Chapters 27 & 19 Interest Rate Options and Convertible Bonds Interest rate options Profits and losses of interest rate options Put-call parity Option prices Convertible Bonds

Chapters 27 & 19 Types of Interest-rate Options Options on physicals Futures options –Mechanics of trading futures options –Gives the buyers the right to buy from or sell to the writer a designated futures contract at a designated price at any time during the life of the option

Chapters 27 & 19 Futures Options Exercise futures options –In case of a call futures option, the option writer must pay the difference between the current future price and strike price –In case of a put futures option, the option writer must pay the amount that the strike price exceeds the current futures price –Example on 642 Margin requirements –For the buyer –For the seller

Chapters 27 & 19 Intrinsic Value The economic value of the option if it is exercised immediately Call option: the difference between the bond price and the strike price –In-the-money –Out-of-the-money –At-the-money Put option: the difference between the strike price and the bond price –In-the-money –Out-of-the-money –At-the-money

Chapters 27 & 19 Example of Intrinsic Value The strike price for a call option is $100. What is the intrinsic value when the current price is (1) $105, (2) $93? How about a put option?

Chapters 27 & 19 Time Value The amount by which the option price exceeds the intrinsic value –The option buyer hopes that at some time prior to expiration, changes in the market yield will increase the value of rights conveyed by the option. –Option price is no less than the intrinsic value –Never exercise it before expiration date

Chapters 27 & 19 Long Call A call option on a particular 8% coupon bond with a par value of $100 and 20 years and 1 month to maturity. The call option expires in one month and the strike price is $100. The option price is $3 Exhibit 27-1, page 647 – bond price. Exhibit 27-2, page 649 – net profit Exhibit 27-3, page 650 – profit/loss diagram Exhibit 27-4, page 651 – Long call/long bond

Chapters 27 & 19 Put Option Exhibit 27-6: profit/loss profile for a long put strategy Exhibit 27-7: profit/loss diagram for a long put strategy Exhibit 27-8: Comparison of a long put strategy and a short bond strategy

Chapters 27 & 19 Put-Call Parity Buy the bond Sell a call option Buy a put option Long bond + short call + long put = 0 Page 660

Chapters 27 & 19 Option Price Black-Scholes Model page 662 Valuing futures options page 668

Chapters 27 & 19 Convertible Bonds Convertible bond: a corporate bond with a call option to buy the common stock of the issuer. Conversion ratio: the number of shares of common stock that the bondholder will receive from exercising the call option of a convertible bond a conversion ratio of 10 allows its holder to convert one bond of par value of $1000 into 50 shares of stock Conversion price = par value/conversion ratio (at the issuance of a convertible bond) $20 of face value per share – conversion price

Chapters 27 & 19 Conversion Value Conversion value = market price of common stock * conversion ratio –Assuming stock price is $17, then conversion value is $850.

Chapters 27 & 19 Minimum Value of a Conversion Bond is the greater of 1.Its conversion value 2.Its value of corporate bond without the conversion option Example: page 435

Chapters 27 & 19 Why Convertible Bonds? Stock price is low, selling stocks could dilute the price of the stock.

Chapters 27 & 19 Exercises Chapter 27, problem 4 chapter 19, Problem 6