# Valuation of callable convertible bonds using binomial trees model with default risk, convertible hedging and arbitrage, duration and convexity.

Aldossary, Fahad (2018) Valuation of callable convertible bonds using binomial trees model with default risk, convertible hedging and arbitrage, duration and convexity. Doctoral thesis (PhD), University of Sussex. PDF - Published Version Download (3MB)

## Abstract

In this thesis, I develop a valuation model to price convertible bonds with call provision. Convertible bonds are hybrid instruments that possess both equity and debt characteristics. The purpose of this study is to build a pricing model for convertible and callable bonds and to compare the mathematical results of the model with real world market performance. I construct a two-factor valuation model, in which both the interest rate and the stock price are stochastic. I derive the partial differential equation of two stochastic variables and state the final and boundary conditions of the convertible bond using the mean reversion model on interest rate. Because it is difficult to obtain a closed solution for the American convertible bond due to its structural complexity, I use the binomial tree model to value the convertible bond by constructing the interest rate tree and stock price tree. As a convertible bond is a hybrid security of debt and equity, I combine the interest rate tree and stock price tree into one single tree. Default risk is added to the valuation tree to represent the event of a default. The model is then tested and compared with the performance of the Canadian convertible bond market. Moreover, I study the duration, convexity and Greeks of convertible bonds. These are important risk metrics in the portfolio management of the convertible bond to measure risks linked to interest rate, equity, volatility and other market factors. I investigate the partial derivative of the value of the convertible bond with respect to various parameters, such as the interest rate, stock price, volatility of the interest rate, volatility of the stock price, mean reversion of the interest rate and dividend yield of the underlying stock. A convertible bond arbitrage portfolio is constructed to capture the abnormal returns from the Delta hedging strategy and I describe the risks associated with these returns. The portfolio is created by matching long positions in convertible bonds, with short positions in the underlying stock to create a Delta hedged convertible bond position, which captures income and volatility.

Item Type: Thesis (Doctoral) School of Mathematical and Physical Sciences > Mathematics H Social Sciences > HG Finance > HG4501 Investment, capital formation, speculation > HG4529 Investment analysis. Technical analysis Library Cataloguing 15 Jun 2018 11:00 15 Jun 2018 11:00 http://srodev.sussex.ac.uk/id/eprint/76492