ABSTRACT
This chapter details the one-factor HJM model in a binomial setting and demonstrates its usefulness in pricing interest rate derivatives. In particular, all examples use an EXCEL spreadsheet approach rather than the theoretical approach with martingale properties. Our approach encourages hands-on activities to understand the models and replicate the numbers. Only two trees, the T-year zero coupon bond evolvement tree and the short rate tree, are used for derivative pricing in the one-factor HJM model. Note that this corresponds to the hedge strategy using one zero coupon bond and a money market fund. This chapter adopts similar examples to Jarrow (2020) to price and hedge the options on bonds, caps, floors, swaps, forwards, and futures on bonds. During the process, it clearly illustrates why some derivatives do not require the HJM model for valuation. In addition, it clarifies why some hedges need to focus only on derivative value at any tree node, while others need to focus on derivative values and derivative cashflows at any tree node. The end of the chapter briefly discusses the estimation of parameters for the evolvement of the forward rates and in so doing completes the demonstration of the model.
