A more interesting type of financial derivative is an option that represents a contract sold by one party (called the option seller or writer) to another party (called the option buyer or holder). This type of contract offers the holder the right — but not the obligation — to buy or sell a security or another underlying financial asset such as stock, commodity, or currency at a specific date T in the future for a fixed price K.
There are many different type of options in the financial market. Here we only consider the basic types, namely:
- call options
a call option gives the holder the right, but not the obligation, to buy the underlying asset at a fixed price on a specific date; and - put options
a put option gives the holder the right, but not the obligation, to sell the underlying asset at a fixed price on a specific date.
The fact that the holder of an option contract has the option to exercise, rather than an obligation to do so, leads to the one-sidedness of the investment.
We can then go on to talk about 'vanilla options' and 'exotic options'. Again, it is important to realize that derivatives can be risky when used in isolation to speculate on the performance of underlying assets in the future. Equally, though, derivatives offer a flexible and efficient method of reducing risk when used in connection with the underlying assets. Effectively, they can be used as insurance against losses.
This example illustrates a case involving a call option.
An example of a call option
Suppose a property investor, Mr Li, is looking to buy some real estate. During his search, he notices someone is selling 10 houses for $1,000,000 each ($10,000,000 total). During this time, he also comes across a very interesting rumour. A friend of his who works in a government office tells him that there is talk of reducing the supply of land in the near future. Mr Li knows that if the land supply is reduced, the price of houses will skyrocket. But if the government provides more land than expected, he knows he'll be stuck with some property he didn't want.
Mr Li presents the seller of the houses with an interesting proposition: he will give her $1,000,000 to let him buy the houses within the next three months. If he decides to purchase, he'll pay the full $10,000,000. If he decides not to purchase, the seller can keep the money.
In other words, Mr Li's not buying the houses; he's buying the right to purchase the houses.
Solution
This would be referred to as a call option, because it allows Mr Li to buy within a given period of time. (A put option would allow him to sell within a given of time.)
The underlying asset would be the 10 houses, because that's what Mr Li would receive if the purchase took place. The other details of the option are as follows:
- The premium would be $1,000,000 because this is the amount he must pay to enter into the agreement.
- The strike price would be $10,000,000 because that's the price he'd pay the seller for the underlying asset.
- The expiration would be three months, which is the total period of time in which the agreement is valid.
If the rumour Mr Li heard proves true, he could exercise his option at the maturity date, and buy the houses for the agreed-upon price of $10,000,000.
Having worked through these examples, we are now going to generalize the difference between the European calls and puts and American calls and puts.
European calls and puts
European calls and puts are call and put options on a single underlying asset. The designation European means the holder may exercise the option only at the maturity time T.
- A European call option allows the holder the right to buy the stock at time T for a specified price X. The payoff to the long position is
- A European put option allows the holder the right to sell the stock at the maturity time for a specified price . The payoff to the long position is
American calls and puts
American calls and puts are also call and put options on a single underlying asset. The designation 'American' means the holder may exercise the option at any time on or before the maturity time T.
- An American call option allows the holder the right to buy the stock at time
for price X. The payoff to the long position is
- An American put option allows the holder the right to sell the stock at time
for price X. The payoff to the long position is
As you've learned in this section, investors and financial officers use derivatives to reduce the risk on transactions they need or want to make in the future. They pay a price for this, either in terms or options premiums, or in reduced potential gain. Speculators can use derivatives to speculate on future price movements of an asset without investing in that asset itself. Derivatives can also be used as leverage instruments.
At the end of this section, it should be pointed out that we have been computing prices using an extremely simple stock model. Fortunately, our answers and our methods can be generalized to more realistic stock models in further studies.
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