Bonds and Options Valuation Using a Conditioning Factor Approach

Abstract

This paper looks at methods to calculate prices (or approximate prices) of bonds (zero coupon as well as coupon bearing) where the interest rates follow a log-normal distribution using two different waysthe first method makes use of a conditioning variable similar to the approach of Basu (1999) and Rogers and Shi (1995), while the second method (only applicable in case of the zero - coupon bond case) is by making use of a direct expansion technique. The conditioning factor based method is then used to approximate the price of the bond (in fact the lower bound to the price of the bond) for the case of coupon carrying bonds - both non-defaultable as well as defaultable ones. Finally, the conditioning factor method is used to value European options on assets with stochastic volatility. The approach used is not one based on numerical solutions to partial differential equations but rather on an approximation to the price of the option that can be arrived at using the conditioning factor approach. As is shown in the tables at the end of the paper, the results obtained by using the conditioning factor based approach is quite accurate - in fact in some cases it is exactly equal to the true prices themselves.