Identification and Estimation of 'Maximal' Affine Term Structure Models: An Application to Stochastic Volatility

2003 ◽  
Author(s):  
Pierre Collin-Dufresne ◽  
Robert S. Goldstein ◽  
Christopher S. Jones
Keyword(s):  
Stochastic Volatility ◽  
Term Structure ◽  
Affine Term Structure ◽  
Affine Term Structure Models ◽  
Term Structure Models

Pricing interest rate derivatives under stochastic volatility

2011 ◽  
Vol 37 (1) ◽  
pp. 72-91 ◽  
Author(s):  
Nabil Tahani ◽  
Xiaofei Li
Keyword(s):  
Interest Rate ◽  
Stochastic Volatility ◽  
Term Structure ◽  
Alternative Methods ◽  
Future Research ◽  
Content Type ◽  
Interest Rate Derivatives ◽  
Affine Term Structure ◽  
Affine Term Structure Models ◽  
Term Structure Models

PurposeThe purpose of this paper is to derive semi‐closed‐form solutions to a wide variety of interest rate derivatives prices under stochastic volatility in affine‐term structure models.Design/methodology/approachThe paper first derives the Frobenius series solution to the cross‐moment generating function, and then inverts the related characteristic function using the Gauss‐Laguerre quadrature rule for the corresponding cumulative probabilities.FindingsThis paper values options on discount bonds, coupon bond options, swaptions, interest rate caps, floors, and collars, etc. The valuation approach suggested in this paper is found to be both accurate and fast and the approach compares favorably with some alternative methods in the literature.Research limitations/implicationsFuture research could extend the approach adopted in this paper to some non‐affine‐term structure models such as quadratic models.Practical implicationsThe valuation approach in this study can be used to price mortgage‐backed securities, asset‐backed securities and credit default swaps. The approach can also be used to value derivatives on other assets such as commodities. Finally, the approach in this paper is useful for the risk management of fixed‐income portfolios.Originality/valueThis paper utilizes a new approach to value many of the most commonly traded interest rate derivatives in a stochastic volatility framework.

scholarly journals Nonlinear Kalman Filtering in Affine Term Structure Models

2014 ◽  
Vol 60 (9) ◽  
pp. 2248-2268 ◽  
Author(s):  
Peter Christoffersen ◽  
Christian Dorion ◽  
Kris Jacobs ◽  
Lotfi Karoui
Keyword(s):  
Term Structure ◽  
Kalman Filtering ◽  
Affine Term Structure ◽  
Affine Term Structure Models ◽  
Term Structure Models ◽  
Nonlinear Kalman Filtering
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