DERI L4.pdf - DERIVATIVES AND RISK MANAGEMENT Warrants and Convertibles(Lecture 4 Matti Suominen January 2018 Example EQUITY AND BONDS AS DERIVATIVES

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DERIVATIVES AND RISK MANAGEMENT Warrants and Convertibles (Lecture 4) Matti Suominen January 2018
EQUITY AND BONDS AS DERIVATIVES Equity and bonds can also be seen as derivative securities of the underlying assets of a firm. Let A denote the value of the assets and B the face value of bonds. Equity payoff when the bond expires is: max {A - B; 0} Example: Shareholders payoff: B = 20 -10 -5 0 5 10 15 20 25 30 0 5 10 15 20 25 30 35 40 45 50 A ð Equity can be seen as a call option to the assets with a strike price equal to the face value of debt.
Risky debt payoff: min {A ; B} = B - max {B - A ; 0} = B - payoff to a put option on A with EX = B ð Debt holders write shareholders a default option! Example: Payoff to debt holders: B=20 -15 -10 -5 0 5 10 15 20 25 0 5 10 15 20 25 30 35 40 45 50 A
CONVERTIBLE SECURITIES We consider two types of convertible securities: 1. Warrants 2. Convertible bonds These are securities that can be converted into equity. 1. WARRANTS Warrants are options to buy shares of the company at some predetermined exercise price EX. The difference with regular call options is that warrants are issued by the firm itself, and that they trigger a new share issue when exercised. Hence, the main difference is dilution. Dilution occurs as the new shares are issued at an exercise price, EX, which is below the market price of the stock (warrants are not exercised if EX is larger than the market price of the stock).
Compare the payoffs from call options and warrants: Example : A firm has n s = 1m shares. The current value of assets is \$50m, u = 1.1 and d = 0.9. The risk free rate is 0%. A u = 55m A 0 = 50m A d = 45m One-period call option with EX= \$50 (= current share price): C u = max(55m/1m - 50,0) = 5 C 0 = C d = max(45m/1m-50,0) = 0
One-period warrant. Let the firm have issued n w = .5m warrants to buy shares at an exercise price of \$50. If the existing assets are worth 55m the warrants are exercised and the share price is: = S u ÷ ø ö ç è æ - + + = 0 , 50 5 . 1 50 * 5 . 55 max m m m m W u ( ) = + * - * + + æ è ç ö ø ÷ max . . . , 55 5 50 50 1 5 1 5 0 m m m m m m W 0 = ( ) = + - 1 1 5 55 50 0 m m m . max , = + n n n C s s w H W d = 0 The payoffs of the warrant are proportional to those of the call. Hence: W n n n C s s w 0 0 167 = + = . ?
2. CONVERTIBLE DEBT Convertible debt is debt that may be converted into equity at a predetermined price per share (the conversion price ).It may also be callable (the firm can call the debt at a predetermined price over a given period of time). The value of convertible debt is made of three separate components: - value as straight bond; - conversion value; - option value. a. Value of straight bond: value if never converted (B = 20). 0 5 10 15 20 25 0 5 10 15 20 25 30 35 40 A
n n n A D s D + 0 b. Conversion value: value if converted immediately. Let n s = existing shares n D = new shares issued with conversion Conversion value = CV A n D /(n s +n D )
c. Option value: value of the option to delay conversion. Total value Option value = + ì í î ü ý þ + max , n n n A D D s D TV A n D /(n s +n D ) CV D Total value
Example 1: Valuing a two-period callable, convertible bond.

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