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Unformatted text preview: Economics 106V Investments : Lecture Note-9 Daisuke Miyakawa UCLA Department of Economics July 11, 2008 9th lecture covers the following items: (1) The concept of option contract, (2) a graphical demonstration of the payo/s from options, (3) several elementary option strategies, (4) Put-Call Parity, and (5) several option-like &amp;nancial objects. 1 What is Option? 1.1 Basic Idea of Option The purpose of this section is to introduce several basic concepts and characteristics of a basic &amp;nancial derivative - option. In short, option is a right to (i) buy or sell a security (e.g., equity), which is called as an originalunderlying security or asset, at (ii) a prepromised price, which is called as a strike or exercise price, (iii) by or on a predetermined date, which is called as a maturity, terminal, or expiration date. If the right is for buying a security, the option is called as a call option while it is called as a put option if it is for selling. And if the option buyer can exercise the option anytime until the predetermined date, the option is categorized as an American option while it is categorized as an European option if the option buyer can exercise it only on the predetermined date. Lets summarize the concept in a table: Characteristics (i) Call if the right to buy a security (i)Put if the right to sell a security (ii) Prepromised price (iii) American if the right can exercised anytime until the maturity (iii)European if the right can exercised only on the maturity There are two additional issues. First, there must be someone providing this option, who is called as an option writer (i.e., counter part of the option buyer). Heshe usually charges a price on the option, which is sometimes called as a premium of the option. Second, the transaction of the option is usually anonymous. 1.2 Notation Throughout this lecture note (and the next lecture note), we will use t and T as the period of evaluat- ingtransacting an option and the terminal period, respectively. X denotes the strike price and C ( t ) and P ( t ) stand for the price of a European call option and European put option. If we add a subscription &quot; a &quot; to the expression for the prices, those represent the prices of American options. The stock price at the period 1 t is S ( t ) and the riskless interest rate is denote by r f , which implies that we are assuming a &amp;at yield curve (why?). 2 A Graphical Demonstration Lets consider an European option for a while. We will see how the value of an option varies with the price of the original security on a maturity. 2.1 Call Option 2.1.1 A Starting Point: Buying a Call Suppose we can ignore the price of option (i.e., the payment of the option buyer to the option writer). This is as if the option buyer receives the option from the writer for free. Figure-1 summarizes how the payo/ from buying an European Call option is determined. First, the dotted 45 degree line maps the stock price on the maturity S ( T ) from the horizontal axis to the vertical axis. Note that from the denition, the stock pricefrom the horizontal axis to the vertical axis....
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This note was uploaded on 09/23/2008 for the course ECON 106v taught by Professor Miyakawa during the Summer '08 term at UCLA.
- Summer '08