The Heath Jarrow Morton Model

This chapter presents the Heath, et al. (Econometrica 60(1):77–105, 1992) model for pricing interest rate derivatives. Given frictionless and competitive markets, and assuming a complete market, this is the most general arbitrage-free pricing model possible with a stochastic term structure of interest rates. This model, with appropriate modifications, can also be used to price derivatives whose values depend on a term structure of underlying assets, examples include exotic equity derivatives where the underlyings are call and put options, commodity options where the underlyings are futures prices, and credit derivatives where the underlyings are risky zero-coupon bond prices, see Carr and Jarrow (A discrete time synthesis of derivative security valuation using a term structure of futures prices, in Handbooks in Operations Research and Management Science, vol. 9 (Springer, Berlin, 1995), pp. 225–249), Carmona (HJM: a unified approach to dynamic models for fixed income, credit and equity markets, in Paris–Princeton Lectures in Mathematical Finance. Lecture Notes in Mathematics, vol. 1919 (Springer, Berlin, 2009), pp. 3–45), Carmona and Nadtochiy (Financ. Stoch. 13, 1–48 (2009)), and Kallsen and Kruhner (Financ. Stoch. 19:583–615, 2015).