EC3333 Notes09 - Notes No. 09 Options: Concepts, Values and...

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Unformatted text preview: Notes No. 09 Options: Concepts, Values and S Vl d Strategies Options are Derivative Securities Derivatives are securities whose prices are determined by or derived from the prices of other securities Options are derivatives Option contracts are written on common stock, stock indexes, foreign exchange, agricultural commodities, precious metals, and interest rates, etc What are the option contracts? Option Contracts An option gives its holder the right to p purchase or sell an asset at a specified p p price on or before some specified expiration date The specified price is Exercise or Strike price p p p The expiration date is also called Maturity date ate The price of the option is called Premium Holder and writer of an option Option Contracts: Call and Put A call option gives its holder the right to purchase ("call away from the writer") an ( call writer ) asset at a specified price on or before some specified expiration date A put option gives its holder the right to sell ( put ("put to the writer ) an asset at a specified writer") price on or before some specified expiration date Categorization by Profitability In the Money - exercise of the option would be profitable Call: market price>exercise price Put: exercise price>market price Out of the Money - exercise of the option would not be profitable p Call: market price<exercise price Put: exercise price<market price At the Money - exercise price and asset price are equal Categorization by Exercise Date American - the option can be exercised at any time before expiration (maturity) date European - the option can only be exercised on p (maturity) date y) the expiration ( Categorization by Underlying Assets Stock Options: use stock price as exercise price, involves delivery of stocks upon exercise Index Options: based on a stock market index such as S&P 500 or the NASDAQ 100. Use index value as exercise price do not price, require actual delivery, instead a cash settlement procedure is used Categorization by Underlying Assets Futures Options: the right to enter a specified future contract at a future price equal to the p q stipulated exercise price Future Contract obliges traders to purchase or sell an asset at an agreed-upon price (i.e. future Price) on a specified future date Categorization by Underlying Assets Foreign Currency Options: offers the right to buy or sell a quantity of foreign currency for a specified amount of domestic currency (exercise price) Interest Rate Options: Options on assets whose prices are determined by interest rate rate, including Treasure notes and bonds, Treasure bills, bills certificates of deposit etc deposit, Values of Options at Expiration - Calls Notation Stock Price = ST Exercise Price = X Payoff to Call Holder (ST - X) if ST >X 0 if ST < X Profit to Call Holder Payoff - Purchase Price Values of Options at Expiration - Calls Payoff to Call Writer - (ST - X) if ST >X 0 if ST < X Profit to Call Writer Payoff + Premium ayo e u Values of Options at Expiration - Puts Payoffs to Put Holder y 0 if ST > X (X - ST) if ST < X Profit to Put Holder Payoff - Premium Values of Options at Expiration Puts Payoffs to Put Writer y 0 if ST > X -(X - ST) (X if ST < X Profits to Put Writer Payoff + Premium Option Strategies Unlimited variety of payoff patterns by combining puts and calls with various exercise prices Popular ones: Protective Puts Covered C ll C d Calls Straddle Spreads Collars Protective Put Purchase of stock combined with a put option that guaranteed minimum proceeds equal to the put's exercise price Value of Protective Put Portfolio at Option Expiration Protective Put (at-the-money option) versus at-theStock Investment Covered Calls A combination of selling a call on a stock together with buying the stock Value of Covered Call Portfolio at Option Expiration Straddle A combination of buying both a call and a put on the same asset, each with the same exercise price and expiration date. The purpose is to profit from expected price volatility The investors who write straddles, selling both a call and a put believe the stock is less volatile. put, volatile They accept the option premium now, hoping the stock price will not change much before expiration Value of a Straddle Position at Option Expiration Spreads A combination of two or more call options (or put options) on the same asset with differing exercise prices or times to expiration. Vertical or Money spread: Same maturity Different exercise price Horizontal or Time spread: Different maturity dates A Bullish Spread Position A money spread in which one call option is bought at a lower exercise price, and a call with higher exercise price is written The holder benefits from price increase The value of a bullish spread position: An option strategy that brackets the value of a portfolio between two bound A collar is appropriate for an investor who has a target wealth goal but is unwilling to risk losses beyond a certain level Suppose your current wealth is $200,000.Your target level is $220,000 to buy an apartment, and you are unwilling to risk losing more than $20,000. A collar established by (a) b i 2,000 shares of ll bli h d b ( ) buying 2 000 h f stock @ $100/share, (b) buying 2,000 puts with exercise $90, and (c) writing 2,000 calls with $90 2 000 exercise $110. Collars PutPut-Call Parity To achieve a payoff with guaranteed minimum value but with unlimited upside p potential, two alternatives: Protective put: a stock position plus a put option on that position Call-plus-Bills: buying a call, in addition buying zero-coupon T-bills with face value y g p equal to the exercise price of the call, and with maturity date equal to the expiration of the option PutPut-Call Parity For both alternatives, when stock price is lower than the exercise price X, the p , value of the portfolio is X; while when stock price ST exceeds X the value is X, ST The two portfolios always provide equal values, they must cost the same amount to establish Otherwise arbitrage establish. Otherwise, PutPut-Call Parity X C S0 P T (1 rf ) The Put-Call Parity Theorem represents the proper relationship between put and p p p p call If the prices are not equal arbitrage will be equal, possible Put Call Parity: q p Disequilibrium Example Stock Price = 110 Call Price = 17 Put Price = 5 Risk Free = 5% Maturity = 1 yr X = 105 X C S0 P T (1 rf ) 117 > 115 Since the leveraged equity is less expensive, acquire the low cost alternative and sell the high cost alternative An Arbitrage Strategy Since the leveraged equity is less expensive, acquire the low cost alternative and sell the high cost alternative g Buy Protective put portfolio, sell call-plus-bill portfolio ...
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This note was uploaded on 10/30/2011 for the course ECON EC3333 taught by Professor Lu during the Spring '11 term at National University of Singapore.

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