Derivative Users Traders of derivatives can be categorized as hedgers, speculators, or arbitrageurs.

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1 OPTIONS THEORY Introduction The Financial Manager must be knowledgeable about derivatives in order to manage the price risk inherent in financial transactions. Price risk refers to the possibility of loss arising from commodity price, interest rate or currency rate fluctuations (interest rate + exchange rates are financial prices). Thus there is a need to hedge organizations against disruptive price fluctuations. The objective of the hedge is thus to reduce an asset s price risk by temporarily offsetting a current or expected position in the market for the asset with a matching but opposite position in futures, forwards or options. Derivatives can simply be defined as financial contracts whose value depends on the value of other financial claims (underlying asset). The value of futures and options is derived from the financial claims on which they are written. These contracts are sometimes referred to as contingent claims because their value is contingent on that of another claim. Financial derivatives include futures, options, interest rate swaps and forward rate agreements. 1 Some of the most common transactions include; hedging the cost of future financing, protecting the price of a financial asset to be sold in the future, reducing income volatility created by interest rate changes, and hedging a commitment to lend money in the future. Derivative Users Traders of derivatives can be categorized as hedgers, speculators, or arbitrageurs. Hedger A hedger is someone who, in a spot or cash market, is exposed to price or interest rate risk, and who wishes to secure protection against such risk by taking an opposite position by means of an option transaction. The hedger in acting to reduce such risks is prepared thereby to forego profits that may otherwise have accrued to him as a result of favorable price movements in the underlying asset market or markets. The hedger using forward exchange rates requires no initial payment whereas option contracts can be quite expensive. For example if you know you are to pay US$1 000 in 90 days. You are exposed to exchange rate risk as what you pay in Z$ then depends on the ruling exchange rate. To hedge against this risk you can enter into a long forward contract to buy $1 000 (at US$1 to Z$60) in 90 days for $ If indeed the exchange rate rises to 1:70, you end up Z$ better off if you hedge. However, if it falls to 1:50, you end up Z$ worse off. Thus the purpose of hedging is to make the outcome more certain but does not necessarily improve the outcome. However, you could buy a call option to acquire $1 000 at 1:60 in 90 days. If the exchange rate after 90 days proves to be above 1:60, you exercise the option and buy the $1 000 at 60, but if it proves to be below 1:60, you buy the US$1 000 in the market the usual way (and throw the option away since they are worthless). In this case you would have insured yourself against 1 Most of these are based on the money and capital market securities.

2 adverse exchange rate movements while benefiting from favorable movements, but at a cost though (you make an upfront payment to enter into the contract and this is the cost of the option) Speculators Speculators transact in options markets purely in the hope of realizing capital gains. Either they are betting that a price will go up or they are betting that it will go down. Forward contracts can ethically be used for speculation. In our example, if you believe that the US$ will increase in value relative to the Z$, you can speculate by taking a long position in a 90 day forward rate on forex. Suppose the anticipated scenario unfolds, say the exchange rate rises to 1:70 then you will be able to purchase US$1 for $60 when they are worth $70. Speculating by buying the underlying asset (in our case currency) in the spot market requires an initial cash payment equal to the value of what is bought. Entering into a forward contract of the same amount of the asset requires no initial cash payment. In practice however a deposit is required upfront to serve as a guarantee that the speculator will honor the contract. Speculating using forward markets therefore provides an investor with a much higher level of leverage than speculating using spot markets. The presence of speculators in the options markets to provide liquidity therein is considered vital for the effective functioning of these markets. Speculators are mainly professional traders and brokers trading for their own account. Arbitrageurs Arbitrage is the purchase and sale of the same asset in different markets. It involves looking in a risk-less profit by entering simultaneously into transactions in two or more markets. The objective of the arbitrageur is to profit without incurring risk by acting on price differentials that may arise from time to time in these separate but related markets. Arbitrage opportunities are a short run phenomenon, as prices in the two markets will quickly adjust to equilibrium due to the market forces of supply and demand. This is why most arguments concerning futures prices and the value of options are based on the assumption that there are no arbitrage opportunities. The transactions costs of arbitrage can eliminate the profit for a small investor. For example consider a stock traded on the ZSE at Z$400 and in London at a 100 pounds at a time when the exchange rate is Z$10 per pound. An arbitrageur can simultaneously buy 100 shares of Old Mutual for instances or NMB at the ZSE and sell them in London to obtain a risk free profit of 100 x ($100 x 10 - $400) = $ in the absence of transaction costs. Investors Options markets offer investors the opportunity to invest synthetically in financial and commodity markets via options as an alternative to investment in the actual physical asset or commodity as such. The advantage of high degree of investment leverage that is inherent in the options/futures mechanism acts as a strong incentive to investors to participate in these markets.

