In-arrears Interest Rate Derivatives under the 3/2 Model

Lie symmetry methods are used to find a closed form solution for in-arrears swaps under the 3/2 model ( ( ) ) ˆ 3 dr = r A t −α r dt + cr 2dZ . As well, approximate solutions are found for short-tenor inarrears caplets and floorlets under the same interest rate model. Comparisons are made of the approximate option values with those obtained with a computationally-intensive numerical scheme. The approximate pricing is found to be substantially fast easy to implement, while the relative errors with respect to the “true” prices are very small.