电子科技大学：《金融学基础》（英文版）Chapter 16: The Valuation of Contingent Claims

Finance School of management Chapter 16: The Valuation of Contingent Claims Objective To explain the theory and application of the Contingent-claim valuation method uesTc

1 Finance School of Management Chapter 16: The Valuation of Contingent Claims Objective •To explain the theory and application of the Contingent-claim valuation method

Finance School of management Chapter 16 Contents Contingent Claims Analysis of Corporate Debt and equity : Convertible bonds valuing Pure State- Contingent Securities uesTc

2 Finance School of Management Chapter 16 Contents ❖ Contingent Claims Analysis of Corporate Debt and Equity ❖ Convertible Bonds ❖ Valuing Pure State-Contingent Securities

Finance School of management Objectives To show how the option pricing method can be applied to pricing of contingent-claims uesTc

3 Finance School of Management Objectives ❖ To show how the option pricing method can be applied to pricing of contingent-claims

Finance School of management Valuation of uncertain cash flows CCA/DCF The dCf approach discounts the expected cash flows using a risk-adjusted discount rate .s The Contingent-Claims Analysis(CCa)uses knowledge of the prices of one or more related assets and their volatilities uesTc

4 Finance School of Management Valuation of Uncertain Cash Flows: CCA / DCF ❖ The DCF approach discounts the expected cash flows using a risk-adjusted discount rate ❖ The Contingent-Claims Analysis (CCA) uses knowledge of the prices of one or more related assets and their volatilities

Finance School of management An Example: Debtco Corp Debtco is in the real-estate business It issues two types of securities common stock(I million shares) corporate bonds with an aggregate face value of $80 million( 80,000 bonds, each with a face value of $1,000) and maturity of 1 year risk-free interest rate is 4% :o The total market value of Debtco is $100 million uesTc

5 Finance School of Management An Example: Debtco Corp. ❖ Debtco is in the real-estate business ❖ It issues two types of securities: – common stock (1 million shares) – corporate bonds with an aggregate face value of $80 million (80,000 bonds, each with a face value of $1,000) and maturity of 1 year – risk-free interest rate is 4% ❖ The total market value of Debtco is $100 million

Finance School of management Debtco: Notation y be the current market value of debtco 's assets ($100 million) V, be the market value of Debtco's assets a year from now e be the market value of debtco's stocks d be the market value of debtco's bonds uesTc

6 Finance School of Management Debtco: Notation – V be the current market value of Debtco’s assets ($100 million) – V1 be the market value of Debtco’s assets a year from now – E be the market value of Debtco’s stocks – D be the market value of Debtco’s bonds

Finance School of management Two Ways to Think about the Debtco's Market value To think of the assets of the firm real estates in Debtco's case, as having a market value of $100 million .o To imagine another firm that has the same assets as debtco but is financed entirely with equity, and the market value of this all-equity-financed twin of Debtco is $100 million uesTc

7 Finance School of Management Two Ways to Think about the Debtco’ s Market Value ❖ To think of the assets of the firm, real estates in Debtco’s case, as having a market value of $100 million ❖ To imagine another firm that has the same assets as Debtco but is financed entirely with equity, and the market value of this all-equity-financed “twin” of Debtco is $100 million

Finance School of management Payoffs for Bond and stock Issues 120 100 各80 E60 Bondvalue Stockvalue 0 0 20406080100120140160180200 Value of Firm(Millions) uesTc

8 Finance School of Management Payoffs for Bond and Stock Issues 0 20 40 60 80 100 120 0 20 40 60 80 100 120 140 160 180 200 Value of Firm (Millions) Value of Bond and Stock (Millions) BondValue StockValue

Finance School of management Probalility Density of a Firm's value 0.09 0.08 0.07 d0.06 0.05 0.04 0.03 0.02 0.01 0.00 020406080100120140160180200 Value of a firm uesTc

9 Finance School of Management Probalility Density of a Firm's Value 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0 20 40 60 80 100 120 140 160 180 200 Value of a Firm Probability Density

Finance School of management Debtco Security Payoff Table ($000.000 Security Payoff State a Payoff State B Firr 140 70 Bond 80 70 Stock 60 0 uesTc 10

10 Finance School of Management Debtco Security Payoff Table ($’000,000) Security Payoff State A Payoff State B Firm 140 70 Bond 80 70 Stock 60 0