Question

Consider an 18-month zero-coupon bond with a face value of $$\$ 100$$ that can be converted into five shares of the company's stock at any time during its life. Suppose that the current share price is $$\$ 20$$, no dividends are paid on the stock, the risk-free rate for all maturities is $6 \%$ per annum with continuous compounding, and the share price volatility conditional on no default is $25 \%$ per annum. Assume that the hazard rate is $3 \%$ per year and the recovery rate is $35 \%$. The bond is callable at $$\$ 110$$. Use a three-time-step tree to calculate the value of the bond. What is the value of the conversion option (net of the issuer's call option)?

   Consider an 18-month zero-coupon bond with a face value of $$\$ 100$$ that can be converted into five shares of the company's stock at any time during its life. Suppose that the current share price is $$\$ 20$$, no dividends are paid on the stock, the risk-free rate for all maturities is $6 \%$ per annum with continuous compounding, and the share price volatility conditional on no default is $25 \%$ per annum. Assume that the hazard rate is $3 \%$ per year and the recovery rate is $35 \%$. The bond is callable at $$\$ 110$$. Use a three-time-step tree to calculate the value of the bond. What is the value of the conversion option (net of the issuer's call option)?

Options, Futures, and Other Derivatives

John C. Hull 10th Edition

Chapter 27, Problem 18

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Step 1

We can assume that each time step represents 6 months. At each time step, the stock price can either go up by a factor of $e^{0.25\sqrt{0.5}}$ or go down by a factor of $e^{-0.25\sqrt{0.5}}$. The risk-neutral probability of an up move is given by: $$p = Show more…

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Consider an 18-month zero-coupon bond with a face value of $$\$ 100$$ that can be converted into five shares of the company's stock at any time during its life. Suppose that the current share price is $$\$ 20$$, no dividends are paid on the stock, the risk-free rate for all maturities is $6 \%$ per annum with continuous compounding, and the share price volatility conditional on no default is $25 \%$ per annum. Assume that the hazard rate is $3 \%$ per year and the recovery rate is $35 \%$. The bond is callable at $$\$ 110$$. Use a three-time-step tree to calculate the value of the bond. What is the value of the conversion option (net of the issuer's call option)?

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