Interest Rate Options and
Convertible Bonds
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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
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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
Chapters 27 & 19