3 From a liquidity viewpoint it may also be easier to buy and sell options based on the price of shares than the shares themselves: the transactions costs relating to options may also be less than those on shares. OPTIONS Options on stocks were first traded on an organized exchange in 1973 and since then there has been a dramatic growth in options markets. The underlying assets include stocks, foreign currencies, debt instruments, & commodities. In the broadest sense an option may be described as the right or power, purchased or acquired, to buy or sell something at a price fixed beforehand, within a given time limit. The price in the contract is known as the exercise price or strike price while the date is known as the expiration date, exercise date or maturity date and this is the date on which the option may be exercised in terms of the option agreement. The fact that the option gives the holder the right and not the obligation to buy or sell the underlying asset clearly distinguishes options from forwards and futures. Types of Options What are stock options? A stock option is a contract that gives you the right -- but not the obligation -- to buy or sell a stock at a pre-specified price (the exercise price) within a pre-specified time, that is, until the option "expires." If the option gives you the right to buy shares of a stock, it is a call option. If the option gives you the right to sell shares of a stock, it is a put option. Exactly how much you should pay for these contracts is determined using the Black-Scholes Formula. Options are usually sold in sets of 100 (which would allow you to buy or sell 100 shares of the underlying stock at a certain price for the duration of the option). Call Options This contract gives the holder the right to buy the underlying asset by a certain date for a certain price. Assume that party A is offering options to sell a particular commodity at $5/kg at any time during the next 90 days. A is selling such options at 15c each. B a manufacturer who will need to purchase the commodity as a raw material during the next 3 months expects the commodity price to rise to $5,30/kg within this period. B accordingly buys a number of the commodity options from A in order to hedge himself against such a possible rise. 75 days later, B needs to purchase the commodity, the market price of which has, in the mean time, risen to $5,20/kg. B accordingly exercises his option, buying the commodity at $5/kg and B s net gain (ignoring transaction costs) is 5c per option (20-15c). This calculation ignores the time value of money.

4 Profit (c) Call Option Payoffs Option holder Option writer S k =500 Loss (c) The strike price is 500c and the break-even price is 515c 2 to both A and B. As long as the price of the commodity rise above the strike price B will exercise his option at such a price. However for a price between $5 and $5.15, B incurs a loss less than 15c per option (loss implied by not exercising the option). Below the strike price, the options held by B will be unexercised and he losses the entire premium he paid. Beyond the break-even price, B will exercise his option and the difference between that price and $5,15 represents a clear gain for B if he exercises his option at such a price. Therefore, as shown in the diagram, the holder s loss is a mirror image of the writer s gain and vice versa. For as long as the commodity market price does not rise above $5/kg or if it falls below $5/kg during the period, A s income from his sale of options to B will be his full premium of 15c per option. For the price between $5 and $5,15, and where B exercises his option, A s premium will be reduced by the difference between the strike price and the commodity price per option, since he will have to buy the commodity at a higher price in the market in order to sell it to B at $5,00/kg. Beyond the break-even price, A will incur a loss equal to B s profit should B choose to exercise the option. Such an option in which the right can be exercised at any time within a specified period at a named price is known as the American call option. Put A put option gives the holder the right to sell the underlying asset by a certain date for a certain price. In our previous example suppose now that B is the market maker i.e. he is offering options to buy the same commodity at the $5/kg, at any time during the next 90 days at 15c each. If A the supplier of the commodity expects the commodity price to fall to $4,80/kg within the next 3 months, A accordingly buys a number of these commodity options from B in order to hedge himself against such a decline in prices. 75 days later the commodity has indeed fallen to 2 Break-even price for call option =(strike price + cost of option)

