The purpose of this thesis is to present convertible bonds and to derive a model for their valuation. The thesis presents a model for the valuation of convertible bonds, based on the valuation of options. As the underlying stock prices and interest rates are among the main factors affecting the value of convertible bonds, we describe their dynamic processes using different binary trees. For the interest rate, we use the discrete version of the Ho-Lee model with an additional assumption that the volatility of interest rates is constant over time. For the stock price, we use the Cox-Ross-Rubenstein model.
The value of the convertible bond is obtained by combining the model for interest rates and the model for the stock price, using the assumption that the interest rates and stock prices move independently. After specifying the parameters of the processes of the stock price and interest rate, the value of the convertible bond can be determined by backward induction. Taking into account the expected value of the convertible bond in each node, the value of the exchange, and the possibility of early termination in case of callable and puttable bonds, we obtain the equation for calculating the value of the convertible bond. We conclude the thesis with numerical demonstrations.
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