The HJM Model: Its Past, Present, and Future, Keynote Address Iafe 1997 Conference

Abstract

When I was I thinking about what to discuss in this address, my mind wandered across many topics. I first thought about discussing martingale probability measures and the topologies of asset pricing. I quickly discarded this topic for obvious reasons(and one not so obvious). The not so obvious one is that I was asked to avoid using any equations. I next thought about preaching on the evils of 'value at risk,' but learned that Steve Ross had talked about this in the past. One doesn't want to imitate a master. So, I rejected that topic. By then I was desperate. To illustrate how much so, I even thought about a banking topic=FE asset/liability management. I rejected this as well because after lunch, there is always the danger of putting everyone to sleep. Then, an inspiration hit. I remembered when I was a graduate student in the late 70s at MIT, how much I enjoyed listening to Bob Merton and Fischer Black talk about the historical development of the Black-Scholes formula. Who did what, and when? What were the stumbling blocks in the development, in particular, solving the Black-Scholes partial differential equation. To this day, I still like recounting those stories to my students. So, I thought I would share my insights and recollections on the development process of the Heath-Jarrow-Morton term structure model with you. In the process, I will take advantage of the historic progression to discuss the salient issues regarding its derivation and implementation. In addition, I will also discuss its extensions to foreign currency and credit derivatives. Finally, I will share my predictions with you on the future of research in this area, and on the future of the field of financial engineering itself.