MFIN 6663 Sobey School ofBusiness Saint Mary’s University Greg MacKinnon Options Options are an example of a type of security referred to as a derivative security. Derivative securities have no value in and of themselves, they only have value because they are in some way related to other securities. That is, they derive their value from another security. An option is simply a financial contract. One party writes the option and then sells it to another party. It gives the holder of the option the right, but not the obligation, to buy or sell (depending on the type of option) an asset at a fixed price, on or before a certain date. Note that the holder of the option is not obligated to do anything. If it would not be wise to use the option then he or she can throw it away. There exists an organized exchange for the trading of options, and the options market has developed its own lexicon: Definitions: 1. Call Option: This type of option gives the holder the right, but not the obligation, to buy an asset at a fixed price from the seller of the option (the seller of an option writes the option, and is referred to as the writer). 2. Put Option: This type of option gives the holder the right, but not the obligation, to sell an asset at a fixed price to the writer of the option. (Note that the writer of an option is obligated to fulfill his part of the contract if the holder desires to use the option. Thus, for a put option, if the holder wants to sell the asset at the fixed price, the writer must buy it. The same holds for a call option.) 3. Underlying Asset: This is the asset (most often a stock) on which the option is written. It is this asset that the holder of the option has the right to buy/sell. For example, an option written on a particular stock is referred to as a stock option. 4. Exercising the Option: This is the act of the holder using the option to buy/sell the underlying asset. 5. Exercise Price or Strike Price: The fixed price in the option at which the holder can buy/sell. This is set at the time the option is written and cannot be changed. 6. Expiration Date or Maturity Date: The option must be exercised on or before the expiration date. After this, it expires and becomes worthless. 7. Premium: The price paid to the writer in order to obtain the option. 8. a) American Option: This type of option (either put or call) can be exercised at anytime up to the expiration date. This is (by far) the most common type of stock option. b) European Option: This type of option (either put or call) can be exercised only on the expiration date. MFIN 6663 Sobey School ofBusiness Saint Mary’s University Greg MacKinnon Call Options Assume that someone writes a call option on Ford Motor Co. stock. The holder of the option has can buy a share of Ford at a strike price of $60 on or before June 30, 1995. Let the expiration date be T (equal to June 30 in this case). Let the price of the stock at time T be ST ( and the price is St at any other time). What is the value of the option at the expiration date? The value of the option will depend on S T . If ST $60; it is cheaper for the holder to buy the stock on the open market rather than use the option. The holder will therefore let the option expire without using it. The call is worthless. If ST > $60; the holder exercises the option and buys a share of Ford at $60, then sells it in the open market for ST to make a profit. The value of the call is this profit, (S T - 60). If, at any time during the life of the call option the stock price is greater than the strike price (S t > $60), the call is said to be in the money. That is, at the current stock price it would be profitable to exercise the option. If, at any time during the life of the call option the stock price is less than the strike price (S t < $60), the call is said to be out of the money. That is, at the current stock price it would not be profitable to exercise the option. If the stock price is equal to the strike price the option is said to be at the money. Also, at stock prices far above the strike the call option is deep in the money and deep out of the money if the stock price is far below the strike. Summary: Let K be the strike price of a call option. Value of a Call Option at the Expiration Date 0 , if ST K ST - K , if ST > K If ST K, then there is limited liability for the holder of the option. No matter how low the stock price goes, you cannot lose any more money. Graphically: Value of Call Option at Expiration ST K MFIN 6663 Sobey School ofBusiness Saint Mary’s University Greg MacKinnon This type of graph for options is termed a Bachelier diagram. Put Options Assume that someone writes a put option on Ford Motor Co. stock that allows the holder to sell a share of Ford on or before the expiration date, T, at a fixed price of K. What is the value of the put option on the day that it expires? If ST < K, the holder buys the stock on the open market at ST and sells it to the option writer (i.e. exercises the put) for K. The value of the put option is then (K - ST ). If ST K, the holder would be better off selling any stock in the open market rather than through the option. Thus the put option is worthless. Summary: Value of a Put Option at the Expiration Date K - ST , if ST < K 0 , if ST K Graphically: Value of a Put Option at Expiration K ST K Writing Options In every option there are two sides, the holder (or buyer) of the option, and the writer who is obligated to buy/sell the stock to the holder if the holder wishes. An option is really a zero-sum game in that whenever the holder of an option profits, the writer loses and vice versa. Thus, we can examine the value of writing an option in the same way as we looked at the value of owning an option. Graphically, the value of the writer’s position at the expiration date of the option is simply the mirror image of the holder’s position. MFIN 6663 Sobey School ofBusiness Saint Mary’s University Greg MacKinnon Value of Writing a Call at Expiration Date K 0 ST Value of Writing Put at Expiration Date K 0 ST K Note: The value to the writer is never greater than zero. Why does anyone write an option? The writer gets a price (the premium) for the option when it is sold and this premium is not seen on the diagrams. Thus, the writer hopes that the option finishes out of the money so that it is not exercised and the writer keeps the premium. MFIN 6663 Sobey School ofBusiness Saint Mary’s University Greg MacKinnon Bachelier diagrams can be drawn in terms of profit at expiration (rather than in terms of value, as we have done). In this way, the premium is included. where: C is the premium on the call P is the premium on the put Similarly, you can draw profit diagrams for writing calls and puts by shifting the diagrams up by the premium. Example: If you buy a call and it ends up that at the expiration date S T < K, you do not exercise. But you lose $C, the price that you initially paid for the option. If you wrote a call and ST < K, then you make a profit of $C as the call is not exercised and you keep the premium that was paid to you initially. The break-even points on the graphs above are those ending stock prices at which you would earn zero profits. For a call, the break-even point is (K+C). For a put, the break-even point is (K-P). Example: Consider a call option that you purchased last month that expires today. The option initially cost you $1.50. K = $20 ST = $21 C = $1.50 Since ST >K, it is best for you to exercise the option. However, even though you exercise (i.e. the option ends up in the money) you still lose money as: ST < K+C You get ($21 - $20) = $1 from exercising the option, but since you paid $1.50 for it you are really losing $0.50 (it is still beneficial to exercise, though, because if you do not you lose the entire $1.50).
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