T22.1 Chapter Outline

Chapter 22Options and Corporate Securities

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T22.2 Option Terminology

American option

Call option

European option

Exercising the option

Expiration date

Striking price

Put option

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T22.3 A Sample Wall Street Journal Option Quotation (Table 22.1)

LISTED OPTIONS QUOTATIONS -Call- -Put-

Option/Strike Exp. Vol. Last Vol. Last IBM 140 Feb 1 28 3/8 614 3/8

167 145 Feb 213 23 1/4 548 5/8

167 150 Feb 32 18 3/4 513 11/8

167 155 Feb 2242 14 4663 17/8

167 160 Feb 435 10 3/4 1544 31/4

167 165 Feb 2616 71/2 2083 5

167 165 Apr 145 111/8 200 8Monday, January 20, 1997

Reprinted by permission of The Wall Street Journal, 1997 Dow Jones and Company, Inc., Monday, January 20, 1997. All Rights Reserved Worldwide.

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T22.4 Value of a Call Option at Expiration (Figure 22.1)

Stock price

at expiration

(S1)

Call option value

at expiration

(C1)

S1 E S1 > E

Exercise price (E)

45°

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T22.5 Value of a Call Option Before Expiration (Figure 22.2)

Stock price

(S0)

Call price

(C0)

Exercise price (E)

45°

Lower bound

C0 S0 - E

C0 0

Upper bound

C0 S0

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Option Payoffs

What are the payoffs to buying 50 February 170 call contracts?

Each contract involves 100 shares, and hence options.

The closing price is $5 per option

The cost of the position is $5*100*50 = $25,000

What are the payoffs?

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Option Payoffs

Price of Option 5$ Exercise Price of Option 170$ Number of Contracts 50Price of Contract 500$ Cost of Investment 25,000$ Price of Stock 167$ Number of Stocks Bought 149.70Ending Stock Price Value of Contracts Net Profit (Loss) % Return Stock Value Net Profit (Loss) % Return

160$ -$ (25,000)$ -100.00% 23,952$ (1,048)$ -4.19%165$ -$ (25,000)$ -100.00% 24,701$ (299)$ -1.20%170$ -$ (25,000)$ -100.00% 25,449$ 449$ 1.80%175$ 25,000$ -$ 0.00% 26,198$ 1,198$ 4.79%180$ 50,000$ 25,000$ 100.00% 26,946$ 1,946$ 7.78%185$ 75,000$ 50,000$ 200.00% 27,695$ 2,695$ 10.78%

Mean 25,000$ -$ 0.00% 25,823$ 823$ 3.29%Standard Deviation 31,623$ 31,623$ 126.49% 1,400$ 1,400$ 5.60%

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T22.6 Five Factors That Determine Option Values (Table 22.2)

Factor Calls Puts

Current value of the underlying asset (+) ()

Exercise price on the option () (+)

Time to expiration on the option (+) (+)

Risk-free rate (+) ()

Variance of return on the

underlying asset (+) (+)

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T22.7 Terminology: Convertible Bonds

Conversion premium

Conversion price

Conversion ratio

Conversion value

Convertibility

Floor value for a convertible

Straight bond value

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T22.8 Minimum Value of a Convertible Bond (Figure 22.3)

Stock price

Minimum convertible bond value (floor value)

Straight bond value greater than conversion value

Conversion value

Straight bond value less than conversion value

Straight bond value

Convertible bond floor value

Conversion ratio

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T22.9 Value of a Convertible Bond (Figure 22.4)

Stock price

Convertible bond value

Straight bond value greater than conversion value

Conversion value

Straight bond value less than conversion value

Straight bond value

Convertible bond values

Conversion ratio

Floor value

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T22.10 The Case For and Against Convertibles (Table 22.4)

If Firm Does Poorly If Firm Prospers

Low stock price and no High stock price and conversion conversion

Convertible bonds issued instead of straight bonds

Convertible bonds issued instead of common stock

Cheap financing because coupon rate is lower (good outcome)

Expensive financing because firm could have issued common stock at high prices (bad outcome)

Expensive financing because bonds are converted, which dilutes existing equity (bad outcome)

Cheap financing because firm issues stock at high prices when bonds are converted (good outcome)

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T22.11 Other Options

Call provision on a bond

Put bonds

Green Shoe provision

Insurance

Loan guarantees

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T22.12 Chapter 22 Quick Quiz

1. What is the difference between a call option and a put option?

2. All else equal, which is more valuable to the holder, an American option or a European option? Why?

3. What is the “upper bound” value of a call option?

4. What is the relationship between the risk-free rate and the value of a call option? Explain.

5. What is the “floor value” of a convertible bond?

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T22.13 Solution to Problem 22.2

Option & Strike Calls Puts

NY Close Price Expiration Vol. Last Vol. Last

Sleight

74 70 Mar 230 3 1/2 160 1 1/8

74 70 Apr 170 6 127 1 7/8

74 70 Jul 139 8 5/8 43 3 3/8

74 70 Mar 230 3 1/2 160 1 1/8

Consider the following options quote.

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T22.13 Solution to Problem 22.2 (concluded)

a. Are the call options in the money? What is the intrinsic value of a Sleight Corp. call option?

The strike price is 70 and the value of the underlying stock is 74. The call options, therefore, (are/are not) in the money.

b. Are the put options in the money? What is the intrinsic value of a Sleight Corp. put option?

The strike price is 70 and the value of the underlying stock is 74. The put options, therefore, (are/are not) in the money.

c. Two of the options are mispriced. Which ones? At a minimum, what should the mispriced options sell for? Explain how you could profit from the mispricing in each case.

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T22.14 Solution to Problem 22.4

The price of Gyrostat stock will be either $75 or $95 at the end of the year. Call options are available with one year to expiration. T-bills currently yield 5 percent.

a. Suppose the current price of Gyrostat stock is $90. What is the value of the call option if the exercise price is

$70?

b. Suppose the exercise price is $90 in part (a). What would the value of the call option be?

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T22.14 Solution to Problem 22.4 (conclusion)

a. What is the value of the call option if the exercise price is 70?

The present value of the exercise price = $70/(1.05) = $66.67

S0 = PV exercise price + C0

$90 = $66.67 + C0

C0 = $23.33

b. Suppose the exercise price is $90 in part (a). What would the value of the call option be?

$90 = _____ + _____

C0 = $4.64

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T22.15 Solution to Problem 22.6

A one-year call option contract on the common stock of Isomer Partners Co. sells for $1,900. In one year, the stock will be worth $30 or $50 per share. The exercise price on the call option is $35. What is the current value of the stock if the risk-free rate is 8 percent?

S0 = _____ x $19 + _____/(1.08) = $53.11