5 $4,82/kg and A decides to exercise his option, and accordingly sells the commodity to B at the strike price, the realized profit is 3c per option. See figure (18-15)c Profit (c) Put Option Payoffs 15 - Option writer 10 - B s point of view Price of commodity -5 - (cents) A s point of view Option Holder S k =500 Loss (c) The strike price is 500c, and the break-even price is 485c to both A and B 3. The analysis is similar to the one under the call option, though this one is an opposite position. If the price does not fall below the strike price, A will not exercise his option in which case B s income will be his full premium of 15c per option 4. Below the strike price, A will exercise his option at that price (i.e. go to the market, buy at less than 500c & sell to B at 500c) 5. Up to the break-even price, A incurs a loss but less than the loss incurred if the option is not exercised e.g. at 495, A incurs a loss of 10c per option instead of the 15c he paid for the option. What happens to A is exactly the opposite of what happens to B, a loss of 10c by A is a profit of 10c by B. Below the break-even price the difference between the price and the break-even price represents a clear profit for A, if he exercises his option. This profit will reflect as a loss to B i.e. $4,85/kg less the price at which A exercises the option. Call and put options on any commodity, financial asset, currency; or similar underlying item will operate similarly. There are two kinds of stock options: American-type and European-type. American-type stock options allow you to buy or sell the shares of the underlying stock at the exercise price ("exercise" the option) any time until the option expires. European-type stock options allow you 3 Break-even price for put option =(strike price - cost of option) 4 The premium is the option writer s maximum income (compensation for taking risk) & it is the holder s maximum loss. 5 Remember that in options, it is always the holder who has the right to exercise the writer simply does as he/ she is told.

6 to exercise the option only at its expiration date. The formula we provide here applies to a European-type call option. You can buy and sell options just like stocks; their value is determined by the likelihood that they will be "exercised" for a payoff ("in the money"). You can calculate the exact value of the call option using the Black-Scholes Formula (if you know what you're doing, of course). A Successful European-Type Call Option Stock ABC is currently trading at $20/share. You pay a premium of $300 and purchase one European-type stock call option -- a contract that enables you to buy 100 shares of ABC at $25/share three months from now. Let's say that three months from now, the stock is trading at $30/share. At that moment, you may choose to exercise your call: Buy 100 shares at $25/share. You can then immediately sell those shares at $30/share. Your payoff in this exchange is $500. Subtract $300, the purchase price of the call option, and you made a net profit of $200 - not bad for an investment of only $300. In this scenario, you exercised your option "in the money": You were able to buy your stocks at a price lower than their current value. You also may sell the call to someone else before it expires. Let's say that one month after purchasing the call option, the stock is trading at $29. The value of the call option is now much greater than when you bought it, and you could sell it to someone. An Unsuccessful European-Type Call Option Stock ABC is currently trading at $20/share. You pay a premium of $300 and purchase one European call option -- a contract that enables you to buy 100 shares of ABC at $25/share three months from now. In three months, however, the stock is only trading at $23/share. In this case, buying the stock at $25/share would not be to your advantage. You can only hope that during the three months, you were able to sell the call option to another investor. As the expiration date approaches, however, the value of the call option decreases. If you don't sell the call option, and it expires in three months "out of the money," you would simply lose the $300 you had spent on the premium. Option Positions There are 2 sides to every option contract. One side is the investor who has taken the long position (i.e. has bought the option). On the other side is the investor who has taken a short position (i.e. has sold or written the option). The writer of an option receives cash upfront but has potential liabilities later. His profit or loss is the reverse of that for the purchaser of the option. Long position investor benefits if price goes up Short position investor benefits if price goes down The holder (buyer) of a call option hopes that the stock price will increase while the holder (buyer) of a put option hopes that it will decrease. From the holder s view, a call option is valuable if the stock price is higher than the strike price while a put option is valuable if stock price is lower than strike price.

7 Four basic option positions are possible A long position in a call option (holder expects asset price to go up) A long position in a put option (holder expects asset price to go down) A short position in a call option (writer expects asset price to go down) A short position in a put option (writer expects asset price to go up)

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