以Hull-White短利模型建構精確多元利率樹

Abstract

本論文將以Hull-White短利模型為基礎，建造一個更為精確的多元利率樹，使得樹狀結構法在評價上造成的兩種評價誤差：分配性誤差以及非線性誤差能加以改善。除了應用求面積法將Hull-White三元樹延伸至多元樹，來減少樹狀結構評價造成的分配性誤差，主要議題將介紹一個創新的造樹方法，來減少樹狀結構評價所造成的非線性誤差。再以此造樹方法處理bond option以及Cap。

This paper proposes an accurate Multi-nomial Interest Rate Tree Model for Hull-White Term structural Model that can effectively decrease the pricing error from distribution error and nonlinearity error introduced by the lattices method. The quadrature method is use to extend the H-W trinomial tree model to a multi-nomial one to reduce the distribution error. A novel tree adjustment method is introduced to reduce the nonlinearity error. Numerical experiments on the bond options and the Cap verify the superiority of the proposed model.