以Hull-White短利模型評價雪球型債券

Abstract

本研究將以Hull-White 短利模型為基礎，提出創新的演算法評價雪球型利率連動商品。雪球型債券為利率衍生性商品，此債券之特色在於其票面利率具有路徑相關之特性，並且付息利率不可小於零，在加上可以提早贖回債券之條款，因此複雜不易評價，也無封閉解存在，因此我們將以三元樹之數值方法估算其價值。雖然蒙地卡羅法也可以評價商品，並利用最小評方法處理提前贖回之條款，但其演算方法複雜不易處理。若 LIBOR 市場模型 (BGM 利率模型) 作為評價債券的利率期限結構，其 non-Markov 性質以及參數太多，不適用於樹狀結構以及複雜的債券付息，因此我們採用簡單的利率模型，Hull-White 短期利率期限結構。之後，我們將根據永豐銀行所發行的雪球型債券作敏感度分析，探討Hull-White 模型的參數、利差定價、以及市場利率對其債券價格之影響。

In this paper, a novel polynomial-time pricing algorithm based on Hull-White term structure model is introduced for pricing snowball notes. Snowball notes are sophisticated inversing floating rate bonds with path-dependent coupons, freeze at zero and redemption articles. Because of no proper closed form of Snowball notes, we must use numerical approach by trinomial tree structure to price these bonds. Although there is another way to solve complex derivatives via Monte Carlo method, it is hard for pricing bonds with both path-dependent coupons and redemption articles. Compare with the advanced interest rate model, LIBOR market model (BGM model),its defect is hard to calculate the complex coupon of interest rate derivatives. Thus, we take simple interest mode, Hull-White short rate term structure, to be the base for pricing sophisticated Snowball notes. Furthermore, numerical experiments and sensitivity analysis are given to show the behaviors of relationship between price and parameters (spreads, zero curves and parameters of Hull-White term structure model) according to the contract issued by Bank SinoPac.