Additional topics consist of the dynamics of derivative prices, pricing derivative products using partial differential equations, partial-integro differential equations, equivalent martingale measures, new results and tools for interest-sensitive securities, modeling term structure and related concepts, the classical and Heath-Jarrow-Morton
(HJM) approach to fixed income, classical partial differential equation analysis for interest rate derivatives, relating conditional expectations to partial differential equations, pricing derivatives via Fourier transform technique, stopping times and American-type securities, and calibration and estimation techniques.
The "arbitrage" approach initiated by Ho and Lee (1986) and generalized by Heath-Jarrow-Morton (1992) (HJM), takes the initial term structure as given and, using the no-arbitrage condition, derives some restrictions on the drift term of the process of the forward rates under the risk-neutral probability measure Q.
The Estimation of the Heath-Jarrow-Morton Model by Use of Kalman Filtering Techniques," Working Paper Series 54, School of Finance and Economics, University of Technology, Sydney.
Transformation of Heath-Jarrow-Morton Models to Markovian Systems," Working Paper Series 53, School of Finance and Economics, University of Technology, Sydney.
Chiarella, 1997, "Transformation of Heath-Jarrow-Morton Models to Markovian Systems", European Journal of Finance 3, 1-26.
Kwon, 1998a, "A Class of Heath-Jarrow-Morton Term Structure Models with Stochastic Volatility", Working Paper No.
The IRS chose to base its software on five seminal derivative models: Ho-Lee, Hull-White, Black-Derman-Toy, Black-Karasinski, and Heath-Jarrow-Morton
, each incorporating one level higher complexity than the last.
the continuous time models of Black and Scholes, followed by interest rate models and the models of Heath-Jarrow-Morton
and the forward Libor model.
He covers the basic financial instruments; fundamental principles of financial modeling and arbitrage valuation of derivatives; the concept of conditional expectation, the discrete time binomial model and its application to stochastic finance; the most important results from the theory of martingales in the theory and application of stochastic finance; more advanced concepts such as the Randon-Nikodym derivative, equivalent martingale measure, non-arbitrage, and complete general markets; American derivative securities using the binomial model and general markets; fixed-income markets and the interest rate theory in discrete time; arbitrage pricing; credit risk; and the Heath-Jarrow-Morton
model for the evolution of forward rate process.
Jarrow, an originator of the Heath-Jarrow-Morton
multi-factor term structure model.
Framework: Immersion of Short-Rate Models and LIBOR Market Model
It has adapted its software to encompass several models including the Black-Derman-Toy (BDT) binomial, Black-Karasinski (BK) trinomial, Heath-Jarrow-Morton
(HJM) 2 factor, Monte-Carlo simulation, and AFT's pre-payment.