Understanding Bonds Pricing and the Risks ‘My Name Is Bond, James Bond’

In this article we illustrate how to price bonds and calculate the accrued interest, clean- and dirty price, from which we can compute a bond invoice i.e., the present value for a given cash investment in the bond. We present the classical bond pricing formulae and show how to modify this formula to account for accrued interest.To be able to evaluate bond cash flows and compute their present value we must compute the yield to maturity (YTM) or the internal rate of return (IRR) of the bond. There is no closed-form analytical solution. Therefore, it must be solved for using an optimization algorithm such as Newton-Raphson. This requires an initial guess for the YTM. In this article, we present a highly accurate approximation formula for the YTM, which can be used as a good initial guess for low latency calculations.To conclude we demonstrate bond pricing with a live market example and compute the accrued interest, clean- and dirty price for a US treasury bond. We show how to solve for its yield to maturity and compute the present value of the bond cash flows. With this information we show how to compute the present value of any cash investment in this underlying bond and assess the DV01 risk, that is the change in value of the investment for a one basis point fall in the bond yield. With this article we provide an Excel workbook to demonstrate all calculations