is known as the exercise price or strike price and the given date is known as the expiry date.

In Chapter 3 we considered as an example a three-month IBM stock call option with an exercise price of $100. There will be a put option for every call option and so we will use the three-month $100 strike put option as an example and leave the issue of what the option cost until later. Consider the situation of the holder (i.e.

the individual long of the put) three months hence on the expiry date. The holder must decide what to do.

1. He can exercise his option and elect to sell IBM stock at the exercise price of

$100. If the market price of IBM shares are lower than $100 he would choose this option. If the stock price were say $94 he could buy 100 shares in the market and exercise his put option, forcing the other party to pay him the higher price of $100 per share. In exercising his option he has "put" stock on to someone else and made a profit of 100 - 94 = $6 per share or 6 X 100 = $600 per option contract. If the market price was even lower than $94, then the profit would be even higher.

2. He can choose not to exercise. If the stock is trading at $104 in the market then it clearly does not make sense to exercise his right to sell at $100. If he wanted to sell the stock he could sell it at a much better price in the market. In this situation he would let the option expire. He would choose this route if the stock price in the market were anything more than the exercise price of $100. In this situation the option would not have any final value at all and the put would expire worthless.

Table 6.1 and Figure 6.1 give the final value of the put option for various stock prices. One can see the attraction of puts to speculators taking a negative view on the stock market. The more the stock price falls, the higher the final put value. On first introduction it is easy to get confused about the purchase of put options.

When one buys a put option one is buying the right to sell something. It is the two conflicting aspects of the previous sentence that sometimes cause confusion— one buys to sell. It is easier sometimes to think of a put option as a contract that gives you a get-out clause. The put gives you the ability, it \ou so choose, to get rid of your stock holdings at a prearranged (vice. The put is like an insurance contract and the put price can be tin night of as simply the cost of insurance.

In point 1 above we calculated the expiring put value by assuming 'h.il the holder would go into the market, buy stock at $94, exercise

Table 6.1 Expiring value of put option with exercise price = $100

Stock price on expiry ($)

Value of put option on expiry ($)

90 10 X 100 = 1,000

92 8 X 100 = 800

94 6 X 100 = 600

96 4 x 100 = 400

98 2 x 100 = 200

100 0

102 0

104 0

106 0

108 0

110 0

his $100 strike option, pass on the stock and receive $100 per share. In practice this is often not necessary. As with calls, the put could be sold at its intrinsic price of $6, saving all the bother and costs associated with the share transactions.

We see that the expiring put option value profile (Figure 6.1) is a vertical mirror image of that of an expiring call option value profile given in Figure 3.1 and this characteristic leads on to some very simple relationships between the two instruments. Both have a discontinuity or kink at $100, both increase in value in one direction and both have

Figure 6.1 Put option value on expiry (exercise price = $100)

zero value in the other direction. Above the exercise price the put value line is horizontal and hence has stock exposure is zero. Below the exercise price the put value increases $100 for every $1 drop in stock price and so the stock exposure is short 100 units.

Put option terminology is similar to that of call options. The only difference is that a put option whose exercise price is above the current stock price is called in-the-money and one whose exercise price is below the current stock price is called out-of-the-money. So a $100 strike put option priced at $5 is in-the-money if the stock price is $97. In this example the intrinsic value of the put is $3 and the time value is $2. If an individual buys this put at $5 outright he is speculating that the stock price will fall. If the stock price falls to $75 by expiry then the put will be priced at $25. This is the attraction to the speculator. In this example the stock price fell only 25% whereas the put increased 400%.