Interest Rate Options and Convertible Bonds

• Interest rate options

• Profits and losses of interest rate options

• Put-call parity

• Option prices

• Convertible Bonds

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

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

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

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?

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

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

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

Put-Call Parity

• Buy the bond

• Sell a call option

• Buy a put option

• Long bond + short call + long put = 0

• Page 660

Option Price

Black-Scholes Model

page 662

Valuing futures options

page 668

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

Conversion Value

• Conversion value = market price of common stock * conversion ratio– Assuming stock price is $17, then conversion

value is $850.

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

Why Convertible Bonds?

• Stock price is low, selling stocks could dilute the price of the stock.

Exercises

• Chapter 27, problem 4

• chapter 19, Problem 6