PT - JOURNAL ARTICLE AU - Phelim P. Boyle AU - Weidong Tian TI - Quadratic Interest Rate Models as Approximations to Effective Rate Models AID - 10.3905/jfi.1999.319221 DP - 1999 Dec 31 TA - The Journal of Fixed Income PG - 69--80 VI - 9 IP - 3 4099 - https://pm-research.com/content/9/3/69.short 4100 - https://pm-research.com/content/9/3/69.full AB - Many of the classic stochastic interest rate models use the instantaneous spot rate as the fundamental sate variable. For both practical and theoretical reasons, it is sometimes convenient to base the model on the effective interest rate over some period such as three months. One disadvantage of this procedure is that the prices of some basic securities and derivatives do not have closed-form solutions. Under some circumstances, accurate values for these instruments can be obtained using an approximation to the true model. The approximation here is based on a quadratic interest rate model. Examples illustrate the accuracy of the approximation.