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Financial Markets & Instruments Chapter 7: Derivatives - Options 7.1 Introduction 7.1 Introduction Financial markets are often characterised by uncertainties such as recessions, depressions and changing political environments. In terms of markets where demand and supply determine the trading in that market, the characteristics of financial markets where the primary product is money, are unique. Because of these unique characteristics of financial markets, certain risks exist which do not exist in other markets and which must be managed. The management of these financial risks by means of derivative products has resulted in an evolution in financial markets in the past few years. The evolution in financial markets had a progressive influence on both the complexity and the available opportunities. Across the world, investors are offered a wide range of investment opportunities - some with great success, others not. Products to manage the risk of financial investments are developing rapidly. Volatile and uncertain financial markets continuously force portfolio managers to develop new instruments to hedge their portfolios. One such a derivative developed to hedge the risks involved in financial transactions and positions in financial instruments is an option. With an option the risk in a position or transaction can be transferred to another party by paying that party an amount (called a premium) for taking on the risk. 7.2 Working of option contracts An option contract has an exceptional characteristic distinguishing it from any other financial instrument - the holder or owner of an option has the right, but does not have an obligation to buy or sell an underlying instrument at a predetermined price during a specific period or at a specific time. If a person buys a Mercedes, and his best friend wants to buy the car from him, the owner can give his best friend the option to buy the car from him at the date when he wants to sell the car, at a certain price. There are two basic types of options:
The formal definition of a call option would be that it grants the buyer the right but does not confer an obligation to purchase a certain quantity of the underlying asset at a predetermined price. The price at which the purchase of the underlying asset will take place if the option is exercised is called the strike price, and this is decided at the initial closing of the option contract. The amount or-price paid for the option when the option is bought, is called the option premium. Likewise, a put option would grant the buyer the right but does not impose an obligation to sell the underlying instrument at a predetermined price. A further parameter of an option is the period that the holder has to exercise the option.
A call option can be illustrated as follows: A R1 million Eskom E168 American call option contract costing R10 000 with an expiry date on the first Thursday of May 1997, and a strike rate of 16,5%. From this strike rate the strike price for the bond (all-in price at the strike rate) can be calculated. The following important characteristics can be identified from this notation: i) option type (American call), ii) underlying instrument (E168), iii) option premium (R10 000), iv) expiry date (first Thursday of May 1997), v) contract size (R1 million), vi) strike rate (16,5%) from which the strike price can be calculated (the all-in price of the E168 bond at a yield of 16,5%). (See appendix 12 for an example of an option contract). 7.3 Parties and risks of option transactions The party that transfers the risk and pays the premium for the option is the buyer and holder of the option. The holder of an option can also sell this option to a new buyer, who becomes the new holder of the option. The original seller of the option is called the writer or grantor of the option and he stays liable to honour the option should the holder exercise the option. The writer of a call option will receive the option premium at the first sale. If the option is sold by a holder to a new buyer, a new premium will be determined, which is paid by the buyer to the seller. Because the writer of an option is bound to the contract until expiry, there is a credit risk attached to the option. An option written by a large corporate company will have less credit risk attached to it than an option written by an individual, because there is more certainty that the corporate company will perform if the option is exercised. The option with less credit risk will also trade more effectively in the secondary market. Options traded through exchanges such as SAFEX are normally guaranteed by the exchange in terms of settlement. 7.3.1 Call options The holder of a call option has paid a premium at acquisition of the option and the option gives him the right to buy an underlying instrument at a price determined in the option contract (the strike price) from the writer of the option. the holder of the option will only exercise the option if the current market price of the underlying instrument is higher than the strike price, giving him the opportunity to buy the instrument at the lower strike price, and sell the instrument at the higher market price. If the market price of the underlying instrument is lower than the strike price, it means that the instrument can be bought cheaper in the market than by exercising the option. The maximum loss for the holder of an option is thus equal to the premium paid for the option. The break-even point for the holder of an option is that point where the profit made on the underlying instrument is equal to the option premium paid. If the market value of the underlying instrument rises above the break-even point the holder starts making a profit on the option transaction, and the writer of the option starts taking a loss. The holder of an option is said to be long on a call option or to have a long position in a call option. The following is a graph of the profit and loss profile of a long call option with a strike price of A and a break-even price of B:
From this graph it can be seen that if the market value of the underlying asset is below price A, the holder of the option will not exercise the option, and the loss will be limited to the premium paid. Between the market price A and B, the loss of the holder will be the premium paid minus the profit on the underlying asset. Above market value B, the holder starts making a profit, and this profit is in theory unlimited. The writer of this call option has a different profit profile, opposite to that of the holder. The maximum profit that the writer can make is equal to the premium that he received when he wrote and sold the option. He will make this profit if the option is not exercised by the holder (in the case where the market price of the underlying asset is less than the strike price as can be seen from fig. 1). In the case where the market price of the underlying asset is more than the strike price of the option, the holder will exercise the option, and the writer will suffer a loss on the underlying asset. Where the loss on the underlying asset is equal to the option premium received by the writer, the break-even point (B in fig. 2) for the writer is found. If the market value of the underlying asset increases above the break-even point, the writer starts making a loss, as depicted in fig. 2. The writer of a call option can also be said to be short of a call option previous to the exercising or expiry of the option.
