Pricing claims under GARCH-level dependent interest rate processes

This article considers the pricing of interest-rate-sensitive claims when the underlying interest rate is driven by a two-state-variable GARCH process. Analytical solutions are established for the case when the innovations in the short rate are normal and/or chi-squared random variables and the volatility of rates take on a special GARCH form. GARCH models that nest level-dependent interest rate models, including the Cox, Ingersoll, and Ross model, are also considered. Algorithms are provided that permit the efficient pricing of American-style interest rate claims under a rather broad array of GARCH-level dependent processes.