**Affine
Diffusions**

Paul L. Fackler, North Carolina State University

Affine diffusions are widely used as models of the underlying factors that affect financial prices. They have been most fully developed in term structure models of interest rates that are used to price bonds and bond derivatives. They have also been used in modeling the term structure of futures prices.

Affine diffusions owe their popularity to the fact that a number of important classes of derivatives prices can be computed without solving partial differential equations (PDEs) or resorting to simulation. This is true for simple, zero-coupon bonds, futures prices and options on spot goods, bonds and futures. The relative simplicity of pricing with affine diffusions becomes particularly important as the number of underlying factors needed to describe price behavior increases.

This site contains a number of working papers that investigate various aspects of affine diffusions and/or use affine diffusions in modeling financial prices.

**Working Papers **(in .PDF format)**
**All of these papers are in draft form - comments are welcome.

"Moments of Affine Diffusions." Discusses the computation of the first and second moments (mean and variance) of affine diffusions with both constant and time varying parameters.

"Specification Issues for Affine Diffusions." Discusses neccesary and sufficient conditions for admissability of affine diffusions and classes of invariant transformations of affine diffusions.

"Multi-factor Option Pricing." Discusses a general framework for pricing European options on spot goods, bonds, futures and bond futures.

"A Collocation Approach to Solving Riccati Equations Arising in Finance." Discusses a numerical strategy for solving the system of ODEs that arises in pricing models assiciated with affine diffusions.

"A Seasonal Stochastic Volatility Model for Futures Price Term Structure," with Yanjun Tian. Discusses pricing and estimation issues of exponential affine stochastic volatility models are discussed. One specific model is estimated in which the instantaneous mean and volatility of commodity spot price are allowed to be time varying. Results for Chicago Board of Trade corn futures are presented.

"A Term Structure Model for Agricultural Futures," with Matthew C. Roberts. Extends Schwartz's term structure model to incorporate seasonality in the convenience yield. Contains an application to Chicago Board of Trade wheat futures.

**Links to Other Reseach
on Affine Diffusions
Home Pages:
**Gregory Duffee

**Papers:
**Mikkel Baadsgaard, Jan Nygaard Nielsen & Henrik
Madsen, Estimating multivariate exponential-affine term structure models from
coupon bond prices using nonlinear filtrering

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