Interest Rate Curve Estimation: a Financial Application for Support Vector Regression

The Support Vector Regression (SVR) is applied on a key problem in financial economics: interest rate curve estimation. The SVR is able to introduce two important types of a priori information into the estimation. First, the kernel and the parameter C can jointly assure an implicit quality requirement on the estimated curve. It is presented a proposition that reduces the search space for the optimal value of this parameter. Second, Vapnik¡¦s Õ-insensitive cost function provides a natural channel to bring into the estimation information about liquidity and the price formation process of the assets from which the curve is extracted. It is captured by a variable observed during assets¡¦ transactions: bid-ask spreads (BAS). This cost function also allows for financial analysis of the assets selected as support vectors. The ƒÕ-insensitive function was modified in order to deal with different values for the parameter ƒÕ in the same estimation, as imposed by the curve estimation problem. It is proved that this change keeps all the SVR properties. This paper models the dollar-Libor interest rate swap curves. It is a small-sample estimation: twelve contracts are available daily, from 1997 to 2001. The proper C-value ranges for some types of kernels were identified. The spline-with-an-infinite-number-of-nodes kernel provided the best out-of-sample specification for the SVR. On average, it required approximately 5 contracts to describe the curves under the desired accuracy fixed by the BAS. However, the support vectors cannot be used as sufficient statistics to analyze curve movements through time. Comparing this SVR with other three different approximation methods, it achieved the best control of the trade-off bias-variance for the interpolation problem. Its extrapolation performance, however, suggested that a new admissible kernel, incorporating long-term interest rate asymptotical behavior, would make the SVR more competitive.