Valuation of Convertible Bonds

This technical paper presents methodologies for valuing callable and putable convertible bonds using advanced numerical techniques within the UnRısk framework. 

Initially, the paper discusses the valuation under a Black-Scholes model, where the Adaptive Integration method is employed to calculate the bond's value by building equity price grids and propagating values backward through time, considering key dates such as dividend, conversion, and coupon dates. The valuation process accounts for different scenarios, including conversion, call, and put options, ensuring accurate pricing of the convertible bond.

The paper then extends the valuation approach to a two-factor model combining one-factor interest rate and one-factor equity models using Finite Elements with Streamline Diffusion. This section provides a detailed explanation of the time and space discretization steps, the calculation of life values on a grid, and the handling of discrete dividends. Additionally, the paper describes the computation of various sensitivities, such as delta, gamma, and vega, under both the Black-Scholes and General Hull & White models.

This comprehensive approach ensures that the complexities of convertible bond pricing, including the interplay between interest rates and equity prices, are accurately captured, providing robust and reliable valuations for financial practitioners.