The holder of a put option has the right to sell an underlying instrument to the writer of the option at a predetermined price, and for this right he pays a premium on acquisition of the option. The holder of a put option will only exercise his option if the market value of the underlying instrument is below the strike price of the option. If this is the case, he can buy the underlying instrument in the market at the lower price, and sell the instrument to the writer of the option at the higher strike price of the option. If the market value is above the strike price, the holder can sell the underlying instrument in the market at a higher price, and will thus not exercise the option. In this case the holder will suffer a loss equal to the premium paid. The profit profile for the holder of a put option is shown in figure 3, where it can be seen that the break-even point (B) is the point where the profit on the underlying instrument is equal to the premium paid (A). If the market value of the underlying instrument decreases beyond B, the holder starts making a profit on the option.
For the writer of a put option, the income profile is opposite to that of the holder. The maximum profit to the writer is the premium that he received at the first sale of the option. If the market value of the underlying asset decreases beyond the strike price of the option, he will start making a loss on the underlying asset position until eventually beyond break-even point B where he starts to make a loss in total on the option. The writer is said to be short of a put option and his income profile is shown in Figure 4.
7.4 Option pricing and value The price of an option (called the premium paid for an option) is split into two different determinants: 7.4.1 Intrinsic value The intrinsic value of an option is the profit or loss that will be made on an option if the option is exercised immediately (ignoring the premium). This is the difference between the strike price of an option and the market value of the underlying asset. The intrinsic value could be positive, negative or equal to 0. Because an option premium cannot be negative, the effect of a negative intrinsic value on an option premium is limited to the amount that will decrease the option premium to 0. If the holder of an option will make a profit on the underlying position by exercising the option immediately, the option is said to be in-the-money and the intrinsic value is positive. This will be the case if:
If the holder of an option will suffer a loss on the underlying position by exercising the option immediately (ignoring the option premium), the option is said to be out-of-the-money and the intrinsic value is negative. This will be the case where
If the strike price is equal to the market value of the underlying instrument, the option is said to be at-the-money and the intrinsic value is 0. 7.4.2 The time value The time value of an option combines the parameters of an option that determines the possibility that the price of the underlying asset of the option will move so that the option becomes more valuable. These parameters can be summarised as:
The calculation of the value of these parameters are quite complex, and historic events and probabilities determine some parameters. The effect of these parameters will briefly be discussed. 7.4.2.1 The quantity of the difference between the strike price and the market value If the market value of an underlying instrument is far from the strike price, the likelihood of the option becoming at-the-money is less. A call option, for instance, where the market value is far below the strike price, is said to be deep-out-of-the-money. The probability of this option moving in-the-money or at-the-money is less than for a call option where the strike price and the market value is close together (assuming the same underlying instrument). The risk to the writer is more where the two prices are close together, and this risk will be discounted in the price of the option. 7.4.2.2 The time left to expiry The more time there is left to the expiry of the option contract, the more uncertainty there is concerning the movement of the market value of the underlying asset. This increases the risk, and the writer of the option has to be compensated for this risk (remember that derivatives is about selling risks!). The time value of the option, however, does not decrease over a straight line. During the last few days before expiry, the time value decreases faster, as there is less uncertainty about the probable market value of the underlying asset at expiry. 