case11sol

# case11sol - Introduction to derivatives Fall 2011 BUSI 588...

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Introduction to derivatives, Fall 2011 BUSI 588, Case 11 solutions Solutions to Botvinnik - pricing risky debt 1. (*) The payoffs to Botvinnik are min( F, A T ) = F + min(0 , A T - F ) = F - max(0 , F - A T ) where F is the face value Botvinnik asks for and A T is the value of Tar Heels Chess Corp at maturity. Figure 1 plots the payoffs to Whatsup V Bank. If Tar Heels Chess Corp undertakes SI (but not KI), then Botvinnik would be receiving the payoff of a risk-free bond ( F ) minus the payoff of a put option on the values of the assets of the firm with strike price F . The value of this portfolio of assets is F 1 . 05 5 - P ( A = 134 , F, r f = 0 . 05 , T = 5 , σ = 0 . 5) where P ( · ) denotes the put price according to Black-Scholes. The face value that makes the debt claim (risk-free minus put) equal to the \$30m they invest into the firm (i.e. the amount that makes them just indifferent betweent investing or not investing) is F = 42 . 7. The implied interest rate they charge is 7 . 3%, i.e. (42 . 7 / 30) 1 / 5 - 1.

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