Option Markets: Introduction •Buy - Long •Sell – Short •Call –Holder has the right to purchase an asset for a specified price •Put –Holder has the right to purchase an asset for a specified price •Key Elements –Exercise or Strike Price •Specified price set in option contract –Premium or Price •Price of option –Maturity or Expiration •When to exercise an option • Option Terminology •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. • Call: market priceX • 0 if ST < X •Profit to Call Holder • Payoff - Purchase Price • Payoffs and Profits at Expiration - Calls • •Payoff to Call Writer • - (ST - X) if ST >X • 0 if ST < X •Profit to Call Writer • Payoff + Premium • Payoffs and Profits at Expiration - Calls Figure 20.3 Payoff and Profit to Call Option at Expiration bod30611_2003 Figure 20.4 Payoff and Profit to Call Writers at Expiration bod30611_2004 •A put options is the right to sell an asset •at the exercise price • •The holder will not exercise the option unless the asset •is worth less than the exercise price • •Payoffs to Put Holder • 0 if ST > X • (X - ST) if ST < X • •Profit to Put Holder • •Payoff - Premium Payoffs and Profits at Expiration - Puts •Payoffs to Put Writer • 0 if ST > X • -(X - ST) if ST < X • •Profits to Put Writer • Payoff + Premium Payoffs and Profits at Expiration - Puts Figure 20.5 Payoff and Profit to Put Option at Expiration bod30611_2005 Equity, Options & Leveraged Equity •Purchasing call option –Bullish strategy –Profit when stock prices are increase •Writing call option –Bearish strategy •Purchasing put option –Bearish strategy •Writing put option –Bullish strategy •Because option values depend on the price of the underlying stock, purchase of options may be viewed as a substitute to direct purchase or sale of a stock Investment Strategy Investment Equity only Buy stock @ 100 100 shares $10,000 Options only Buy calls @ 10 1000 options $10,000 Leveraged Buy calls @ 10 100 options $1,000 equity Buy T-bills @ 3% $9,000 Yield Equity, Options & Leveraged Equity IBM Stock Price $95 $105 $115 All Stock $9,500 $10,500 $11,500 All Options $0 $5,000 $15,000 Lev Equity $9,270 $9,770 $10,770 Equity, Options Leveraged Equity - Payoffs IBM Stock Price $95 $105 $115 All Stock -5.0% 5.0% 15% All Options -100% -50% 50% Lev Equity -7.3% -2.3% 7.7% Rates of Return Figure 20.6 Rate of Return to Three Strategies bod30611_2006 Option strategies Protective Put •Investing in a stock but with unwillingness to bear potential losses beyond some given level –Investing in stock with purchasing a put option on stock Table 20.1 Value of a Protective Put Position at Option Expiration bod30611_t2001 Figure 20.7 Value of a Protective Put Position at Option Expiration bod30611_2007 Figure 20.8 Protective Put versus Stock Investment (at-the-money option) bod30611_2008 Covered Calls •The purchase of a share of stock with a simultaneous sale of a call on the stock –The call is covered because the potential obligation to deliver the stock is covered by the stock held in the portfolio •Writing covered call options has been a popular investment strategy among institution investors •The written call guarantees the sale will occur as planned Table 20.2 Value of a Covered Call Position at Expiration bod30611_t2002 Figure 20.9 Value of a Covered Call Position at Expiration bod30611_2009 •A long straddle buying both a call and a put on a stock with the same exercise price •For investors who expect move a lot in price but are not certain about direction of the move •The straddle position will do well regardless of the outcome because its value is higher when the stock price makes extreme upward or downward move from X •The worst scenario for straddle is no movement in the stock price •Bets on volatility •Strips and Straps –variations of straddle Option Strategies Table 20.3 Value of a Straddle at Option Expiration bod30611_t2003 Figure 20.10 Value of a Straddle at Expiration bod30611_2010 Option Strategies •Spread is a combination of two or more call options (or two or more puts) on the same stock with differencing exercise prices or times to maturity •Some options are bought, sold or written •A money spread –Purchase of one option and the simultaneous sale of another with different exercise price •A time spread –The sale and purchase of options with differing expiration dates Table 20.4 Value of a Bullish Spread Position at Expiration bod30611_t2004 Figure 20.11 Value of a Bullish Spread Position at Expiration bod30611_2011 Option Strategies •Collars •Brackets value of portfolio between two bounds The Put-Call parity relationship •Protective put portfolio provides a payoff with guarantees minimum value, but unlimited upside potential • • • C + X / (1 + rf)T = S0 + P •Put-call parity theorem –Proper relation between put and call prices •If the prices are not equal arbitrage will be possible. • Put Call Parity •Stock Price = 110 Call Price = 17 •Put Price = 5 Risk Free = 5% •Maturity = 1 yr X = 105 • C + X / (1 + rf)T > S0 + P • • 117 > 115 • •Since the leveraged equity is less expensive, acquire the low cost alternative and sell the high cost alternative. • Put Call Parity - Disequilibrium Example Table 20.5 Arbitrage Strategy bod30611_t2005 •More general formulation of put-call parity •P = C – S0 + PV (X) + PV (dividends) • Optionlike Securities •Callable Bonds •Convertible Securities •Warrants •Collateralized Loans Callable Bonds •Corporate bonds are issued with call provisions –Issuer can buy bonds back from bondholders at some time in the future at a specified call price •Callable bond –Straight bond and concurrent issuance of a call option •Compensation for conveying this implicit call option to the firm –If callable bond is issued with coupon rate, it would sell at a lower price than the straight bonds •Difference would equal the value of the call –To sell callable bonds at par, firms must issue them with coupon rates higher than the coupon an straight debt Figure 20.12 Values of Callable Bonds Compared with Straight Bonds bod30611_2012 Convertibles Securities •Convertible preferred stock convey options to the holder of the security rather than to the issuing firm •Right to exchange each bond or share of preferred stock for a fixed number of shares of common stock, regardless of the market prices of the securities at the time •Most convertible bonds are issued “deep out of money” –Issuer sets the conversion ration so that conversion will not be profitable unless there is a substantial increase in stock prices or decrease in bond prices from the time of issue Figure 20.13 Value of a Convertible Bond as a Function of Stock Price bod30611_2013 Warrants •Call option issued by a firm •Exercise of a warrant requires the firm to issue a new share of stock – total number of shares outstanding increases •Warrants result in a cash flow to the firm when the warrant holder pays the exercise price –Warrants values will somewhat from the values of call options with identical terms •Issued in conjunction with another security – Collateralized Loans •Many loan arrangements require that the borrower put up collateral to guarantee the loan will be paid back –This arrangements gives an implicit call option to the borrower Exotic Options •Asian Options •Barrier Options •Lookback Options •Currency Translated Options •Digital Options Financial Engineering •One of the attractions of options is the ability they provide to create investment positions with payoffs that depend in a variety of ways on the values of other securities. •Index-linked certificate of deposit –Small position in index options •Guarantee a minimum rate of return the market fall • •The index-linked CD is clearly a type of call option –If market rises, the depositor profits according to the participation rate or multiplies –If the market falls, the investor is insured against loss •Bank offering these CDs –Writing call options –Hedge its position by buying index call •Multiplier bod30611_2015