7.4.2.3 The short-term risk-free borrowing rate The writer of a call option must buy the underlying instrument and carry (hold) this instrument to expiry if he wants to hedge his risk in writing the option. To buy the instrument it is assumed that he either borrows the money at the short-term risk-free interest rate, or uses internal funds that will cost him the cost of capital from his business. The writer must thus be compensated for the cost of carrying the asset, and this cost will be incorporated in the price of the option. 7.4.2.4 The volatility of the underlying asset The volatility of an asset is a measure of risk involved in an asset due to price fluctuations of that asset. In general, the more the price of an asset is likely to fluctuate, the more volatile the asset. Volatility can only be measured by using historic values. Historic fluctuations of the price of an asset is thus used to determine a value for the volatility to be used as a parameter in deciding the price of an option. The market as a whole can sometimes be more volatile than at other times. In times of high volatility in the markets, options tend to be more expensive than in times of low volatility. 7.4.3 Valuation models used A few mathematical models were developed to calculate the value of options of which the most popular are:
7.5 OTC and exchange trading of options and warrants For a long time in South Africa, no formalised exchange existed where options could be traded. Options were traded in the informal or OTC market between parties. This resulted in non-standardised options being created and traded and consequently the secondary market was not as active as is the case with standardised options. Many options are still traded in the OTC market by telephone between dealers and players in the market. Standardised options, however, exist such as options on long bonds, which are quoted on computerised systems. The traders can see the bids and offers on standardised options on the screen and still close the deal by telephone or through an exchange for those options traded on exchanges. The financial exchanges and the JSE attempted to standardise certain options on instruments traded on the exchanges. Options are available on SAFEX on the futures traded on SAFEX (options on futures) and on certain individual shares. The trading of options on bond futures grew more than 300% in the first six months of 1997 compared to the first six months of 1996. The first effort at establishing traded options on the JSE was called the TOM (traded options market). This concept, however, did not succeed and subsequently other systems and procedures have been put in place. Warrants are now listed on the JSE and can be traded through the exchange. Warrants are long-dated call or put options written by certain banks such as Standard Bank. On the C1 Sasol warrant, for instance, ten warrants can be exchanged for one ordinary Sasol share on 15 June 2000 at a price (strike price) of 7000c per share. Options traded on exchanges differ in a few aspects from options traded OTC. Two of the main differences are:
The following is an example: On 1 Jan. Mr A buys a call option at a premium of R10 000. He sells the call option on 4 Jan. for R11 000 in the secondary market. The market values at the end of the day on the following dates are: 1 Jan. R10 500 2 Jan. R 9 000 3 Jan. R10 000 The following applies to the cash flow on an OTC and exchange basis:
7.6 Option strategies Options can be used to hedge certain risks attached to an open position, as previously discussed. They can also be used to create a position similar to that of holding the physical asset or being short in the physical asset. An advantage of using options to create such positions is that the cash flow outlay of acquiring an option is mostly much less than for buying or selling the physical asset (called the gearing effect). As an example, when buying a call option, the risk profile is similar to a long position in the underlying asset except that the loss is limited to the premium paid. A combination of physical positions and options can also be used to create the desired risk profiles. If a trader thinks that prices will go up but wants to limit his cash outflow and risks:
This strategy is called a bull spread (so called because the traders in instruments with the expectation of prices going up are called bulls). Figure 5 shows the income profile of a bull spread.
In the above example, the strike price of the call option was A and the strike price of the put option was C with the break-even price for this strategy at B. If the market value of the underlying asset is above B at the time the option is exercised, the trader taking this position will make a profit on the bull spread. The profit is, however, limited to the premium received for the put option. Thus with combinations of options, physical instruments and other derivatives, the desired income profiles can be created for different market situations.
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