Lecture12_OptionApplication - NBA 6730: Derivative...

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1 NBA 6730: Derivative Securities Lecture 12: Option Applications 10/05/2010 George Gao NBA6730-Derivative Securities I 2 Agenda We will see how to apply option pricing theory to the valuation of corporate securities and to the valuation of real investment decisions. Pricing corporate securities as options equity, debt, warrant Real options value of delaying investment
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2 NBA6730-Derivative Securities I 3 (1) Equity and Pure Discount Bonds Equity and bonds are viewed as options on the value of a firm ( the value of the firm’s expected future earnings ) Assume the claims on a firm’s assets are only split between equity and zero-coupon bonds (no other claims) Notations: the face value of outstanding debt is ܭ the debt matures at time ܶ the market value of the debt at time ݐ is ܦሺݐሻ the market value of equity at time ݐ is ܧሺݐሻ the (market) value of the firm’s assets (both tangible and intangible) at time ݐ is ܸሺݐሻ ܸሺݐሻ ൌ ܦሺݐሻ ൅ ܧሺݐሻ NBA6730-Derivative Securities I 4 (1) Equity and Pure Discount Bonds The payoff for debtholder and shareholder: What do these payoff diagrams look like?
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3 NBA6730-Derivative Securities I 5 (1) Equity and Pure Discount Bonds Equity is a residual claim on the firm’s value, provided that the market value of the firm’s assets exceeds ܭ , the total outstanding debt ܧ ܶ ൌ maxሾ0, ܸ ܶെܭ Equity is a European call on the firm value with strike equal to the face value of outstanding debt and maturity equal to its debt maturity: ܧ ݐൌܿ ܸ ݐ,ܭ Debt is really a position of long bond and short put ܦ ݐൌܸ ݐെܧ ݐ , (i.e., “own” the firm’s assets but short a call) By put-call parity: ܦ ݐൌܭ ݁ ି௥ ்ି௧ െ݌ ܸ ݐ,ܭ , where ݌ is the price of a put on the firm value if the debt were default free, its value = ܭ݁ ି௥ ்ି௧ NBA6730-Derivative Securities I 6 (1) Equity and Pure Discount Bonds Values of outstanding debt (green) and equity (blue) claims, as a function of the value of firm assets. Figure assumes debt has face value of ܭൌ1 and matures in
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4 NBA6730-Derivative Securities I 7 (1) Equity and Pure Discount Bonds Implication for corporate finance: a conflict exists between shareholders and bondholders High variance (volatile) investments equity becomes more valuable (it is a long “call”) bonds become less valuable (it is a short “put”) Large dividends payment good for equity bad for bonds make the put more in-the-money increase the default probability The firm can also increase the value of equity by selling more debt with the same seniority for old debtholders: issuing new debt at the same seniority increases the put value and decreases their bond value
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This note was uploaded on 10/26/2010 for the course JOHNSON 6730 taught by Professor Georgegao during the Fall '10 term at Cornell University (Engineering School).

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Lecture12_OptionApplication - NBA 6730: Derivative...

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