Valuing Securities as Options

Question 1

What does the Black and Scholes formula express?

Answer 1

The value of a call option as a function of:
• Current price of the underlying asset
• Exercise price of option
• Time to maturity of option
• Rf interest rate
• Std of the return on the underlying asset

Question 2

What are the two approaches to price the debt?

Answer 2

• MM theorem

* Risk-neutral pricing

Question 3

How can the default/credit spread be computed as a function of?

Answer 3

• Leverage ratio
• Volatility of returns on underlying asset
• Debt maturity

Question 4

How can the risk-neutral default probability be computed as function of?

Answer 4

• Leverage ratio
• Volatility of returns on underlying asset
• Debt maturity

Question 5

What are the four ways stockholders maximize their wealth at the expense of bondholders?

Answer 5

• Dividend payout: increasing dividends significantly
• Claim dilution: borrowing more on the same assets
• Asset substitution: taking riskier projects than those agreed to at the outset
• Underinvestment: rejecting positive NPV projects and increasing the probability of default

Question 6

How to solve the problems where stockholders maximize their wealth at the expense of bondholders?

Answer 6

• Dividend payout: limits on dividends
• Claim dilution: restrictions on financing, security provisions
• Asset substitution: limitations on financial assets, max. leverage ratio or min. interest coverage ratio, convertible debt
• Underinvestment: restrictions on financing

Question 7

What is a convertible bond?

Answer 7

Corporate bond with a provision that gives bondholder an option to convert each bond owned into fixed number of shares of common stock

Question 8

What is the conversion ratio?

Answer 8

Number of shares received upon conversion of a convertible bond

Question 9

What is the conversion price?

Answer 9

Face value of convertible bond divided by number of shares received if bond converted

Question 10

When can we get the value of the convertible bond using the Black and Scholes model ?

Answer 10

• Promised payment on bond is F
• Maturity of bond is T
• Bond can be exchanged for a fraction α of firm’s equity
• Bond only debt outstanding

Question 11

What can be shown using the Black and Scholes model for any value of the convertible debt contract?

Answer 11

• Reducing exercise price of option or increasing number of shares obtained upon exercise, decreases F and risk of default, and the yield on debt
• Effect is stronger when volatility higher